Philosophical Letters of David K. Lewis: Volume 1: Causation, Modality, Ontology 0198855451, 9780198855453

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PHILOSOPHICAL LET TERS OF DAVID K . LEWIS

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Philosophical Letters of David K. Lewis VOLUME 1 Causation, Modality, Ontology

Edited by

HELEN BEEBEE A.R.J. FISHER

1

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1 Great Clarendon Street, Oxford, OX2 6DP, United Kingdom Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Compilation, preface, introduction, and editorial matter © Helen Beebee and A.R.J. Fisher 2020 Letters © the Estate of David Kellogg Lewis 2020 The moral rights of the authors have been asserted First Edition published in 2020 Impression: 1 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, by licence or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this work in any other form and you must impose this same condition on any acquirer Published in the United States of America by Oxford University Press 198 Madison Avenue, New York, NY 10016, United States of America British Library Cataloguing in Publication Data Data available Library of Congress Control Number: 2020938859 ISBN 978–0–19–885545–3 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.

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Dedicated to the memory of Steffi Lewis

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PREFACE The letters of eminent philosophers throughout the history of philosophy—such as Jeremy Bentham, René Descartes, William James, Bertrand Russell, and C.S. Peirce, to name a few—are often published for the sake of posterity, research, and the his­ tory of philosophy. David Kellogg Lewis (1941–2001) is clearly of this stature. He was one of the most influential analytic philosophers of the twentieth century, making significant contributions to almost every area of analytic philosophy and setting the agenda for various debates, many of which carry on today. In several respects he remains a contemporary figure, but enough time has passed for historians of phil­ oso­phy to begin to study his place in the history of analytic philosophy. This book is the first volume of a two-volume work of Lewis’s philosophical letters, selected from his vast correspondence and organized into thematic categories. In this volume the categories are Causation, Modality, and Ontology. We have aimed to show the origins and development of Lewis’s philosophy in its historical context as well as to offer a new window into his philosophy, sometimes with new arguments and different opinions to what he stated in his published writ­ ings. This two-volume work is intended to constitute a body of material for students of Lewis’s philosophy and for scholars focused on analysing his place in the history of analytic philosophy. We hope it becomes an indispensable resource for Lewis scholarship and fuels research on his philosophy. The editorial task has been challenging. Lewis’s correspondence consists of thou­ sands of pages of letters, both from and to Lewis. We began with extracting Lewis’s side of the correspondence from approximately 16,000 pages. That got us down to about 7,000 pages, of which 4,000 were of philosophical content. In terms of letters that was roughly 1,500 letters. At this point we started the arduous task of selecting letters and assigning them to a category that represents a major area of his philo­ soph­ic­al interests. Overall, we selected 742 letters. We intended to strike a balance between breadth and depth and to provide an accurate impression of his work, its evolution, and the debates he pursued in correspondence. Given the vast quantity of letters, it would have been too cumbersome for the philo­soph­ic­al public to consume the letters without categorization, and since r­ eaders will most likely be interested in studying a single topic in Lewis’s work as it unfolds in his correspondence, we judged it more appropriate to divide the letters the­mat­ic­ al­ly. Fortunately, Lewis typically wrote each letter on a single topic. Hence, his letters

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viii Preface were conducive to thematic categorization. However, this norm is sometimes ­broken, for whatever reason, and we had to make a decision about where to allocate a letter. Sometimes it was obvious—given the context, usually—that a letter on pos­ sible worlds and de se attitudes was more suitably placed in Part 2: Modality than Part 4: Mind. Sometimes it was arbitrary whether a letter about actualism and mereology belonged to Part 2: Modality or Part 3: Ontology. We hope the indexes to both vol­ umes will assist readers in tracking down material that has not been placed in the category where one might expect to find it. This is the first substantive printing of letters by Lewis. Except for a handful of excerpts (such as Lewis 2004c, 176–7) and quotations used by correspondents in their articles over the years, the only other place where his letters have been prepared for publication is The Correspondence of David Armstrong and David Lewis, edited by Peter Anstey, A.R.J.  Fisher, and Stephanie  R.  Lewis. We have been in close consultation with the editors of that volume in selecting letters for this work, intending to avoid significant overlap. But the importance of Lewis’s relationship with Armstrong can­ not be overlooked, so we had to include several significant letters from Lewis to Armstrong. The Correspondence of David Armstrong and David Lewis also contains letters from Lewis to other recipients besides Armstrong, and some of those letters appear in these volumes. We have provided minimal annotation and little commentary, restricting our­ selves to references and information required to understand the content and context of the letter. In particular, we generally leave it to the reader to follow up the refer­ ences to the published works (by Lewis and others) being discussed in order to fill in any gaps in understanding, resorting to substantive footnotes only where the required information is not to be found in published work. In cases where it has proved il­lu­ min­at­ing we have cross-referenced letters in either volume to help the reader connect ideas, arguments, and recurring themes across letters. Our intention from the outset has been to let the letters speak for themselves and to serve as a primary resource. We have used a number of editorial principles in putting the text together (really, a mixture of precedent and idiosyncrasy). We have corrected minor typos but have not indicated them in the text. Most minor grammatical mistakes have been cor­ rected in the same way. In some cases we have inserted words to render the sentence meaningful or to note that some portion of the MS is illegible or that a letter is incomplete (because the MS is typographically defective). These have been indicated with angled brackets, as per the Key to Symbols. We have used square brackets plus italics for other editorial insertions, the most common of which has to do with infer­ ring Lewis’s location where it is not written on the letter (again, see the Key to Symbols). The footnotes are ours, except for those signified by an asterisk or similar (non-numerical) symbol.

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Preface

ix

Copyright of the letters is held by the Estate of David K. Lewis, specifically Lewis’s widow and literary executor: Steffi Lewis. After Lewis’s unexpected death Steffi was left with his correspondence, unpublished essays, student notes and essays, and docu­ments relating to his publications. She took it upon herself to organize his archive into its present state. Since his correspondence consists of both sides of cor­ respondence, it amounts to a reasonably intact record of late twentieth-century ana­ lytic phil­oso­phy. As self-appointed archivist and a philosopher by training, Steffi had the ambitious idea of editing multiple thematic volumes of Lewis’s correspondence (both sides). Because of the scale of such a project and unforeseen setbacks, she has managed, eventually with the help of others, to co-edit The Correspondence of David Armstrong and David Lewis. She has also published informative articles about Lewis’s life (2015a) and his correspondence on philosophy of religion (2015b). One of us (Anthony) had the pleasure of working closely with Lewis’s correspond­ ence in 2014–16 at the Lewises’ residence before it was kindly deposited by Steffi in the Princeton University Library, February 2016. It is now the David Lewis Papers (C1520), housed in Princeton’s Firestone Library (https://findingaids.princeton.edu/ collections/C1520). Building on Steffi’s earlier efforts, we had the idea of publishing a comprehensive and systematic selection of Lewis’s letters (one-sided) as part of a project funded by the AHRC in the UK. Without Steffi’s initial toil and vision we would have had an even higher mountain to climb in editing this work. We are greatly indebted to her. Analytic philosophy owes her a great debt as well. The letters reproduced in this book are from the David Lewis Papers, except for Letter 121. To Dagfinn Føllesdal, 6 March 1966, which is located in the W.V. Quine Papers, Houghton Library, Harvard University, and Letter 229. To Donald C. Williams, 12 May 1971, which is located in the Donald Cary Williams Papers, Pusey Library, Harvard University. We are aware that originals sent to the recipient may have inter­ lineations or extra notes that were not recorded on the copy Lewis kept. Since we have offered a record of what is in the David Lewis Papers (with the exception of a  few letters acquired from other sources), these discrepancies—almost entirely unknown to us—are not reproduced here. We have been helped by many people. First and foremost, we thank Steffi Lewis for providing access to Lewis’s correspondence and for her kind permission to publish Lewis’s letters, courtesy of Princeton University Library, as well as John Cooper for assisting us in this matter. We thank Harvard University Archives for permission to  publish Letter 121. To Dagfinn Føllesdal, 6 March 1966 and Letter 229. To Donald C. Williams, 12 May 1971. We thank Brianna Cregle, Don C. Skemer, and other staff at Princeton’s Firestone Library for their archival expertise. For helpful advice and feedback on conceiving of this work we thank Peter Anstey, John Bigelow, David Chalmers, Frank Jackson, Hugh Mellor, Daniel Nolan, Jonathan Schaffer, and

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x Preface Dean Zimmerman. We thank Aaron Wilson, Maeve MacPherson, Andries De Jong, Simon Walgenbach, Justin Mullins, and Kendall Fisher for transcribing many of the letters at Manchester. For kindly contributing to the Lewis crowdsource transcription project on crowdcrafting.org we thank Daniel Nolan, David Ingram, Robert Boyd Skipper, Sara  L.  Uckelman, Samuel Boardman, and many others. We thank Mike McLeod for transcribing the letters to D.M. Armstrong and are especially grateful to Peter Anstey for answering our queries and supplying documents as we worked through the correspondence between Armstrong and Lewis. We thank John Bigelow and Steffi Lewis for transcribing the letters to Jack Smart. We thank Jonathan Farrell for proofreading one Part of the letters of this volume. We thank Jonathan Farrell and Simon Walgenbach for compiling the index of this volume. Further thanks to Jonathan Bennett, Jessica Collins, Peter Forrest, Ned Hall, Allen Hazen, Frank Jackson, Hugh Mellor, Laurie Paul, Charles Pigden, Graham Priest, and Jonathan Schaffer for consulting or providing copies of their originals in order to help us piece together illegible portions of Lewis’s letters, or for helping us with missing references. Thanks to Quetzil Castañeda (son of Hector-Neri Castañeda), Gene Cline, David Copp, Allen Hazen, Alvin Plantinga, and Peter van Inwagen for kind permission to publish por­ tions of letters to Lewis, where such quotation was deemed necessary for understand­ ing the content of the letter in question. We thank Roz Chast for allowing us to reproduce her cartoon ‘Parallel Universes’. Finally, we thank John Bigelow, whose passing remark to one of us (Helen)—nearly ten years ago—about the existence of Lewis’s letters in Steffi’s spare room eventually led to the publication of these volumes. This two-volume work is one output of the project The Age of Metaphysical Revolution: David Lewis and His Place in the History of Analytic Philosophy, funded by the UK’s Arts and Humanities Research Council [grant no.: AH/N004000/1]. We acknowledge the generous support of the AHRC and are grateful to our project team members: Frederique Janssen-Lauret and Fraser MacBride. HB & ARJF Manchester, UK 31 August 2019

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CON TEN TS Introduction List of Letters Key to Symbols Feature Letter

xiii xxv xxxvii xxxix

LETTERS Part 1:  Causation Part 2:  Modality Part 3:  Ontology

1 237 439

References Index of Terms and Names Index of Lewis’s Works Cited Index of Recipients

795 813 827 829

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I N TRODUCT ION David Lewis was one of the most influential analytic philosophers in the second half of the twentieth century. He made substantial contributions to philosophy of lan­ guage, philosophy of mathematics, philosophy of mind, philosophy of science, epis­ temology, decision theory, and most significantly metaphysics. More than that, he set the agenda for many debates in these areas. While his work remains part of con­ temporary discussion, enough time has passed for historians of philosophy to study the later stages of the twentieth century and its relation to the rest of that century and to us right now. Thus Lewis’s place in the history of analytic philosophy is and should be of interest and importance to historians of philosophy. Lewis published over one hundred articles and four books. But one way he did philosophy—perhaps just as important as his published writings—was in the form of letter-writing. He constructed, developed, and refined his philosophy through a life-long correspondence with around a thousand other philosophers—including many other leading figures such as D.M.  Armstrong, Saul Kripke, W.V.  Quine, J.J.C.  Smart, and Peter van Inwagen. His letters were the undercurrent of his pub­ lished writings, the medium through which he proposed many of his well-known theories and discussed a wide range of philosophical topics in depth. In certain cases some of his published writings were the end product of his correspondence. Lewis’s letters reveal a story about the origins and development of his thought, detailing how he came to endorse various doctrines. Some letters clarify his views or offer new arguments for his theories or alternative formulations thereof. Some let­ ters contain rich, substantive comments on someone else’s views (usually a com­ petitor’s) that often advance his own views in an illuminating way. Some contain arguments that are not explicit in his published writings, not to mention historically significant exchanges that have altered the face of analytic philosophy, such as his discussions with Armstrong about natural properties or his correspondence with van Inwagen about possible worlds or his letters to Smart about the identity theory of mind. Some letters provide cases of Lewis ‘talking back’ in such a way that he adds a new step to a current dialectic. Some letters contain Lewis’s reflective thoughts on his own philosophical development. Arguably, the area that Lewis affected the most was metaphysics—so much so that it exhausts Volume 1. Metaphysics in the analytic tradition, of course, encom­ passes a wide range of topics. Therefore, we have divided this volume into three

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xiv Introduction parts: Causation, Modality, and Ontology. Even these broad headings do not reveal the full extent of the topics covered in each Part. Part 1 covers not only causation but also counterfactuals, laws of nature, and such related topics as dispositions and free will, amongst others. Part 2 includes letters on modality, modal logic, counterpart theory, and possible worlds. Part 3 contains letters about the metaphysics of time, personal identity, time travel, properties, philosophy of mathematics, set theory, nominalism, supervenience, ontological reduction, meta-ontology, realism, mere­ ology, intrinsicality, truthmaking, philosophy of physics, and more. The topics in Part  1 naturally fit together: Lewis analyses causation in terms of counterfactual dependence, which leads to the need to provide a theory of counter­ factuals; and his theory of counterfactuals, in turn, employs the concept of a law of nature. Of course, every question is related to every other question in philosophy, at least as Lewis saw it, and his theory of counterfactuals also appeals to the concept of a possible world and, in particular, similarity relations between worlds. Letters directly about possible worlds are in Part 2, but the reader will see possible worlds at work in Part 1. The letters of Part 2 form a natural unity around the topic of modality, which is general enough to encompass technical issues about modal logic, debates about the nature of possible worlds and possible individuals, and counterpart the­ ory. The letters of Part 3 form a more miscellaneous collection; as a result, there are more letters in this Part than in any other (including Volume 2). But, broadly speak­ ing, all the letters of Part 3 loosely fall under the question of what exists and what it is like. Part 1: Causation begins with letters on causation. Lewis’s enormous influence on debates about causation stems in large part from a single paper (‘Causation’, 1973a), together with the Postscripts added in Philosophical Papers II (1986d). He wrote just two other papers on causation, both towards the end of his life: ‘Void and Object’ (2004e) and ‘Causation as Influence’ (2000a, 2004a). But his interest in causation began as an undergraduate at Swarthmore College, where in the Fall semester of 1958 he wrote a term paper for Jerome Shaffer’s course wherein he proposed a coun­ terfactual theory of causation. H.L.A.  Hart and Tony Honoré had considered this theory but rejected it in Causation in the Law (1959), which Lewis had clearly read, at least in part. The letters to Michael Scriven in 1961 see Lewis thinking through some aspects of his view that have become core issues in contemporary debates about caus­ation, such as transitivity, overdetermination, and indeterministic causation. By that time he had already absorbed the upshots of his studies from his 1959–60 stint at the University of Oxford, where, under the tutorship of Iris Murdoch, he read Moore, Hume, Leibniz, and works by J.L.  Austin, Hart, Gilbert Ryle, and Ludwig Wittgenstein. He explains the influences of his time at Oxford in his letter to the Dean of the Graduate School at Princeton University in 1961. This letter shows us the

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Introduction

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extent to which Oxford analytic philosophy from this period played a part in shap­ ing his approach to philosophy. After leaving Swarthmore for graduate school at Harvard University his interests developed in different directions, but roughly in line with his new teachers, most notably Nelson Goodman, W.V. Quine, and Donald C. Williams. Certain interests in philosophical psychology and moral philosophy that were of great concern to him as he entered Harvard had to compete with the cutting-edge work in philosophy of language, mind, and science that he encountered at Harvard and MIT. (Game theory was also cementing its place in Lewis’s thought and this he owes, in part, to his time at the Hudson Institute from the same period.) Despite his very early work on causation, he went on to publish his research on counterfactuals first. His theory of counterfactuals began life in Richard Montague’s Fall 1967 seminar at UCLA (see Letter 15. To Frank Vlach, 21 March 1971 and Letter 20. To Peter Woodruff, 2 June 1971). On this view, the counterfactual ‘were it the case that P, it would be the case that Q’ is true at some world w iff there is some world v in which P and Q are both true such that v is more similar to w than any other world in which P is true and Q is false. Sometimes the condition is put in terms of ‘closeness to actuality’. Closeness relations are cashed out in terms of overall comparative simi­ lar­ity. About the same time Robert Stalnaker independently proposed a similaritybased approach to counterfactuals (with appeal to possible worlds). Lewis’s letters to Stalnaker in 1968 outline how they both arrived roughly at the view and canvass some of the crucial differences between their theories such as whether there is some unique world that is closest to w. After securing an Associate Professorship at Princeton, with one-year leave to study at Oxford, Lewis set out to write ‘Completeness and Decidability of Three Logics of Counterfactual Conditionals’ (1971b) and then Counterfactuals (1973b). His theory of counterfactuals required him to say something about laws of nature, because laws of nature play a crucial role in determining closeness of match across worlds. In some early letters to Richard Jeffrey in 1967 Lewis toyed with an account of lawlikeness that appeals to confirmation theory, but later that year he put forth the first, ‘tentative’ formulation of what would become known as the Mill-RamseyLewis theory of laws (see Letter 427. To J.J.C. Smart, 17 October 1967, Volume 2: Part 4: Mind).1 The Mill-Ramsey-Lewis theory of laws says that laws are axioms of our best theory or theories of the universe that characterize regularities in terms of an appro­ priate balance between the virtues of simplicity and strength. As his correspondence indicates, he arrived at the view through discussions with Smart and not by reading 1   For letters that are not in the Part we are presently discussing, details of the volume and Part in which they are located have been supplied.

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xvi Introduction Ramsey or Mill. (This was a productive time for Lewis. Counterfactuals contains sev­ eral independent ideas that he develops later on, for example truth in fiction and probabilities of conditionals.) As Counterfactuals hit the shelves, Lewis was finally in a position to publish his counterfactual theory of causation. But by early 1984 (Letter 60. To Louis Loeb, 21 February 1984), Lewis had started to worry about the problem of late pre-emption (where the non-cause c2 is pre-empted not by some intermediary between the cause c1 and effect e, but by e itself) and expressed dissatisfaction with the idea of dealing with it by appealing to a difference in the time at which e occurs—the ‘fragility’ solu­ tion that he considers and reluctantly rejects in his ‘Postscripts to “Causation” ’ (1986d, 203–5). In other letters from this period he encounters further obstacles to his analysis (see Letter 66. To D.H. Mellor, 3 November 1987). Peter Menzies (1989) observed that in indeterministic cases of pre-emption, the pre-empted non-cause c2 may well raise the chance of e and hence wrongly count as a cause of e according to Lewis’s analysis. (Menzies himself solves the problem by requiring a continuous causal chain running from the cause to the effect; Lewis eschews this solution because it rules out action at a temporal distance a priori.) Lewis was stuck, and remained stuck: Menzies’s problem was one that Lewis never solved (see Lewis 2000a, n. 1; Lewis 2004a, 79–80). While Lewis wrote a few letters on the topic of causation from the late 1980s to the mid-1990s, he seems to have largely let the topic lie until an intensive burst of activity from 1996 to 1999, including running Fall semester graduate seminars on causation at Princeton in 1996 and 1998, hearing Jessica Collins present a version of her ‘Preemptive Prevention’ at a Princeton seminar in March 1997, and attending a oneday conference in New York organized by Collins in December 1998, at which both Ned Hall and L.A. Paul presented papers (see Collins 2000).2 In his March 1997 letter to Phillip Bricker, Lewis mentions three additional problems with his analysis: ­double prevention, prima facie counter-examples to transitivity, and pre-emption involving action at a temporal distance (prompted by Schaffer’s ‘two wizards’ case—later Merlin and Morgana in (Schaffer 2000)). A month after his March 1997 letter to Bricker, however—and just a week after saying to Hall, ‘I wish I had a theory of causation again!’ (Letter 91. To Ned Hall, 22 April 1997)—Lewis wrote to Hall and Paul (ex- and current PhD students of his respectively; Paul had also attended his causation seminar the previous semester, along with Schaffer) with a first pass at the view that appeared as ‘Causation as Influence’ (Lewis 2000a, 2004a). He credits the basic idea to Hall, saying, ‘I really like 2   Jessica Collins was then known as ‘John Collins’. This clarificatory footnote has been added at her suggestion.

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Introduction

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Ned’s idea of treating . . . cases of trumping overdetermination in terms of the sensi­ tivity of the details of the effect to the details of the cause, but not to the details of the preempted alternative’, and summarizes his own nascent view pithily: ‘Here’s the theory: c causes e iff c and e are distinct events (or they are distinct absences of events, or one is an event and one is an absence) and c influences e to a substantial extent. The end’ (Letter 92. To Ned Hall and L.A. Paul, 29 April 1997, p. 180). He traces the origin of this view to some comments of Hugh Rice’s after a talk at Oxford in 1984, which had initially affected Postscript E (Redundant Causation) to ‘Causation’ (1986d, 193– 212), but the series of letters to Hall, Paul, and Schaffer between 1997 and 1999, as well as the evident influence of Collins’s work, serve to underpin Lewis’s following remark at the start of the 2004 version of ‘Causation as Influence’: ‘[t]his paper mostly pre­ sents the latest lessons I’ve learned from my students. Under the customs of the nat­ ural sciences, it should have been a joint paper, the coauthors being (in alphabetical order) [Jessica] Collins, Ned Hall, myself, L.A. Paul, and Jonathan Schaffer’ (2004a, 75). Similarly, his theory of counterfactuals underwent several criticisms in the litera­ ture throughout the rest of his career. Various letters capture Lewis’s responses to these objections and his comments on competing theories (see, inter alia, Letter 25. To John Bigelow, 8 November 1974 and Letter 52. To Jonathan Bennett, 21 April 1981). One of the more salient problems was how to account for the temporal asym­ metries of certain counterfactuals within Lewis’s similarity-based approach to coun­ terfactuals. Lewis was compelled to appeal to the notion of time’s arrow because of Kit Fine’s criticisms in his Critical Notice of Counterfactuals (Fine 1975) and proposed more detailed measures of similarity. This problem remained with him and resur­ faced in some of his final letters to Bennett and Adam Elga in 2001. As with caus­ ation, Lewis continued to think about counterfactuals and laws of nature for his entire career. His work in these areas still plays a central role in ongoing debates in these areas. Part 2: Modality starts with Lewis’s attempts to develop counterpart theory as a substitute for quantified modal logic. This began while he was a graduate student at Harvard, after he took a philosophy of language course with Quine (PHIL148, Spring semester, 1963), read Word and Object for the first time, and reflected on criticisms in Kripke’s paper ‘Quantified Modality and Essentialism’, which Kripke wrote for Quine’s Seminar in Philosophy of Language, Fall semester 1961 (recently published: (Kripke 2017)).3 In this paper, Kripke responds to Quine’s objection that quantified modal logic rests on obscure Aristotelian essentialism. Kripke shows that a pure

3   PHIL248, Seminar in Philosophy of Language, Harvard University, Fall semester 1961 (1961–2 Courses of Instruction for Harvard and Radcliffe, Faculty of Arts and Sciences. Official Register of Harvard University, vol. 58).

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xviii Introduction semantics of quantified modal logic can be given in such a way that ‘essentialism’ becomes the watered-down (and hence acceptable) doctrine that modal operators apply to open sentences (Kripke 2017, 233, n. 11). Towards the end of the paper Kripke discusses the ‘intuitive problem of essentialism’: which attributes are acciden­ tal and which are essential to some object? He framed the problem as one that demands us to preserve identity across possible worlds. As laid out in his 1966 letter to Dagfinn Føllesdal, Lewis proposes his own reply to the problem of essentialism. No individual is numerically identical with some other individual in another world, but one individual can be a counterpart of another in some other world—just like the same self-identical individual need not exist at each time of its existence but rather have numerically distinct temporal parts at those times. This affords the ana­ lysis: some attribute F had by some object a is thereby essential if every counterpart of a has attribute F. On Lewis’s view, identity across worlds is not preserved, but in understanding the truth conditions of statements concerning essential attributes in terms of counterparts the prospects of using possible worlds and possible in­di­vid­ uals in philosophical analyses are improved greatly. In other early letters from Part 2 Lewis clearly states that extensional identity conditions of worlds endow them with the kind of clarity one needs to use them in philosophical theorizing (see Letter 126. To W.V. Quine, 1 October 1968). In 1968 he takes possible worlds as not reduced to anything else—say, statedescriptions or consistent sets of sentences. Worlds are meant to be entities that one has a clear grasp of. To help secure this clarity he needed to explain what it means for something to be actual. As he explains to Paul Fitzgerald in 1969, the word ‘actual’ is an indexical, just like the word ‘present’. The word ‘actual’ does not refer to some primitive absolute property had by our world; analogously, ‘present’ does not refer to some ontically privileged time. Our world and its contents are no different in kind from other worlds and their contents. By early 1970 Lewis had admitted actual and possible concreta into his ontology. He says: ‘My working ontology is actual and possible concreta, together with any sums or sets over these’ (Letter 226. To Charles Chastain, 8 March 1970, Volume 1: Part 3: Ontology, p. 443). Robert Black remarked that Lewis ‘was already a closet modal realist when he wrote “Anselm and Actuality” [in 1970]’ (Black 2000, 87). But in response Lewis was puzzled. He writes: ‘Why “closet”? The modal realism in “Anselm and Actuality” [1970a] seems pretty overt to me!’ (Letter 217. To Robert Black, 28 January 1999, p. 423). The reason why it might seem covert in ‘Anselm and Actuality’ is that Lewis does not say explicitly that possible worlds are concrete. However, he was averse to this characterization because in discussing possible worlds with others he realized that it was not clear what ‘concrete’ and ‘abstract’ meant, and hence whether the corresponding concepts do any real work.

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Introduction

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By 1980 more and more articles on Lewis’s modal realism began to appear, and more and more philosophers raised objections. During this same period, philo­ sophers refined ways to construct alternative theories of possible worlds. By this point many philosophers agreed with Lewis that possible worlds are respectable entities ripe for exploitation in philosophical analyses but disagreed with him about their ontic status. Thus Lewis set out to write a book on modal realism: On the Plurality of Worlds. He wrote the book from December 1982 to May 1984, portions of which were delivered as his Locke Lectures at Oxford, Trinity Term, 1984 (the manuscript as it appeared in print was completed more or less by June 1984). The second half of the letters in Part 2 can be divided into letters that lead up to the publication of On the Plurality of Worlds and letters that deal with further discussion and ongoing reaction after its publication. Out of the four books that Lewis wrote, this one owes its char­ acter and identity to his correspondence the most. It is to some extent a product of his correspondence with such philosophers as van Inwagen, John G. Bennett, Brian Skyrms, Allen Hazen, Peter Forrest, Kit Fine, and Armstrong about the main argu­ ments of the book—e.g. demarcation of concrete possible worlds, the difference between existence and actuality, knowledge of spatiotemporally disconnected worlds, the status of impossible worlds, the Humphrey objection, the prospects more generally about counterpart-theoretic translation schemes for de re modal ascriptions, explanations of contingent and necessary facts, principles of plenitude, haecceitism, and much more. Of course, a central component of Lewis’s case for modal realism is that no competing theory is equally or more fruitful and less costly than modal realism. Thus many of his letters from this period critically discuss com­ peting doctrines. The competing theory that received the most attention in his cor­ respondence is magical ersatzism, particularly as defended—along Plantingan lines—by van Inwagen (1986b). After the publication of On the Plurality of Worlds in 1986, Lewis reacted to several reviews of the book and answered follow-up questions about various aspects of modal realism. In the 1990s he was compelled to address a new alternative, modal fictionalism, in letters to Gideon Rosen and others. Armstrong’s combinatorialism is one variant of fictionalism that Lewis took seriously, as evidenced by his running comments on drafts of Armstrong’s A Combinatorial Theory of Possibility (1989a), although these letters are not reproduced here.4 Another issue for Lewis in the 1990s concerned arguments against his shape and size restrictions on possible worlds, par­ ticularly in response to Daniel Nolan’s ‘Recombination Unbound’ (1996). Towards the end of his correspondence on modality he continued to address the question of essence—the very issue that led him on the path to modal realism—and maintained   These letters are in The Correspondence of David Armstrong and David Lewis.

4

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xx Introduction that robust essentialism is unfairly dogmatic. It is safe to say that every argument and every aspect of his modal realism, as well as the way he set the agenda for debates about modality, figures in the letters of Part 2. To date, given that modal realism is the only fully reductive theory of modality on the table, it continues to be the prize jewel that few of us can embrace because of its bizarreness; yet it continues to be taken seriously. Put differently, only a select few have the courage to follow the argument where it leads, and that is exactly what Lewis unabashedly did. Let us turn to Part 3: Ontology. In comparison to the other Parts of both volumes the earliest letters in Part 3 begin relatively late, with just two letters dating from the 1960s. Some of this is due to our selection of letters, but it is largely because most letters from the 1960s are on other topics—causation, counterfactuals, meaning, theoretical terms, counterpart theory, and philosophy of mind. The initial papers that fall under one or more topics in Part 3 are ‘Finitude and Infinitude in the Atomic Calculus of Individuals’ (co-authored with Wilfrid Hodges) (1968), ‘Nominalistic Set Theory’ (1970d), and ‘Analog and Digital’ (1971a). These papers represent Lewis’s early concerns with set theory and his interests in Goodman’s work, as well as in Goodman’s reading of Carnap in The Structure of Appearance (Goodman 1951). Another relevant paper from this time is ‘Holes’ (1970) (co-authored with Steffi Lewis), which is about a topic that would receive increasing attention as a result of this paper. But ‘Holes’ is also an important illustration of Lewis’s philosophical method—some­ thing he revisits in the Introduction to Philosophical Papers I, wherein he describes the goal of philosophy as mapping reflective equilibria between our ‘opinions’ (which include both our ordinary, commonsense opinions and our philosophical theories) (Lewis 1983d, x; see also Beebee 2018). The early letters of this Part show that Lewis more or less endorses a set-theoretical version of nominalism along Quinean lines. Our best theories quantify over sets (or classes), so sets exist. Sets or classes can then play the role of properties (and rela­ tions). We arrive at the view that properties are sets or classes of individuals. The property being red, for instance, is the class of red things. Since Lewis had adopted modal realism by 1970, candidate members of classes extend beyond the actual world. Thus the property being red is the class of actual and possible red things. The influence of Richard Montague is also present here. In ‘On the Nature of Certain Philosophical Entities’, for instance, Montague proposes that ‘two properties are identical just in case they are coextensive in every possible world, not simply if they are coextensive in the actual world’ (Montague 1969, 160, his italics). For Lewis, this provided the resources to handle the nominalist problem of identifying intuitively distinct properties (e.g. having a heart and having a kidney). On the whole, Lewis is more interested in using this kind of nominalism in his theorizing and less interested in arguing for it. When he considered the option of admitting universals into his

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Introduction

xxi

ontology, he figured they would count as another kind of individual and so would be members of classes. That is, if Lewis had to include universals in his ontology, he would not thereby deny the existence of classes and let universals play the role of properties. Another noteworthy topic from this early period is the metaphysics of time. As with his adoption of nominalism, he accepts uncritically a four-dimensionalist the­ ory of time according to which past, present, and future are ontically on a par. One of his main interests in the metaphysics of time was the possibility of time travel. Although his landmark article on the subject—‘The Paradoxes of Time Travel’—was published in 1976, he delivered lectures on time travel as early as 1969 (at UCLA). During his 1970–1 fellowship at Oxford, he finished ‘Could a Time Traveler Change the Past?’, which he read to the Jowett Society at Oxford in November 1970, and wrote his Gavin David Young lectures, which he delivered at the University of Adelaide in  July 1971.5 The letters to Williams (1971), Jack Meiland (1972–3), and William Newton-Smith (1975) reveal the extent of his discussions about time travel  with others at the time. For example, he agrees with Williams on the fourdimensionalist picture of time but disagrees about whether the temporal parts of a time traveller need to be in direct causal contact with each other. For Lewis, a time traveller can have a broken four-dimensional worm so long as their temporal parts are causally dependent on each other in the appropriate manner, which for Lewis means they are counterfactually dependent on each other. His discussion with Meiland explains his opposition to accounts of time travel that posit an extra dimen­ sion of time beyond the temporal extent of the four-dimensional manifold. Out of this interest in time travel comes other work on personal identity, as evidenced by his letter to Derek Parfit in May 1971, which forms the basis of his paper ‘Survival and Identity’ (1976c). From 1980 onwards Lewis’s interest in metaphysics steadily grew—so much so that he blossomed into the metaphysician we have come to recognize. He spent a lot of his time in the 1990s and right up until his untimely death working on how to define intrinsic properties, problems to do with tensed quantifiers in relation to the ontology of time, how to find truthmakers and the best formulation of the truth­ maker intuition, and ways to theorize about fundamental/perfectly natural proper­ ties. The origins and development of his adoption of a division between natural and non-natural properties must be mentioned at this point (and as a result we will have no space to outline the remaining topics in this Part). 5   ‘Could a Time Traveler Change the Past?’ is the early paper-length version of ‘The Paradoxes of Time Travel’. For Lewis’s Gavin David Young lectures on The Paradoxes of Time Travel, see (Janssen-Lauret and MacBride forthcoming).

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xxii Introduction Originally, Lewis endorsed an egalitarian view about properties: there is no ob­ject­ ive division between properties; there are no privileged properties that perform spe­ cial tasks or have some unique ontic status. The theory of properties that identifies properties with sets of possibilia is all that one needs. An early proposal by his peer Michael Slote to solve Goodman’s new riddle of induction (using differential proper­ ties) failed to convince Lewis. In reaction to Slote’s proposal, he said: ‘I want to know the real essence of the species of natural properties, if it has one; I think you’ve found one more proprium, if not accident’ (Letter 644. To Michael A. Slote, 16 February 1966, Volume 2: Part 6: Epistemology, p. 387). But after visits to Australia in 1971, 1976, and 1979 Lewis had encountered Armstrong’s ongoing research on universals, start­ ing with ‘Materialism, Properties, and Predicates’ (Armstrong 1972) and ending with Universals and Scientific Realism (Armstrong 1978a, 1978b). Lewis was still uncon­ vinced by 1976 that Armstrong’s theory of universals demanded that Lewis change his mind about property-egalitarianism. Interestingly, in 1978 Lewis wrote to Gary Merrill in reaction to Merrill’s (1980) paper on Putnam’s model theoretic argument against metaphysical realism. Lewis agreed with the realist reply that Merrill offered in response to Putnam: there are genuine relations out there that can be used to fix the appropriate interpretation of our terms in some theory or language. However, for Lewis, this solution alone is not enough to accept the division between natural and non-natural properties. Motivated by serviceability concerns, he required further uses for the division before he could accept it. It is part of his methodology that he only introduces extra ontology if it serves several theoretical or explanatory purposes (compare his serviceability argument for modal realism). In conversation with Armstrong and as a result of his own study of Armstrong’s theory of universals, Lewis realized how natural properties could figure in his analyses of intrinsicality and duplication, materialism, determinism, causation, laws of nature, supervenience, content of language and thought, and determinacy of reference. The fact that naturalness is so serviceable is his main reason for introducing the distinc­ tion into his theory of properties. (For Lewis, in the first instance, it is an extra-logical, descriptive piece of primitive ideology that applies to some classes of possibilia and not others.) This fact of serviceability is independent of whether the notion can be analysed and, if so, how it is to be analysed in terms of some ontology. Only after his serviceability concerns were met was Lewis convinced that Armstrong’s demand must be accepted. It was at this point that Lewis was more confident than before that the notion of naturalness is legitimate and should be exploited to its fullest extent. If he had lived longer, he would have no doubt continued to work on this topic. Later histories of twentieth-century philosophy, we believe, will mark the rise of natural­ ness in the late twentieth century as a significant turning point in the development of analytic metaphysics.

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Introduction

xxiii

In sum, Lewis’s influence is enormous in metaphysics and the letters in this vol­ ume offer the philosophical public an organic story of the origins, development, breadth, and depth of his metaphysics in its historical context. In addition, the letters in this volume provide a new window into his metaphysical views, with important elaborations that are not found in his published writings. We anticipate that this vol­ ume will become an indispensable resource for contemporary metaphysics and that these letters will further scholarship and research in metaphysics, especially from the Lewisian perspective.

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LIST OF LET TERS Part 1:  Causation Letter

Recipient

Date

Page

1 2 3

Michael Scriven Michael Scriven Dean of the Graduate School, Princeton University Richard Jeffrey Richard Jeffrey Ann Wilbur Robert C. Stalnaker Robert C. Stalnaker Richard Braithwaite F. Jeffry Pelletier Richard Braithwaite Lennart Åqvist Risto Hilpinen John G. Bennett Frank Vlach John G. Bennett Dagfinn Føllesdal Robert C. Stalnaker Peter Woodruff Peter Woodruff Ken Kress Bas van Fraassen Jaegwon Kim John Pollock John Bigelow Kit Fine Thomas McKay and Peter van Inwagen Thomas McKay C.B. Daniels

16 February 1961 21 July 1961 21 November 1961

3 4–5 6–10

3 February 1967 12 March 1967 30 January 1968 31 May 1968 24 June 1968 14 November 1970 24 December 1970 18 January 1971 9 March 1971 16 March 1971 19 March 1971 21 March 1971 12 May 1971 1 April 1971 11 May 1971 18 May 1971 2 June 1971 7 November 1972 28 March 1973 11 August 1973 15 April 1974 8 November 1974 3 February 1975 9 February 1976 17 February 1976 8 April 1976

10–12 12–14 15–16 16–17 18 19 19–20 20–1 21–3 23–5 25–6 26–7 28–30 30 31–2 33–5 35–6 36–8 38–9 39–40 40–2 42–6 46–9 49–51 51 52–4

4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

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xxvi 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68

List of Letters Richard J. Hall Peter Gärdenfors Alvin Plantinga Frank Jackson Hector-Neri Castañeda Holly Goldman Terence Horgan Pavel Tichý Robert C. Stalnaker Donald Nute Frederick Kroon Hans Herzberger D.M. Armstrong D.M. Armstrong D.M. Armstrong Jonathan Bennett Elliott Sober Thomas Nagel Peter van Inwagen Allen P. Hazen Keith Lehrer Keith Lehrer Jonathan Bennett Robert Pargetter Peter van Inwagen David Copp Terence Horgan D.H. Mellor Brian Skyrms P.N. Johnson-Laird Louis Loeb Louis Loeb Hugh Rice Terence Horgan David Sanford Frank Jackson and Robert Pargetter D.H. Mellor Gene Cline Peter van Inwagen

12 May 1976 7 October 1976 22 October 1976 3 December 1976 21 December 1976 26 December 1976 18 April 1977 12 September 1977 13 September 1977 27 September 1977 22 February 1978 18 August 1978 23 January 1979 13 March 1980 10 April 1980 7 November 1980 23 February 1981 4 April 1981 7 April 1981 8 April 1981 9 April 1981 10 April 1981 21 April 1981 4 August 1981 18 October 1981 12 November 1981 2 November 1982 2 December 1982 13 June 1983 10 October 1983 21 February 1984 13 March 1984 5 June 1984 7 July 1984 16 February 1987 8 May 1987 3 November 1987 21 December 1987 30 November 1989

54–6 56–7 57–61 62–5 65–7 67–9 70 71–2 73–5 75–7 77–8 78–9 80–1 81–3 83–5 85–6 86–7 87–8 88–92 93–4 94–5 95–6 96–9 99–100 101–3 103–5 105–6 106–7 108 109–11 111–12 112–13 113–14 114–17 117–19 120–5 125–7 127–9 129–31

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69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107

List of Letters Peter van Inwagen Galen Strawson John Earman Donald Bedford and Henry Stapp Rob Clifton Daniel M. Hausman Huw Price James Woodward Alvin Plantinga Adam Morton Ken Gemes Michael McDermott Peter Menzies T.L.S. Sprigge Michael McDermott Michael McDermott Michael McDermott C.B. Martin Wolfgang Spohn Wolfgang Spohn Murali Ramachandran Phillip Bricker Ned Hall Ned Hall and L.A. Paul Galen Strawson Ned Hall Ned Hall Hugh Rice U.T. Place Jonathan Schaffer Alexander Bird Bruce Langtry Helen Beebee Bruce Langtry Ned Hall Jonathan Schaffer Helen Beebee Ned Hall D.H. Mellor

xxvii 15 January 1990 16 July 1990 12 February 1991 11 April 1991 11 June 1991 16 June 1991 23 September 1991 4 February 1992 18 May 1992 20 January 1993 25 January 1993 1 July 1993 6 July 1993 15 November 1993 10 August 1994 2 March 1995 8 May 1995 18 January 1996 13 February 1996 14 February 1996 17 October 1996 13 March 1997 22 April 1997 29 April 1997 23 June 1997 23 June 1997 24 June 1997 27 June 1997 13 August 1997 30 January 1998 27 February 1998 14 August 1998 28 August 1998 11 September 1998 9 October 1998 9 October 1998 17 November 1998 23 December 1998 19 January 1999

131–3 134–5 135–6 137–41 141–3 143–4 144–5 145–9 150–5 155–7 157–8 158–9 160–1 162 163–4 165–7 167–8 168–9 170 171 171–5 176–7 177–9 180–5 185–6 187–9 189–90 190–3 193–4 194–7 197–200 200–2 203–5 205–6 206–8 208–10 210–11 211–12 213

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List of Letters

xxviii 108 109 110 111 112 113 114 115 116 117 118 119

Jonathan Schaffer Nicholas White Mary Kate McGowan Helen Beebee Christopher Hitchcock James Coley Peter Godfrey-Smith Daniel Dennett D.H. Mellor Jonathan Bennett Jonathan Bennett Adam Elga

9 February 1999 26 March 1999 1 April 1999 12 April 1999 17 May 1999 21 October 1999 3 December 1999 26 June 2000 26 February 2001 26 February 2001 6 June 2001 6 June 2001

214–16 217 218–19 220–1 221–3 223–4 224 225 225–6 226–33 233–4 235–6

Part 2:  Modality Letter

Recipient

Date

Page

120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142

Jerome A. Shaffer Dagfinn Føllesdal Richmond Thomason A.N. Prior Peter Geach John Wallace W.V. Quine Edward L. Keenan Paul Fitzgerald Alvin Plantinga John Wallace Fabrizio Mondadori Fabrizio Mondadori G.H. Merrill G.H. Merrill Fred Feldman Alvin Plantinga Alvin Plantinga Jordan Howard Sobel Paul Teller Bryan Norton Brian Skyrms Allen P. Hazen

17 October 1965 6 March 1966 26 February 1967 6 April 1967 16 May 1967 27 September 1968 1 October 1968 10 April 1969 30 June 1969 16 October 1969 4 March 1970 19 March 1971 6 May 1971 27 September 1971 15 October 1971 7 March 1972 20 April 1972 21 May 1972 24 January 1974 5 February 1974 15 September 1975 26 November 1975 2 August 1977

239–40 241–6 246–7 247–8 248 249–51 251–2 253–4 254–6 256–7 257 258–9 259–60 261–2 262–4 264–6 266–70 271–3 274 275–6 276–7 277–9 280–1

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143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181

List of Letters Allen P. Hazen Michael A. Slote Peter van Inwagen Peter van Inwagen John G. Bennett John G. Bennett Allen P. Hazen John Leslie Peter Forrest Peter Forrest Sally McConnell-Ginet Peter van Inwagen Peter van Inwagen Peter van Inwagen Peter van Inwagen John Leslie Peter van Inwagen David Kaplan Peter van Inwagen Kit Fine Peter van Inwagen Allen P. Hazen Peter van Inwagen Allen P. Hazen Peter van Inwagen Peter van Inwagen Graeme Forbes Alan McMichael Colin McGinn Roz Chast Christopher Peacocke Max Cresswell Graham Priest Alan McMichael Margery Naylor John Bigelow Graeme Forbes Alvin Plantinga John Coker

xxix 12 August 1977 13 June 1978 23 May 1979 2 October 1979 20 February 1980 10 April 1980 2 December 1980 4 April 1981 29 July 1981 26 August 1981 11 May 1982 24 May 1982 3 August 1982 14 September 1982 1 October 1982 8 November 1982 28 December 1982 9 February 1983 16 February 1983 8 March 1983 16 April 1983 19 April 1983 21 April 1983 11 May 1983 23 May 1983 7 July 1983 7 December 1983 6 January 1984 30 May 1984 15 June 1984 1 July 1984 23 October 1984 22 July 1985 Fall 1985 14 January 1986 30 May 1986 23 June 1986 18 November 1986 5 February 1987

281–2 282–4 285–6 286 287–9 289–91 291–2 292–3 294–5 295–7 297–8 299–301 301–2 302–4 304–6 306–8 308–11 311–12 312–15 315–17 318–19 319–20 321–5 325–6 327 328–33 334 335 336–9 340–1 341–2 342–3 344–5 345–7 348 349–51 351 352–3 353–4

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xxx 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220

List of Letters Philip P. Hanson Jaegwon Kim Jack Copeland Robert C. Stalnaker E.J. Khamara Paul Tappenden Charles Huenemann Alexander Rosenberg Murali Ramachandran Phillip Bricker John Martin Fischer Michael Jubien Charles Pigden Richard B. Miller Catherine Z. Elgin Sydney Shoemaker Peter van Inwagen Peter van Inwagen William G. Lycan Charles Pigden Megan McLaughlin William G. Lycan Gideon Rosen Charles Pigden and Rebecca E.B. Entwisle Quentin Smith Jan Cover and John Hawthorne Peter Menzies and Philip Pettit Robert C. Stalnaker Hud Hudson Allen P. Hazen and David Kaplan Daniel Nolan Robert C. Stalnaker Richard B. Miller Daniel Nolan Bradley Monton Robert Black Tyler Doggett Graham Priest Hud Hudson

27 March 1987 31 March 1987 22 June 1987 28 July 1987 21 September 1987 21 December 1987 1 February 1988 7 June 1988 18 October 1988 2 February 1989 27 April 1989 14 June 1989 22 September 1989 28 March 1990 4 April 1990 17 September 1990 20 December 1990 14 January 1991 26 June 1991 13 November 1991 21 January 1992 4 June 1992 16 June 1992 19 January 1993 4 October 1993 31 January 1994 6 May 1994 26 April 1995 8 May 1995 4 October 1995 16 January 1996 28 February 1996 12 March 1996 13 December 1996 28 May 1998 28 January 1999 18 May 1999 9 January 2001 3 April 2001

355–6 356–9 359–60 360–1 361–4 364–5 365–6 366–9 369–72 372–3 373–4 375–8 378–80 380–1 381–4 384–8 388–9 390–1 391–2 393–4 394–6 396–7 397–8 399–402 403 404 405–7 408–9 409 410–12 412–15 416–17 418 419–20 421–2 423–5 426 427–9 429–32

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221 222 223

List of Letters Phillip Rutherford Michael C. Rea Michael C. Rea

xxxi 20 April 2001 24 August 2001 7 September 2001

432–5 435–7 437–8

Part 3:  Ontology Letter

Recipient

Date

Page

224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255

J.J.C. Smart W.V. Quine Charles Chastain J.J.C. Smart T.G. Gardiner Donald C. Williams Derek Parfit Jonathan Harrison George Boolos Jack W. Meiland Jack W. Meiland Charles Fillmore Allan Gibbard W.H. Newton-Smith Peter Unger Peter Unger Jonathan Bennett D.H. Mellor G.H. Merrill D.H. Mellor Toomas Karmo D.M. Armstrong Michael Devitt Michael Tooley Allen P. Hazen Lloyd Humberstone D.M. Armstrong Jerry A. Fodor Jerry A. Fodor Hilary Putnam Paul Churchland Hilary Putnam

31 July 1969 18 August 1969 8 March 1970 1 May 1970 1 October 1970 12 May 1971 13 May 1971 20 July 1971 2 December 1971 13 December 1972 6 January 1973 29 January 1974 22 November 1974 12 November 1975 29 July 1976 1 November 1976 29 March 1977 2 December 1977 11 October 1978 19 March 1979 10 July 1980 18 December 1980 31 August 1981 21 October 1981 30 May 1982 12 August 1982 26 November 1982 26 November 1982 3 January 1983 3 January 1983 2 February 1983 8 February 1983

441–2 442–3 443–4 444–5 446 446–9 449–54 454 455–6 456–60 460–1 461–2 462–5 466–8 468–9 469–70 470–2 472–3 473–4 474–5 476–7 478–80 481 482–4 484–5 485–6 486–7 488–9 489–90 490 491 492

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xxxii 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294

List of Letters D.M. Armstrong Hartry Field D.M. Armstrong J.J.C. Smart Paul Teller Hartry Field D.M. Armstrong Hartry Field Peter Unger Peter Unger Alan McMichael Hartry Field Alan McMichael Paul Teller J.J.C. Smart Terence Horgan D.M. Armstrong John Bigelow Peter Forrest George Boolos J.J.C. Smart D.M. Armstrong Peter van Inwagen Michael Tooley Peter van Inwagen Max Cresswell D.M. Armstrong Barry Taylor Peter van Inwagen Keith Campbell William G. Lycan Keith Campbell D.M. Armstrong William G. Lycan Nelson Goodman John Bigelow and Robert Pargetter Earl Conee Terence Parsons Peter van Inwagen and Hartry Field

17 February 1983 29 March 1983 30 March 1983 31 March 1983 16 April 1983 23 May 1983 8 June 1983 6 July 1983 5 October 1983 24 October 1983 16 January 1984 7 February 1984 8 February 1984 9 February 1984 14 February 1984 22 May 1984 6 January 1985 8 January 1985 30 January 1985 6 June 1985 13 July 1985 1 October 1985 25 February 1986 4 March 1986 1 April 1986 27 May 1986 28 July 1986 5 August 1986 4 November 1986 11 December 1986 11 February 1987 31 March 1987 6 May 1987 18 June 1987 22 September 1987 28 September 1987 9 December 1987 21 January 1988 24 February 1988

492–5 495 496–8 498–502 503 503–5 506–9 509–14 515–17 517 518–19 519–20 520 521–2 522–4 525–6 526–9 529–31 531–3 533–7 537–42 542–8 548–9 549–51 551–3 553–5 555–63 563–5 565 566–7 567–75 575–6 577–80 580–1 581–2 582–3 583–4 585 585–9

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295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333

List of Letters George Boolos Allen P. Hazen Allen P. Hazen Paolo Dau Eli Hirsch Phillip Bricker W.V. Quine Barry Taylor W.V. Quine Murray MacBeath Hartry Field W.V. Quine Allen P. Hazen George Boolos John Etchemendy John Bigelow D.M. Armstrong Steve Pyke John Burgess Douglass Smith Mark Hinchliff Douglass Smith Peter van Inwagen Michael Devitt Peter van Inwagen George Bealer Alex Oliver D.M. Armstrong Donald Morrison J.J.C. Smart D.M. Armstrong Stephen Pollard J.J.C. Smart Seamus Murphy Michael Devitt Alex Oliver George Bealer Alex Oliver Phillip Bricker

xxxiii 24 April 1988 2 May 1988 18 June 1988 23 November 1988 27 December 1988 13 June 1989 8 August 1989 8 September 1989 21 September 1989 22 September 1989 5 October 1989 10 November 1989 20 November 1989 1 December 1989 15 December 1989 26 February 1990 28 March 1990 27 July 1990 1 August 1990 28 September 1990 15 October 1990 13 November 1990 6 February 1991 27 February 1991 5 March 1991 8 March 1991 20 May 1991 3 June 1991 19 June 1991 14 July 1991 24 July 1991 13 August 1991 22 August 1991 24 September 1991 24 December 1991 7 January 1992 6 February 1992 18 February 1992 6 April 1992

590–2 593–4 594–7 597 598 598–600 600–1 601–3 603–4 604–5 605–8 608–9 610 611 612–14 614–15 615–16 616–17 617–23 623–5 625–7 627 628–30 630–2 632–5 635–7 638–9 640 641–3 643–5 646–9 649–50 650–2 653–5 655–6 656–8 658–9 659–60 660–6

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xxxiv 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372

List of Letters Catherine Z. Elgin Douglass Smith Peter van Inwagen Frederick Kroon Gideon Rosen John Leslie D.M. Armstrong Phillip Bricker Gideon Rosen Brian Ellis and Caroline Lierse C.B. Martin Denis Robinson T.L.S. Sprigge Catherine Legg D.M. Armstrong John Bigelow Hilary Putnam Peter van Inwagen Theodore Sider John Bigelow Geoffrey Hellman Bas van Fraassen Reinhardt Grossmann Rae Langton Peter Vallentyne Peter Vallentyne Bas van Fraassen Rae Langton George Molnar J. Michael Dunn Rae Langton Dean W. Zimmerman Dean W. Zimmerman D.M. Armstrong Dean W. Zimmerman Daniel Nolan D.M. Armstrong Mary Kate McGowan Graham Oppy

17 April 1992 5 May 1992 4 July 1992 11 August 1992 24 November 1992 2 February 1993 18 February 1993 7 March 1993 22 June 1993 9 July 1993 28 September 1993 5 February 1994 25 February 1994 18 March 1994 28 October 1994 19 December 1994 2 January 1995 4 January 1995 4 January 1995 12 January 1995 19 January 1995 13 February 1995 16 June 1995 21 August 1995 15 September 1995 26 September 1995 10 January 1996 7 May 1996 20 June 1996 20 June 1996 27 August 1996 12 June 1997 14 September 1997 7 October 1997 17 October 1997 3 February 1998 23 February 1998 4 March 1998 27 March 1998

666–7 667 668 668–9 669–72 672–3 673–4 675–6 676–7 677–8 679–81 682–4 685 685–7 687–8 688–90 690–1 692–3 693–5 695–6 697–8 698–9 699–700 701–2 702–4 704–5 705–6 706–8 708 709 709–10 710–15 715–16 716–17 718–19 719–20 721–2 722–4 724–7

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373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411

List of Letters David Sanford D.H. Mellor D.H. Mellor Linda Wetzel Josh Parsons Dean W. Zimmerman Theodore Sider Dean W. Zimmerman Theodore Sider John Bigelow Donald L.M. Baxter Theodore Sider D.H. Mellor Thomas Baldwin D.M. Armstrong D.H. Mellor Theodore Sider Mark Hinchliff Lloyd Humberstone D.M. Armstrong D.H. Mellor Phillip Bricker Donald L.M. Baxter Jonathan Schaffer Jonathan Schaffer Scott Sturgeon L.A. Paul L.A. Paul Jonathan Schaffer Josh Parsons and Dan Marshall Theodore Sider J.J.C. Smart Jonathan Schaffer Josh Parsons Peter J. Lewis D.M. Armstrong Alan Hájek Peter J. Lewis Peter J. Lewis

xxxv 22 May 1998 13 August 1998 31 August 1998 8 December 1998 23 December 1998 18 January 1999 31 January 1999 9 June 1999 9 June 1999 16 June 1999 21 June 1999 27 July 1999 27 July 1999 28 July 1999 28 July 1999 29 July 1999 2 August 1999 6 August 1999 13 August 1999 19 August 1999 26 August 1999 27 August 1999 4 October 1999 2 December 1999 15 December 1999 18 April 2000 7 July 2000 12 July 2000 14 July 2000 28 September 2000 8 October 2000 17 October 2000 15 December 2000 9 March 2001 7 April 2001 12 April 2001 4 May 2001 4 May 2001 26 May 2001

727–8 729–33 733–4 734–6 736–7 737–8 738–9 740 741–2 742–3 743–5 745–6 746–7 747–8 749–50 750–1 751–2 752–4 754–5 756–7 757–9 759–61 762 762–3 764–5 765 766–7 768 769–70 770–1 771–2 772–3 773–5 775–6 776–7 777–8 779–80 780–2 783–4

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List of Letters

xxxvi 412 413 414 415 416 417 418 419

Jonathan Schaffer Jeremy Butterfield Kit Fine L.A. Paul Earl Conee Mary Kate McGowan Jeremy Butterfield Peter Momtchiloff

5 June 2001 25 July 2001 16 August 2001 7 September 2001 10 September 2001 20 September 2001 2 October 2001 8 October 2001

784–5 785–6 786–7 787–90 790–1 791–2 793 794

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KEY TO SYMBOLS /to/

No such word in MS. It has been inserted by the editors.

Melbourne

Word crossed out in MS. Such instances are only indicated so as to give sense.

Conjectural restoration of disfigured word(s) in MS, except for ordered pairs.

Word(s) torn away, unreadable, or concealed in MS.

[. . .]

Editorial redaction of content.

[comment]

In-text editorial comment.

All footnotes have been inserted by the editors except for footnotes signified by an asterisk or similar, non-numerical symbol. Instances of ellipses without square brackets are in MS. Cases of non-italicized text in square brackets are in MS. Typographical and minor grammatical errors have been silently corrected.

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PART 1 Causation

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1.  To Michael Scriven, 16 February 1961 [Swarthmore, PA] Dear Mr. Scriven, I’ve read the explanations thing, throughout but quickly.1 I haven’t thought much about this, so won’t comment; I think I entirely agree with it. On cause: I’m much struck by the fact that I am inclined everywhere to take ‘It wouldn’t have happened without’ and ‘It would have happened anyway’ (especially the latter) as conclusively establishing and refuting causal claims. My treatment is based on this. But I also make (legitimately) and balk at causal claims other than in accordance with these two tests. 1. Where the cause is very remote, I balk, but can be persuaded to swallow it with a ‘. . . well, strictly I suppose so, but . . .’ or a ‘. . . yes, in a sense’. My grandfather’s birth caused you to get this letter. I balk especially in a legal context; I find it gets quite palatable in the train of thought: a thousand years ago a leaf fell; the consequences ramified through the ages; eventually a man caught a cold, lost his job, left town, met a girl; my grandfather was born; I wrote this letter, etc; in a thousand years think what great changes in the world caused by the fall of a single leaf! If you still don’t like it, suppose the leaf fell by divine intervention, the only such since the creation. 2. When it would have happened anyway, but in a different way, I may still accept a causal claim in a coroner’s report or historical account (your man running upstairs, my plant manager) but am also prepared to reject it. 3. Where A caused B, but most things like A don’t cause things like B. A doctor has competently but mistakenly diagnosed a case, and competently performs a trivial almost always safe operation. The man dies. It is discovered that the illness he had was not, as supposed, fatal, so he would otherwise have lived. Did the operation cause his death? Remember, such operations generally don’t. I say sure, but an intelligent [sic] has argued this with me. I don’t know any such case that worries me. I think the proper strategy is to analyse ‘cause’ as a basic meaning, and then examine deviations. We need a better theory of mis-speaking than simply ‘we wouldn’t say this’, ‘true’, ‘false’, ‘odd’. We need e.g. ‘strictly true but inappropriate’ and so on categories. ‘True’ and ‘false’ are here very inappropriate tests. Glad you appreciate the numerology! David Lewis

  Probably ‘The Limits of Physical Explanation’ (Scriven 1963).

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2.  To Michael Scriven, 21 July 1961 [Swarthmore, PA] Dear Mr. Scriven, I enclose a copy of a paper on cause.1 I wrote this for an essay contest here, and in hopes that it would be not too far from a publishable form. I have a Dolfinger-McMahan grant this summer; blank check for anything having vaguely to do with meta-ethics.2 I’ll be working under Beardsley. One of the things I will do is to try to do some final polishing and get the wretched thing published. I think the only thing here you haven’t seen is the treatment of overdetermination. I was talking to Manove,3 and he showed me a model of ‘cause’. I’m not sure how much of it is his, the terminology is yours, and it is at least quite similar to what you showed me early last summer. I reword it to compare it with mine: Situation A caused situation B if and only if: Manove-Scriven

Lewis

There is a partial state description S such that A is a part of S (S → A) and: M-S 1 S was in fact the case

L1 A was the case

M-S 2 Whenever S is the case, R is the case (later); and B is an instance of R.

L2 B was the case (later)

M-S 3 Whenever S is the case, except that A is deleted, no R follows of which B is an instance.

L3 Had A been deleted, B would not have followed.

M-S #2 and #3, and L #3 are natural laws or their derivatives. When I speak of ‘deleting’ A, I mean (in either model) replacing it by any of various (counterfactually specified) comparison cases. I do not mean any situation (or partial state description) so that it is not the case that A. Comments: 1. M-S model is much more convenient for overdetermination than mine. But, the treatment turns out to be very closely similar.

1   ‘Particular and General Causal Claims’. Three versions of this paper have survived, one of which is dated 15 April 1961. The most polished version is from July 1961. It is published in (Janssen-Lauret and MacBride forthcoming). 2   Lewis wrote Can Ethics Be Reasonable? (honours thesis), 16 August 1961. 3   Michael Manove, who went on to become Professor of Economics, Boston University.

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2.  To Michael Scriven, 21 July 1961

5

2. If one cared to remove the temporal-sequence condition, M-S would suffer less than mine. 3. On the other hand, consider this case.4

When the center shield is removed, the counter registers irregularly, but on the average four times a minute. When the center shield is in place, it practically never registers. I pull back the center shield for a fraction of a second, and the counter registers. I say pulling back the shield caused the counter to register. But M-S #2 is not satisfied unless we include in S a ‘gremlin’ – the Co-60 being about to disintegrate. (I assume quantum indeterminacy.) Or to put it another way: pulling the trigger caused the gun to fire even if I was playing Russian Roulette. Incidentally, Manove first disagrees with me as to what we would say in the lead-shield case. Since there are such differences in feeling of language, I think it is gratuitous to decide that one or the other model is both correct and complete. 4. I think on either model, whether ‘cause’ is a transitive relation between particular situations depends on the method of selecting comparison cases in the context in which transitivity is asserted. To me it is very important that long causal chains are legitimate. This is part of the reason for my feeling as I do about matter #3; lest the chain be broken by something happening that would have been more likely not to. Sincerely, David Lewis PS ‘Swarthmore College’ is my address for the coming summer. PS Further objection to M-S; it’ll be very hard to specify S. But I don’t know that that matters very much.

  The following diagram was redrawn because the original could not be reproduced clearly.

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Philosophical Letters of David K. Lewis

3.  To Dean of the Graduate School, Princeton University,1 21 November 1961 Swarthmore College Swarthmore, PA Dear Sir: My plans for the future are simple and fairly definite: I intend to take a Ph.D. in philosophy as soon as I can, and then teach philosophy in a college or university. I have been deeply interested in philosophy since 1959–60; I spent that year at Oxford (the center of a certain variety of philosophy) taking about half of my formal instruction in philosophy, and doing a good deal of extra reading. To explain what my interests are within philosophy, I begin, since philosophy is deeply divided into schools which do not understand one another, by saying where my sympathies lie. To do this I will say what I think philosophy is: philosophy is the study of the logical dependences relating concepts to other concepts which surround them in a working conceptual system, within which system alone they have meaning. I think this description fits all philosophy; but it applies obviously to that of the three philosophers to whose work I feel most in debt: the later Wittgenstein, John Wisdom, and Gilbert Ryle. I don’t agree with those who think that our conceptual equipment is in a state of confusion and needs to be rebuilt. Still less do I care for the idea that only those concepts are worth studying, that all of us use every day. I think that sometimes an artificial, composed construction, or a conceptual invention of some past philosopher, or a simplified, distorted variant of a concept from common usage, might be just the thing to make clear the ‘logical powers’ of some concept (from whatever source) that interests and puzzles us. In this opinion, I fear that I differ from some of those with whom I otherwise most agree. The concepts which I am particularly interested in trying to elucidate are those we use in saying interesting things about people’s states of mind. I would like to understand what it is to feel guilty, to see something in one’s mind’s eye, to understand somebody else’s actions ‘from the inside’, to regard a machine ‘as though it had feelings’, or to see the world as a harmonious unity. I think that these concepts are pervaded by metaphors making them seem clearer than they otherwise would, but making trouble when carried too far. (As in the speckled hen problem, for instance. Counting spots on a picture before my mind’s eye isn’t like counting spots on a picture before my eye. It’s like picking an arbitrary number.) I might call this field philosophy 1   Donald R. Hamilton, who was Dean of the Graduate School at Princeton University from 1958 to 1965.

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3.  To Dean of the Graduate School, Princeton University, 21 November 1961

7

of mind, except that to call it so would too much suggest the mind-body ontological problem. Often (all but the second example here) it is also a part of moral philosophy. My philosophical training so far is badly unbalanced in favor of contemporary British analytic philosophy. I should know more about the history of philosophy, and perhaps I should know more about contemporary European philosophy. I would like to learn from those who know how to interpret theologians, idealists, and ex­ist­ en­tial­ists – but I doubt if I myself have any talent in this direction. My impression is that here ideas of considerable interest are hidden in words so obscure and pretentious that analytic philosophers might better hope to rediscover these ideas than to understand those who now expound them. A limited topic that interests me (and might perhaps make a thesis) is the moral philosophy of William Wollaston, an English writer somewhat before Hume. He tried to prove moral injunctions by assimilating bad actions to false beliefs thus: all actions express beliefs, and bad actions are those that express false beliefs. If I take your horse, I show that I falsely believed it is mine; since it isn’t, I shouldn’t have. Nobody now, surely, would want to say that Wollaston’s attempt works. It would be interesting to see how Wollaston might have come to think that it did, and how good a run for its money he managed to give it. Sincerely, David K. Lewis [Attached document] I grew up in Oberlin, Ohio with the exception of two years when I was nine and ten. My father is in the Government Department there, and my mother was for a time in the History Department. I absorbed a familiarity with the way a college works, and with the attitudes toward learning and toward social questions that are characteristic, I think, of much of the academic profession. I continue to be very narrow and ­provincial – not to understand really what it’s like not to live around a college. In elementary school I skipped second grade because I had learned to read early; and therefore had some difficulties in writing and arithmetic for the next three or four years. I caught up by seventh grade, and became much interested in chemistry. This interest remained throughout high school; at first as a hobby and later as a field of learning. I maintained a laboratory in my basement, and spent a great deal of time hanging about the Oberlin College chemistry building. I was encouraged by the high school science teachers, the college department of chemistry, and my parents; and took for granted that I was going into chemistry. My parents and I were concerned about the difficulty of getting a liberal education with a major in chemistry; the American Chemical Society requires a heavy

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Philosophical Letters of David K. Lewis

program of people who are to be considered by the profession as properly trained, so most chemistry departments make extraordinary demands on their majors’ time. I had managed to work at an unusual rate in high school, for various reasons, so in my senior year (third year) I was permitted to take introductory courses in math­em­ at­ics, chemistry and German at Oberlin College; thus freeing time for social sciences and humanities in college. However, I was thus left at the end of high school more than adequately prepared for college but a little short of requirements for graduation from high school; so I am not a high school graduate. Toward the end of high school I also became interested in mathematics. The sources of this interest are two: a well-taught high school course in geometry, and a Scientific American article on Gödel’s theorem. A member of the Oberlin Mathematics Department helped me to pick up a certain amount of symbolic logic and set theory. By the time I went to Swarthmore I had no idea whether I would end up in chemistry or mathematics. But by the middle of my sophomore year, I had become disappointed with chemistry and dropped it. The theory seemed to me sloppy and chaotic, the experimental work seemed to be either cookbook-following or engineering, and the field seemed altogether too big and too rapidly growing for comfort. I had learned some history and political science, and regretted that I would not be able to go on with them. I expected to continue in mathematics and do some physics as well, but did not feel content with the prospect. In the academic year 1959–60 (which would otherwise have been my junior year at Swarthmore) my father went to Oxford as a Fulbright visiting professor. I had the opportunity of an extra year of undergraduate study at little cost, and decided to use it to study somewhat more philosophy and social science before concentrating entirely in mathematics. I took the Philosophy, Politics, Economics program (‘P.P.E.’), and soon found myself deeply absorbed in philosophy. Oxford is a center of one sort of analytic philosophy, and I had the chance to hear lectures by some people of the first rank in the field: J.L. Austin, Gilbert Ryle, A.J. Ayer, H.L.A. Hart, and Sir Isaiah Berlin. My tutor, Iris Murdoch, is one of those who are at home both in Oxford analytic philosophy and in European metaphysics; I am much indebted both to her teaching and to her articles. I read a good deal beyond the requirements of my tu­tor­ ials; the books which taught me most would be: Ludwig Wittgenstein, Philosophical Investigations and The Blue and Brown Books; John Wisdom, Philosophy and Psycho-analysis; and Gilbert Ryle, The Concept of Mind. My present views and interests in philosophy are direct developments of those I had at the end of my year at Oxford. On returning to Swarthmore, it became quite clear to me that I wanted to remain in philosophy. I have gone on in mathematics and physics, but am now formally a philosophy major. I intend to work for a Ph.D. in philosophy: concentrating as much as possible in philosophy of mind and moral philosophy. My interests are in

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3.  To Dean of the Graduate School, Princeton University, 21 November 1961

9

analytic philosophy as applied to the philosophy of mind and moral philosophy. Now, though, I think that what I lack is not so much training in analytic philosophy as in the history of philosophy, and in contemporary European philosophy. I feel that I ought to know more social science, particularly politics and history; I hope that it will be possible for me to do some in graduate school. With a Ph.D., I will pre­sum­ ably be able to get a satisfactory academic position including opportunities for research and for teaching advanced students. It seems to me very unlikely that I would go into any other profession than college teaching. I have been interested in politics for some time. When I was in high school, I  was simply a partisan of the Democratic party and of righteousness in general. Somewhat after I came to college I read some of the fashionable critiques of American culture (Riesman, Vance Packard, and the like) and was much disturbed by them; I now think that it is absurd and presumptuous to make ethical criticisms of a whole society, containing a rich variety of forms of social life, and that the thought going into such criticisms would be better employed in formulating ethical concepts that could be used to think about this or that within society. I now believe that it is better to think of politics as (in normal times, at least) a struggle between group interests, harnessed by institutional machinery so as to tend to the common good. The prac­ tical techniques of conducting power struggles between groups which have some conflicting and some common purposes seem to me very interesting. I have read a good deal on arms control, disarmament, and military strategy; probably the book I  learned most from was Thomas  C.  Schelling, The Strategy of Conflict, a theoretical book with applications here and there throughout social and political relations. My other principal interests are folk music (particularly British ballads) and cave exploring. I am in no organised extra-curricular activities this year, but in the past I have worked for WSRN (the Swarthmore student radio station), the Little Theater Club (light crew), and the Grouse (a shoestring student publication devoted to criticism of the college). I have been active in the Outing Club, and in the Swarthmore branch of the National Speleological Society. Last year I won the Brand Blanshard prize for a philosophy essay.2 (I have submitted it to the Journal of Philosophy, and will send you a reprint if they accept it.) Last summer I was awarded a Dolfinger-McMahon research grant to write a short thesis in moral philosophy, developing some of the ideas I had been thinking about during the year.3 This semester I am taking a seminar in Social Philosophy and a seminar in Radiation and Statistical Physics. I am auditing a seminar in Economic Theory to   1961. ‘Particular and General Causal Claims’ (Janssen-Lauret and MacBride forthcoming).   Can Ethics Be Reasonable? (honours thesis), Swarthmore College, 16 August 1961.

2 3

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review some of the material I studied at Oxford. I will take a seminar in Aesthetics and a seminar in Modern Algebra next semester. (In the Swarthmore honors program one takes only two subjects at a time; thus this is my full program.) I regret that, as I misread your announcement and thought that the deadline was 30 November, my Oberlin transcript will reach you about a week overdue. I hope this will not matter: note that in the three fields concerned (mathematics, chemistry, and German) my Swarthmore transcript gives grades for subsequent courses. My apologies. David Kellogg Lewis

4.  To Richard Jeffrey, 3 February 1967 UCLA Los Angeles, CA Dear Professor Jeffrey: One of our graduate students, Hal Lauter, is writing his dissertation on Reichenbach’s conditions for nomologicality,1 and has now come to the one requiring a nomological statement to be ‘verifiably true’. This is the only condition that might be able to discriminate between, say: G) All gold spheres are less than 105 kilos. (accidental) U) All U235 spheres are less than 105 kilos. (lawlike) Even if G is true, it couldn’t be confirmed (except maybe a little bit by enumerative induction). U, on the other hand, could be and has been highly confirmed by evidence for the laws of nuclear fission. Donald Kalish advised Lauter to try restating Reichenbach’s condition in terms of confirmation theory, whereupon I suggested that you had done just that in ‘Goodman’s Query’.2 This led to a fruitful conversation between Lauter and myself. I would be glad to hear how you like the fruit. I should suppose that a hypothesis h of the form (x)(Qx ⊃ Px) is lawlike iff P is projectible relative to Q. OK? If so, then your definition of pragmatic projectibility says that h is lawlike iff the instance confirmation of h by favorable evidence

  One article derived from Lauter’s dissertation is (Lauter 1970).   

1

  (Jeffrey 1966).

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4.  To Richard Jeffrey, 3 February 1967

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c­ onsisting of n positive instances approaches 1, as n increases. I would like to try generalizing from there. Often we must appeal to some sort of background knowledge to discriminate between accidental and lawlike generalizations. Thus in the case of G and U above. So I suggest replacing ‘instance confirmation of h by favorable evidence’ by ‘instance confirmation of h by favorable evidence and total background evidence’, and taking the explicandum as ‘h is lawlike relative to background evidence b’. Often a generalization is more readily confirmed by some sort of indirect favorable evidence than it is by favorable evidence consisting of positive instances. Thus in the case of U above. So I suggest removing the specification that the fa­vor­ able evidence consist of positive instances. The amount of favorable evidence of unspecified sort is no longer measured by a number like your n; but we can still define the limit of instance confirmation of h as the amount of favorable evidence increases, by means of the partial ordering of bodies of evidence by ‘entails but is not entailed by’. So we’re here: h is lawlike relative to background evidence b iff the instance confirmation of h by favorable evidence e and background evidence b approaches 1, as the amount of evidence e increases. But now there’s a problem. The favorable evidence e is not evidence we already have for h; that is included in b, and would be very hard to sort out. Rather it is hypothetical new evidence for h that might result from further investigation into the truth of h beyond what is mentioned in b. It is not limited to favorable evidence consisting of positive instances; but neither can it be just any possible favorable evidence. For take any hypothesis; there is some possible favorable evidence that would both confirm it and persuade us that it was lawlike. For instance the instance confirmation of G could be raised by some sort of evidence which tended to persuade us that gold is fissionable with critical mass .5 × 105 kilos. I suggest that e should be any favorable evidence which is likely (relative to b) to accrue if further investigation into the truth of h is carried out and h is in fact true. That is, e must meet the condition: c(e, I(h) & h & b) is high (where I(h) is the propos­ ition that the truth of h is investigated). That cannot be the only condition on e; if it were, e could be h itself. I reluctantly suggest that e should consist of observation statements, and hope there is some less suspect way of accomplishing the same ­purpose. Now we’re here: h is lawlike relative to background evidence b iff the instance confirmation of h by favorable evidence e – consisting of observation statements highly confirmed by I(h) & h & b – and background evidence b approaches 1, as the amount of evidence increases.

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Instead of using a c-function and relativizing to a body of background evidence b, we must use a subjective conditional probability function and relativize to a person at a time. But that is further from ‘Goodman’s Query’ and from Lauter’s project. I don’t know that h is accidental just in case it isn’t lawlike. Maybe h is accidental relative to b iff the instance confirmation of h by favorable evidence e – consisting of observation statements highly confirmed by I(h) & H & b – and b remains equal to (or approaches as a limit) the instance confirmation of h by b alone, as the amount of evidence increases. Is this getting anywhere? Yours, David Lewis cc: Hal Lauter, Donald Kalish, David Kaplan

5.  To Richard Jeffrey, 12 March 1967 UCLA Los Angeles, CA Dear Dick, Thanks very much for your letters; sorry about my delay in answering. We do seem to be getting somewhere. If we could characterize laws (or lawlike generalizations) by a necessary and sufficient condition in terms of c-functions, what would we have? Maybe a better understanding of what a law is – or maybe a condition for rationality of c-functions, resting on our prior understanding of what a law is. I don’t much care which – the point is to get the connection. But Goodman wouldn’t think his problem was solved, and he’d be right. Notation: ‘c’ will be either some rational c-function or somebody’s personal c-function, as modified by the background evidence b (so that I don’t have to keep writing b as an argument). So relativity to c henceforth includes relativity to b. You say the proposition I(h) – the truth of h will be investigated – is a dim sort of proposition. Investigated how? I think that can be left up to c. Suppose b guarantees that I(h) can come true in two ways I1(h) and I2(h). (Say, h will be investigated by NASA alone or by USAF alone.) Then for any p c(p, (Ih) & h) = c ( p, I1 (h) & h) c(I1 (h) I,h) + c(p, I2 ,( h) & h)c(I2 (h), I(h)).

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5.  To Richard Jeffrey, 12 March 1967

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But I have a different worry about my use of I(h). What if I(h) is relevant to h? Maybe h is a sociological hypothesis about what sort of questions tend to get investigated! I’m not sure what exactly will go wrong, but I’m fairly sure something will. So I agree that we should relativize to a sequence P of partitionings of b, at least for the time being. But we should keep in mind that the interesting sequences of partitionings are those such that the members of P(n) differ just with respect to the outcomes of the next n stages of some sort of investigation – or with respect to what those outcomes would be if the investigation were done. More notation: ‘L(h)’ for ‘h is a law (relative to P and c)’; ‘LL(h)’ for ‘h is lawlike i (relative to P and c)’; ‘ Pn ’ for ‘the ith member of the nth partitioning in P’; ‘ Pnt ’ for ‘the w true member of the nth partitioning in P’; ‘ Pn ’ for ‘the member of the nth partitioning in P which contains possible world w’. You gave this definition of law: L(h) iff c( h, Pnt ) ® 1 and c ( Pnt+1 , Pnt & h ) ® 1. n

n

In view of the first clause, couldn’t the second clause be simplified to c( Pnt+1 , Pnt ) ® 1? n

Better yet, couldn’t the second clause be dropped altogether? What’s it for? It seems to be descended from my requirement that we consider increments of favorable evidence, but I thought taking the true member of the partitioning was your substitute for taking the favorable one. Which is supposed to approach 1: confirmation of h, instance confirmation of h, or qualified instance confirmation of h? If it is instance or qualified instance confirmation, we can’t handle hypotheses which are not such as to have instances. If it is just confirmation, on the other hand, we’re in trouble with generalizations over finite classes: even an accidental generalization can get confirmation 1 from evidence indicating that the class is exhausted. We also have to be sure that we have one of the c-functions that does sometimes confirm generalizations. Now for lawlikeness. How about LL(h) iff c (L(h), h ) = 1?



This is to say that a lawlike hypothesis is one which is a law if it is true at all, taking ‘if’ as a conditional probability. We get garbage when c(h) = 0, but I’m not sure we need to mind that. What is needed is that h can be lawlike although false, and that we’ve got. I wondered for a while whether L(h) was a legitimate argument for a c-function; but I don’t see why not. It is a set of possible worlds, namely { w : c ( h, Pnw ) ® 1} if you n accept my suggestion to drop the second clause in the definition of L(h).

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An alternative definition of lawlikeness (maybe equivalent to the first, I don’t know) is LL ( h ) iff åc( Pni , h )c( h, Pni ) ® 1. n

i

This is closer to my original proposal. Instead of looking at the confirmation of h in the true member of the nth partitioning, let’s look at the confirmation of h in that member of the nth partitioning which represents the outcome (of n stages of investigation) to be expected if h is true. But there isn’t just one outcome to be expected if h is true; so consider all the outcomes, weighted by their probability if h is true. We can think of the sum

åc(P , h)c( h, P ) i n

i n

i

t

as the expected value of c(h, P n ) – the confirmation of h after n stages of investigation – on condition that h is true. Both definitions of LL(h) can be roughly stated thus: the confirmation of h is expected to approach 1 as investigation continues, on condition that h is true. We might define the degree of lawlikeness of h – DLL(h) – either as c (L(h), h) or as lim å c( Pni , h )c( h, Pni ) n®¥

(maybe the two are equal). Either way, LL(h) iff DLL(h) = 1. My doubts about whether it’s the confirmation or the instance confirmation of h that we are interested in apply also, of course, in dealing with LL(h). I see that we need some special gimmick to deal with a hypothesis like your h1 which is too precise to be confirmable. Since the gimmick may be troublesome, we needn’t have it in the general definition of L(h) and LL(h); rather we can say that an over-precise hypothesis like h1 can be a law (or lawlike) only in a special sense: namely, by being the infinite conjunction of a sequence of laws (or lawlikes). Yours, David i

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6.  To Ann Wilbur, 30 January 1968

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6.  To Ann Wilbur, 30 January 1968 UCLA Los Angeles, CA Dear Ann, I didn’t want to bring this up Monday, since it’s a bit elaborate. I’ve been thinking about subjunctive conditionals; and my theory gives the non-equivalence you want between (1) and (2):

(1) P is causally sufficient (under the circumstances) for Q. (2) Q is causally necessary (under the circumstances) for P.

Let P and Q report events; events which did in fact occur, for I’m not after nonequivalence merely in degenerate cases in which P or Q is false. And let’s understand (1) and (2) both as neutral with respect to the time-order of the events; I’m not a­ fter that kind of non-equivalence either. I trust I’m conforming to your intentions in making the ‘under the circumstances’ explicit. OK on the preliminaries? Now let’s believe in possible worlds, as all right thinking philosophers ought to do. And let’s pretend we have a comparative notion of distance between worlds: we can say that world U is farther from world W than world V is. This distance is a measure of the number, degree, and importance of differences between the worlds, in various respects. Importances of respects will vary like mad with conversational context, hence so will distances; but let’s take any one comparative distance relation. Let’s call a world causally possible iff all the laws of nature prevailing in the actual world hold in it.1 Let’s call a set of possible worlds a sphere around world W iff there is a world U such that for any world V, V is a member of the set iff U is farther from W than V is. The idea is that any world will be surrounded by a lot of nested spheres. Each sphere contains just those worlds which are less than a certain distance from the central world, i.e. similar to the central world to more than a certain degree. The smaller the sphere, the more similarity to the central world is required to belong to it. For any sentence (statement? proposition?) S, we call a sphere S-neutral iff it contains some worlds in which S holds and some worlds in which S doesn’t hold. The minimal S-neutral sphere around world W is that S-neutral sphere around W, no proper subset of which is also an S-neutral sphere around W. It represents the highest standard of similarity to W which you can set without settling the question whether S holds.   Cf. ‘Counterpart Theory and Quantified Modal Logic’ (Lewis 1968, 124).

1

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(Bug: depending on the exact properties of the comparative distance relation, there may not be a minimal S-neutral sphere, just the way there is no such thing as the smallest open real interval on the real line containing 0. A complication of the theory is available to deal with this case, but never mind how.) Now I propose these truth-conditions for (1) and (2) respectively: ( 1*) In every causally possible world in the minimal P-neutral sphere around the actual world, either Q holds or P doesn’t hold. (2*) In every causally possible world in the minimal Q-neutral sphere around the actual world, either Q holds or P doesn’t. Intuitive motivation: (1) is a subjunctive conditional with antecedent P. (2) is a subjunctive conditional with antecedent not-Q: if not-Q were the case, not-P would have been the case. The truth of a subjunctive conditional should depend on the truth of the corresponding material conditional not only in the actual world, but also in other sufficiently near possible worlds. How near is sufficiently near? Set as high a standard of nearness (similarity) as you can without settling the truth-value of the antecedent. So for (1) we need P-neutrality; for its contrapositive (2) we need not-Q-neutrality, which is the same as Q-neutrality. (1*) and (2*) are independent. Subject to our stipulation that P and Q be true at the actual world, we can have (1*) without (2*). This happens if the nearest not-P world to the actual world is nearer than the nearest not-Q world, and the nearest not-Q world is also a P-world. So you can have (1) without (2). Is that the direction of nonequivalence you wanted? You can’t have the converse: P and Q and (2*) entail (1*). Yours, David

7.  To Robert C. Stalnaker, 31 May 1968 UCLA Los Angeles, CA Dear Professor Stalnaker, You and I have proposed very similar theories of conditionals, as I learned from talking to Thomason at Irvine, and from reading ‘A Theory of Conditionals’.1 (Could you please send me pages 9–12? They’re missing in the copy he gave me.) The   (Stalnaker 1968).

1

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7.  To Robert C. Stalnaker, 31 May 1968

17

motivation seems just the same. The only real difference is this: you look for a single nearest antecedent-world, whereas I look for a set of nearest antecedent-worlds. If  the consequent holds in some of them, the might conditional is true; if in all of them, the would conditional is true. If the antecedent is impossible, or holds nowhere near the base world, the set may be empty; so I don’t need the absurd world. I told Thomason I’d send some dittoed notes I prepared for Montague’s sem­ inar; but these turned out to be rather clumsy, and not at all self-contained. So I’ve written a new paper – enclosed.2 I’ve done nothing by way of axiomatizing, or even listing, valid sentences and inferences. Howard Sobel has done a bit; I’ll ask him to send the appendix on counterfactuals from his paper about Lyons on act and rule utilitarianism.3 Lyons’ equivalence thesis turns out to depend on arguments like this: if A disarmed, he alone would disarm and there would be war. The same is true of B, and of C, and of nobody else. So if everybody of whom it is true – viz, A, B, and C – were to disarm, there would be war. So act and rule utilitarianism agree in telling A not to disarm. Sobel noticed that the argument was bad intuitively; and it also turns out bad on my analysis, and doubtless also on yours. But it’s good on a usual analysis. Φ⁄Ψ iff {Laws} ⊨ Φ → Ψ, or iff {Laws & fixed background} ⊨ Φ → Ψ. Montague has worked on defining subjunctive conditionals by means of a combination of tense operators and causal modalities. He tries to measure the distance between two worlds i and j by the interval between the present time t and the latest time tʹ such that i and j were alike up to time tʹ. That is, you think of branching worlds, and see how far back you have to go to find the branch point. (If i and j didn’t start out alike, their distance is infinite, and j will not be in any sphere around i.) This is clear enough, but I don’t think it really yields any intuitive notion of distance between worlds. I would say that distance depends on innumerable similarities and differences between worlds, weighted by their importance – which, of course, will depend like mad on conversational context! Sameness of laws will tend to be an important – but I think not overriding – consideration, which is my explanation of why laws tend to support counterfactuals. I’ll be very interested to hear from you and Thomason about the comparison of our theories. Yours, David Lewis

2  Possibly an early version of ‘Completeness and Decidability of Three Logics of Counterfactual Conditionals’ (Lewis 1971b). 3   (Sobel 1970).

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8.  To Robert C. Stalnaker, 24 June 1968 UCLA Los Angeles, CA Dear Professor Stalnaker: Thank you for the new copy of ‘A Theory of Conditionals’, and for the accompanying technical paper and the paper on conditional probability.1 I think you might do well to send the latter also to Brian Ellis (LaTrobe University, Bundoora, Victoria, Australia); he has shown me a draft of something similar.2 I don’t understand it very well – it’s entirely non-semantic – but he, like you, tries to get subjunctive conditionals out of conditional probabilities, and he showed some recognition when I told him my line. Why don’t I require {s} ∈ Si? I’m not at all sure I don’t want to, but I’m hesitant enough to remain noncommittal. I’m not sure a subjunctive conditional with true antecedent and true irrelevant consequent ought automatically to come out true. It should be true if the consequent is true throughout some sphere around the base world (as in your counterexample to the connection theory), but what if the consequent is false very near the base world? That is, I’m still somewhat inclined to require either that there be a connection, or that the base world be in the interior of the ­consequent. Perhaps I should require {s} ∈ Si, but make another change: ˹Φ⁄Ψ˺ is true at i iff ˹Φ⁄Ψ˺ is true throughout some Φ-neutral sphere around i, where a sphere is Φ-neutral iff it overlaps both ⟦Φ⟧ and ⟦¬Φ⟧. This makes no difference to genuinely counterfactual subjunctive conditionals, since a sphere is Φ-neutral for false Φ iff that sphere overlaps ⟦Φ⟧; but, as desired, truth of Φ and Ψ doesn’t guarantee truth of their conditional. This is not ad hoc; it’s suggested by the theory that ˹Φ⁄Ψ˺ is true iff background ⊨ ˹ Φ ⊃ Ψ˺, background being as strong as it can be and still be Φ-neutral. The background proposition (not necessarily expressible) is taken to be just the smallest Φ-neutral sphere, assuming for convenience that the spheres have the compactness property so there is a smallest. Yours, David Lewis

  ‘Probability and Conditionals’ (Stalnaker 1970).   ‘An Epistemological Concept of Truth’ (Ellis 1969).

1 2

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9.  To Richard Braithwaite, 14 November 1970

19

9.  To Richard Braithwaite, 14 November 1970 St. Catherine’s College Oxford, England Dear Professor Braithwaite, In ‘General Propositions and Causality’,1 Ramsey refers briefly to an unpublished note of 1928 in which he had suggested that laws are ‘consequences of those propositions which we should take as axioms if we knew everything and organized it as simply as possible in a deductive system’. (Foundations of Mathematics, p. 242.) According to an editorial footnote, the 1928 note was not reprinted in Foundations of Mathematics because it was superseded by the later paper ‘General Propositions and Causality’, in which Ramsey rejects his 1928 suggestion. I find Ramsey’s 1928 theory extremely interesting and plausible (more so than the later theory), and so I wonder whether the 1928 note is available anywhere to be read or copied. I would be most grateful if you could tell me what has become of it, and how I might arrange to see it. Sincerely, David Lewis

10.  To F. Jeffry Pelletier, 24 December 1970 Headington Hill Oxford, England Dear Jeff, Here’s the only paper on counterfactuals I can now send: a technical satellite to the main paper.1 The main paper is a big thing – 60 pages of manuscript, with five sections still to be written. In fact, it may turn out to be a very short book rather than a very long paper – if all goes well, in the same series as David Wiggins, Identity & Spatio-Temporal Continuity.2 Though I want to circulate it, I don’t quite see how I can afford to: I don’t here have much free xeroxing, and no free typing or postage. If I do find a way, you’re on the list.   (Ramsey 1931).

1

  ‘Completeness and Decidability of Three Logics of Counterfactual Conditionals’ (Lewis 1971b).   (Wiggins 1967).

1 2

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Philosophical Letters of David K. Lewis

I don’t believe that completeness and decidability theorems contribute very much philosophical understanding; I did them partly for the fun of it, and partly for the sake of those misguided people who think an analysis is interesting only if it does lead to some sort of theorem. [. . .] Yours,

11.  To Richard Braithwaite, 18 January 1971 Headington Hill Oxford, England Dear Professor Braithwaite, I hereby agree to conditions (1)–(3) in your letter of 15 January 1971, regarding the use I may make of my Xerox of Ramsey’s ‘Universals of Law and of Fact’. It seems to me that these conditions are entirely appropriate. Under condition (1), let me now ask your permission to show the paper to my wife, Stephanie R. Lewis; and to J.J.C. Smart. Some years ago, I thought of the theory myself and wrote a letter to Smart about it;1 only last fall did I find the passage in Foundations of Mathematics and learn that the theory had already been proposed by Ramsey. (I would not mail the paper to Smart in Adelaide, but rather take it with me when we go to Adelaide next July.) I don’t now plan to write anything directly about laws; but I will want to accept Ramsey’s 1928 theory of laws as a working hypothesis in the course of my own discussions of counterfactuals and causation. I’m now working on two booklength manuscripts: one called Counterfactuals, and one called Paradoxes of Time Travel. In both places, I shall at least mention the unpublished 1928 paper (in the form specified in your condition (2)), but I probably will not want to quote it, since there is a very good concise statement of the 1928 theory available in the paper published in Foundations, and I can quote that and supplement it with a statement of the theory in my own words. I think, though, that it is highly desirable that part of Ramsey’s 1928 paper should be published. It’s a good theory, and Ramsey should have the credit for it. Now that I know that it was Ramsey’s idea first, I will not write a paper setting forth the theory – not even with due credit to Ramsey’s anticipation – though I will men  Letter 427. To J.J.C. Smart, 17 October 1967, Volume 2: Part 4: Mind.

1

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12.  To Lennart Åqvist, 9 March 1971

21

tion the theory, as Ramsey’s, in writing about related topics. I think it would be wrong to let Ramsey’s 1928 paper be published without remarking that he gave up the theory later, since that would misrepresent his final views; but I think there would be nothing wrong with publishing part of the 1928 paper together with a note mentioning that he did change his mind, saying why he did, and referring the reader to Foundations for his later theory. As you say, the first half duplicates what is in the paper published in Foundations – though I would say that his own theory begins not in para. 11 but in para. 8, and that paras. 11–17 are not a self-contained unit as paras. 8–17 are. I urge you, therefore, to consider submitting paras. 8–17, plus an explanatory note, to a journal (provided, of course, that Lettice Ramsey would permit it).2 Thank you very much for your hospitality. We’ll surely see you again this year: probably at Cambridge in better sight-seeing weather, and probably also in London when you give your paper on belief and preference. Sincerely, David

12.  To Lennart Åqvist, 9 March 1971 Headington Hill Oxford, England Dear Åqvist, I set out to write to Bengt Hansson about the parallels between my semantics of counterfactuals and his way of doing conditional deontic logics (as in Noûs 1969)1 and before I was done the letter grew into the enclosed.2 I wonder what you and he have been doing along these lines; something in a duplicated paper Chellas sent me (dated 31 October 1970) seems to imply that Chellas knows of something.3 For that matter, I’d quite like to know more about what Chellas is up to! The British postal strike has left me isolated from my fellow-counterfactualists from mid-January until yesterday.

2   ‘Universals of Law and of Fact’, first published (Ramsey 1978) and reprinted (Ramsey 1990). A  copy of the original handwritten manuscript can be found at: http://www.dspace.cam.ac.uk/handle/ 1810/194721.

  ‘An Analysis of Some Deontic Logics’ (Hansson 1969).   Presumably, ‘Section 5.1 Conditional Obligation’, Counterfactuals (1973b, 96–104). 3   ‘Basic Conditional Logic’ (Chellas 1975). 1 2

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Philosophical Letters of David K. Lewis

I’ve become a bit interested in betterness. In the enclosed paper there is something about maximax betterness: P better than Q iff some P-world is better than any Q-world.4 But that’s a peculiar sort of betterness: in terms of your example, whiskeyor-cyanide is no worse than whiskey. I’ve tried also to use counterfactuals (or rather, the machinery built for counterfactuals) to define ceteris paribus intrinsic betterness. Like this: let P and Q be non-overlapping, nonempty sets of worlds, and let a betterness relation among worlds be given. P is better than Q (from the point of view of P) iff, for any P-world i, i is better than any Q-world j that is one of the closest Q-worlds to i. P is better than Q (from the point of view of Q) iff, for any Q-world j, j is worse than any P-world i that is one of the closest P-worlds to j. P is better than Q iff P is better than Q both from the point of view of P and from the point of view of Q. All this seems intuitive and nice, but there comes a nasty surprise: there’s no reason that

4  ‘Section 8.1 Intrinsic Betterness’, excised from Counterfactuals (David Lewis Papers, C1520, Counterfactuals, Partial Drafts, 1970–1, Box B-000692 Folder 4, Princeton University Library). Cf. Letter 678. To Frank Jackson, 16 December 1982, Volume 2: Part 6: Epistemology.

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13.  To Risto Hilpinen, 16 March 1971

23

betterness so defined should be transitive! Even if we rashly assume that similaritydistance between worlds has all the nice properties of spatial distance, still there’s no reason that betterness should be transitive. There’s no reason that a closest R-world to a closest Q-world to a P-world i should be a closest R-world to i – just as there’s no reason why the closest point in Sweden to the closest point in Norway to Oxford should also be the closest point in Sweden to Oxford. Which leads me to a different subject: there’s some chance that Steffi and I may be traveling in Sweden again in April (or possibly late March). It depends whether a certain lecturing invitation that was left in an extremely vague state before the postal strike can be revived so that I can earn our passage. In case this does work out, we probably will come through Uppsala at some point. If so, we’ll hope to see you and the Kangers. When are you there? I presume you have a spring vacation, but I have no notion when it is. Yours, David Lewis

13.  To Risto Hilpinen, 16 March 1971 Headington Hill Oxford, England Dear Hilpinen, Your letter of 30 January got stuck in the British postal strike and arrived only this morning. I’m glad to hear that you agree that we may hope to regulate the relative biases in favor of Ct-simplicity and Q-simplicity otherwise than by means of the new kind of parameter τ. You are welcome to describe or quote my letter of 12 January, on one condition: that you are satisfied that what I said there was sensible. I wrote hastily, and without reassurance from you I would not be quite sure I did not make some silly mistake. I am working now on a short book about counterfactuals.1 The idea is this: suppose we have a notion of comparative similarity of worlds, so that we can say that a world j is closer than another world k to a third world i (e.g. our world). Then a ‘would’ counterfactual is true at i iff the consequent is true in all the closest antecedent-worlds to i. Like Stalnaker-Thomason, only without the implausible stipulation that there is   Counterfactuals (Lewis 1973b).

1

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Philosophical Letters of David K. Lewis

to be exactly one closest antecedent-world. (The truth conditions are actually somewhat more complicated than I said, in order to deal with the case in which no ante­ cedent world is closest to i because for each one there are others still closer.) Mostly I’m concerned only with counterfactuals de dicto (that is, no quantifying in), but there’s to be one section on counterfactuals de re. I’ve therefore been rereading your paper on the relativised modalities, especially the part about New York City in Georgia. I shall want to do something similar, but to make it more a matter of degree. If the two counterfactuals about New York City in Georgia were de dicto, I’d be sunk: equivalent antecedents are interchangeable salva veritate. My only hope would be to deny the apparent fact that there is a difference. So what I think I will do is to take them as de re, using counterpart theory with a more and a less stringent counterpart relation. Also, I’m inclined to think that closeness of antecedent-worlds might trade off a bit with closeness of counterpart relations. So here’s the plan (obviously, I’m stating a simplified version for this case, not a general version). Combine the assignment of values to variables and the possible world into a single entity called an index. (As in my ‘General Semantics’,2 but with fewer co­ord­in­ ates for the case at hand.) An index is thus a triple where i is a possible world, a is a thing, b is a thing. A formula (with no free variables other than ‘x’ and ‘y’) is true at an index iff, roughly, it is true at the world i when ‘x’ is taken to denote a and ‘y’ is taken to denote b. Just as I originally had a comparative similarity relation for worlds, so now I have a comparative similarity relation for indices. Let us consider only indices such that a and b are things that exist at the world i; this means, in my opinion, that they exist at i and nowhere else. (I don’t believe in trans-world identities, at least for particulars: rather, the inhabitants of one world are related by similarity to their counterparts in other worlds.) The overall similarity of two indices and is a weighted average of the overall similarity of i to j, the overall similarity of a to c, and the overall similarity of b to d; but the similarity of a to c is to be weighted more heavily than the similarity of b to d. Thus and are close to the extent that (1) the worlds i and j are similar, (2) c is a close counterpart in j of a, and (3) d is a perhaps-not-so-close counterpart in j of b. A counterfactual is true at an index iff the consequent is true at all the closest indices to where the ante­ cedent is true. An existential quantification ∃xΦ is true at iff for some e, that exists at i, Φ is true at ; an existential quantification ∃yΦ is true at iff for some e that exists at i, Φ is true at . Now I say that the counterfactuals about New York City in Georgia will come out right if they are taken to be   (Lewis 1970b).

2

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14.  To John G. Bennett, 19 March 1971

25

∃x∃y(x = New York City & y = Georgia &     (if x were in y, then y would not be entirely in the South)). ∃x∃y(y = New York City & x = Georgia &     (if y were in x, then y would be in the South)). The last sentence of your ‘Relativised Modalities’3 speaks of applications to be discussed in greater detail elsewhere. If this discussion elsewhere is not also located elsewhen, I’d like very much to see it. Yours,   David Lewis

14.  To John G. Bennett, 19 March 1971 Headington Hill Oxford, England Dear John, We got the sad news about Richard1 from Hans Kamp, who telephoned from Amsterdam, and since also by letter from Monty.2 We were very upset, partly by the fact of murder, but mostly because we had come to like him very much. I fear it may have seemed otherwise when I spoke of his part in department affairs; but he was kind to us, and we enjoyed his company, and of course he taught me a significant part of whatever I know about philosophy. We shall miss him very much. If Monty is taking the responsibility of telling people what has happened, he may wish to know that the following have heard through us, directly or indirectly: Wilfrid Hodges, Robin Gandy, Michael Dummett, Kit Fine, Mary Prior, Richard Wasserstrom. [. . .] [. . .] you will soon be the lucky recipient of several xeroxed pages of guff about counterfactuals, truth in fiction, and intrinsic betterness – sections from something I’ve been writing called Counterfactuals, overgrown paper turning into undersized book. These pages of guff are jointly for you and Warren,3 since half of it developed out of conversations with you and half out of conversations with him. Comments will be most welcome, but are absolutely not demanded.

  (Hilpinen 1969).

3

  Richard Montague, who was murdered 7 March 1971.   Montgomery Furth (1933–91), formerly Professor of UCLA.   

1 2

  Warren Quinn.

3

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Philosophical Letters of David K. Lewis

We continue to flourish. Oxford is a perfect place to live – the right size, small enough so that we know our way around better than we ever did in LA, big enough so there’s no prospect of exhausting it. Much beauty even in winter, which everyone agrees is nothing compared to what it will be in spring. Oxford is a little bit past it in general philosophy, but Dummett and Kenny are still major attractions; also two young guys, Derek Parfit and a logician Kit Fine; also all the visitors. And it’s very good for Steffi in  philosophy of law; probably no place better. She’s had a very exciting year; thesis advances, as does general education in philosophy of law, and philosophy otherwise. Oxford has three short terms, with 6-week vacations between. The Easter vacation has just begun. I find we’ve allocated it twice over: another week or two here to finish Counterfactuals, a week in London would be nice, two weeks using our British Rail passes in Wales and Scotland (if the railstrike that threatens doesn’t happen), a week or two driving in Scotland, and two or three weeks in Scandinavia! The Scotland part is the least expendable. Various abbreviations of the Scandinavia are possible, e.g. ship from Newcastle to Bergen, train to Oslo, 2–3 days there, and fly back. Planning impossible: thanks to the British postal strike, I haven’t heard from the Scandinavian universities that were maybe going to pay our fare in return for learning the truth about counterfactuals. Planning impossible also thanks to uncertainties about British Rail, and uncertainties about how hard I can make myself work on the counterfactuals. I should not, e.g., be procrastinating by writing this letter, and anyway the sheet’s almost used up, so best wishes,

15.  To Frank Vlach, 21 March 1971 Headington Hill Oxford, England Dear Frank, I must first tell you the sad news that Richard Montague has been murdered. Two weeks ago, at his house, by an unknown person (or, there’s some reason to believe, persons), for unknown motive. No point speculating. We have been very upset, not only by the fact of murder, but because Richard had gradually become a good friend. He was kind to us, and we enjoyed his company, to say nothing of the

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15.  To Frank Vlach, 21 March 1971

27

fact that he taught me a lot about philosophy. We had the news first from Hans Kamp, by phone from Amsterdam, and soon after in a letter from Furth. My counterfactuals, which you’ll recall from Richard’s seminar in 1967, have grown this year first into an over-grown paper and then into an undersized book. Enclosed is a fragment thereof, more or less self-contained, which I send to you because it’s a new use of ideas from your dissertation.1 That was almost done when I left UCLA, as I recall; I trust it’s now all done, except for problems of a trans-Pacific final oral and signing ceremony perhaps. Can you give me a reference for the footnote? Preferably to a paper rather than the dissertation itself: I hereby urge you to write up the main idea (with or without the formal trimmings) as a paper for some such journal as Noûs, Theoria, or Journal of Philosophical Logic (a new thing being launched soon by Bas van Fraassen and his friends). You probably know that I’ve left UCLA for Princeton, and am now on first-year leave from there. We’re having a fine time in Oxford. I’m working on Counterfactuals and on The Paradoxes of Time Travel and going to miscellaneous lectures; Steffi’s studying philosophy of law (there called jurisprudence and going strong) and writing her UCLA dissertation therein. We’ll soon be traveling for a few weeks (Old North Wales, Scotland, maybe Norway); back at the above address approx. 25 April–15 June; and in Australia throughout July and August. We’ll be briefly in Sydney when we first arrive, 29–30 June; staying with Armstrong, who will know our plans. Mostly we’ll be in Adelaide, where I’m to lecture on time travel; but as much other (spatial) travel as possible, including more Sydney (under the auspices of Armstrong, again) on approx. 27–30 July, and including the A.A.P. So I trust we’ll see you soon; I certainly hope so. Our best to Karen. Sincerely yours, David Lewis

  (Vlach 1973).

1

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16.  To John G. Bennett, 12 May 1971 Headington Hill Oxford, England Dear John, Thank you very much indeed for your very helpful comments on my stuff about intrinsic betterness1 and truth in fiction.2 I’m afraid I’ve been slow to get around to working on it; I was traveling, and when I got back I was incapacitated for a couple of weeks by a virus. Recovered now, and getting back to work. Let me comment on your comments – I’ll assume you’ve kept a copy. If we had a clear notion of a priori probability, it would be good for lots of things, and in particular it would be good for going from values of worlds to intrinsic values of propositions. But what is a priori probability? This: the degree of belief that any perfectly rational agent would have prior to all experience (so that his subsequent degrees of belief could be explained as produced by conditionalization from the a priori probabilities and his history of experience (= total evidence)). Now it’s one hell of an idealization to think of an agent as having degrees of belief at all, let alone as being perfectly rational, prior to all experience. But let that pass. Why on earth should there be only one probability measure that any such superbaby could have? So I didn’t even consider this suggestion worth discussing. Right you are: ⁄ is the counterfactual conditional connective, to be read (subject to some qualifications) as ‘if it were the case that . . . then it would be the case that___’. Warren’s counterexample seems to me a serious objection to my account of intrinsic betterness. No misunderstanding. I have no good answer. I’m inclined to say: let i be a world where Jones is happy to degree 5 and the envious King is present; let j be the closest world where Jones is happy to degree 10 and the envious King therefore kills him, so that j is worse than i; and let k be the closest world where Jones is happy to degree 10 and (as in i) the envious King nevertheless does not kill him, so that k is better than i. Then k is closer to i than j, so no problem. The similarity of k to i in respect of Jones not being killed outweighs the similarity of j to i in respect of the regularities pertaining to the behavior and character of the king. If I say all that, I’m out of trouble as far as intrinsic betterness goes; but that goes against what I want to say otherwise. For I want to say that 1  ‘Section 8.1 Intrinsic Betterness’, excised from Counterfactuals (David Lewis Papers, C1520, Counterfactuals, Partial Drafts, 1970–1, Box B-000692 Folder 4, Princeton University Library). 2   ‘Section 8.2 Truth in Fiction’, which was also left out of Counterfactuals, but developed into (Lewis 1978).

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16.  To John G. Bennett, 12 May 1971

29

(*) Jones were 10 units happy ⁄ the King kills him is true at i, and in order to have (*) true at i, I have to have j closer to i than k. You ask for examples of the failure of transitivity; I’d give some if I could, but I don’t have any. What I suspected was that there is some condition which generally holds which prevents such cases from arising; but I couldn’t think what that condition would be. In the light of Warren’s counterexample, though, I think that maybe the reason I can’t illustrate failure of transitivity by examples is just that the analysis of ceteris paribus betterness is all wrong. I’m discouraged with it, and may scrap the section. I don’t know Pale Fire,3 your example of a fiction in which part of what is written is not really part of the told story, let alone true-in-the-story. But if I understand from you what the problem is, then I think I would incline to do what you suggest: ‘regard the whole thing as being in quotation marks and asserted by one of the characters’. I think perhaps we should start with the easy cases of truth in fiction: those where there are no tricks (like first-person narration by a madman) and so it’s a routine matter to go from the fiction to the sentential paraphrase. There is a problem of truth in fiction for such fictions; that’s the problem I purport to solve. You hope that a theory of truth in fiction that will work in that case will already be adequate to deal with cases like Pale Fire; I don’t share that hope, and think that there are two distinct levels of difficulty. Wouldn’t you distinguish two tasks: 1) Recount the plot of Pale Fire in a literal, straightforward way. 2) Say whether things are true in the world(s) of Pale Fire. I would allow that maybe there are fictions for which the first task cannot be carried out; if so, the second cannot either. I agree with you that if we don’t buy the concept of truth in fiction on which unknown or little-known facts about the actual world are relevant to truth in fiction (and don’t buy your second, audience-relative one, which I find implausible), then we want to give the author a special place. The author should not be allowed to be an exceptional member of the ‘community of origin’: one who does not share the beliefs otherwise overt in it, or one who does not share the others’ general ascriptions of these beliefs to one another. It might be better if, where I speak of beliefs overt in the community of origin, I spoke instead of beliefs overt between the author and the community of origin, this being defined in the obvious way. Or perhaps it is enough to say that the exceptional members of the community of origin are not really members of it at all (cf. Convention, p. 77, first two lines),4 and say that the author must not

 (Nabokov 1962).   4  (Lewis 1969).

3

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be thus excluded. (If the author is suitably alienated, I suppose the community of origin would then consist of the author alone. I guess that’s OK.) I don’t want to misrepresent Beardsley, but I do want to discuss exactly the view set forth on 8.2.19.5 I think the thing to do is to discuss this view not as Beardsley’s, but as that of a straw man: I’ll call him ‘the purist’. Yours, David

17.  To Dagfinn Føllesdal, 1 April 1971 Headington Hill Oxford, England Dear Føllesdal, Since I wrote you on 9 March, our plans for coming to Scandinavia this month have become definite: it will be a brief visit to Uppsala, returning to Oxford by way of Oslo, Bergen, and Newcastle. I hope we’ll see you in Oslo. We leave Oxford on 17 April, going first to Amsterdam and then to Uppsala, where I do my stuff on counterfactuals. We reach Oslo most probably on 21 April (by the ‘Norgepilen’ arriving 13:50), but possibly a day later if it proves convenient to stay longer at Uppsala. We leave on 23 April (by train to Bergen departing 10:00). I tried to telephone to see whether you would be in Oslo at the time, but you were away when I telephoned. We’ll be out of communication for the next two weeks – leaving tomorrow for Scotland – but we’ll be back through Oxford to look at our mail on 16 April, the day before we leave for Europe. I’ve just turned Counterfactuals over to a possible publisher, Blackwell’s, after working harder for a longer stretch to finish it than I have since the last days (and nights) of my dissertation – if then. From a paper it became an undersized book, and now a middle-sized book. There’s actually some more work to be done on the logic chapter: the present chapter is a paper I wrote last fall, and I can do things much better now. But at least there’s a manuscript which goes from beginning to end! I decided to finish at all costs before going away on vacation, and that got it finished (at the expense of almost two weeks of our vacation, though). See you in Oslo in three weeks, we hope. Yours,   Section 8.2.19 of manuscript of Counterfactuals.

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18.  To Robert C. Stalnaker, 11 May 1971

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18.  To Robert C. Stalnaker, 11 May 1971 Headington Hill Oxford, England Dear Bob, Thank you for your letter commenting on my chapter comparing my theory of counterfactuals and yours;1 I’m glad you think it will do. I wish I could send you the whole business, but (since I’ve never bestirred myself to get money from the NSF) xerox and postage are prohibitively expensive – it’s 385 pages. I don’t believe the following three sentences are consistent, as you say they are: 1) If HHH had been elected, he might have appointed Fulbright. 2) "   "   he would have appointed Ball. 3) "   "   he would not have appointed both. Maybe my intuitions have been corrupted by my theory so that I’m no longer a fit judge, but I don’t think so. However, I think I can explain why 1), 2), 3) seem to you consistent: 1), 2ʹ), 3) are consistent and, speaking loosely, 2ʹ) could be expressed by 2). 2ʹ) If HHH had been elected, he would probably have appointed Ball. I take 2ʹ) as meaning roughly this: in most of the closest HHH-worlds to ours, he appointed Ball. ‘Most’ can’t be understood in terms of cardinality – I think we’ll have the same infinite cardinality of closest HHH-worlds with Ball and without – but rather in terms of some sort of probability measure. Here employ your favorite concept of probability. I’ve thought about this using a different example. I put my watch in front of the Geiger counter, and nothing happens. I say, somewhat carelessly 4) If there’d been radium on the dial, the counter would have clicked. But someone reminds me that you never really know with radioactivity. The radium could just sit without radiating, or it could radiate away from the counter, or . . . . I therefore say that by 4) I really meant 4ʹ ), and grant that also 5): 4ʹ) If . . ., the counter would very probably have clicked. 5) If . . ., the counter might not have clicked.

  Chapter 3 of Counterfactuals (1973b; see esp. 77–83).

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I agree that the might-counterfactual can be paraphrased by a wouldcounterfactual with ‘maybe’ prefixed or inserted. I would have to claim that these paraphrases are deceptive: they don’t really involve the would-counterfactual connective at all. But I don’t much mind saying that, because it’s parallel to what I already must  say about would-probably-counterfactuals; these seem to be, but are not, ­compounds involving the ordinary would-counterfactual and a 1-place operator ‘probably’. Granted that there might be contexts that would break the tie in closeness between the closest Bizet-Italian-worlds and the closest Verdi-French-worlds; and then, for all I know, you could pick a unique closest Bizet-and-Verdi-compatriotsworld. But set aside such tie-breaking contexts; then what? You say you don’t have to be able to choose. How can that be? You must be speaking here not from the point of view of the selection-function theory itself, but rather from the point of view of some more complicated and realistic theory: a theory of the determination or underdetermination (as the case may be) of the selection-function by context. It seems to me that in the letter you’re favoring a theory like the ‘half-way house’ theory I expound on 4.4.11–14. That is: selection functions select unique worlds; however, a given context may under-determine the selection function, and therefore a counterfactual may come out indeterminate in truth-value because some of the selection functions permitted by the context make it come out true and others make it come out false. I spoke of underdetermination of the selection function by comparative similarity, rather than underdetermination of it by context; but that’s no real difference, because (as I say elsewhere) I take it that the influence of context is to change the relative importances of respects of similarity and thereby change the comparative similarity of worlds. Instead of a cluster of total selection functions, you might prefer a single partial selection function, undefined for some arguments; but again, there’s no real difference, since 1) the partial selection function is obtained from the many total selection functions by considering only the cases in which they agree, and in the other direction 2) the total selection functions are obtained from the partial selection function by extending it in all admissible ways. Yours, David Lewis

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19.  To Peter Woodruff, 18 May 1971

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19.  To Peter Woodruff, 18 May 1971 Headington Hill Oxford, England Dear Peter, I’m sending you the section on selection functions from my Counterfactuals manuscript. It’s not perfectly self-contained, but I think that you’ll easily gather what goes on in the other parts referred to, since you have the Theoria paper.1 I mentioned in my letter that the axiomatization could be simplified; you’ll see from the conditions of standardness on 2.6.2.1 how the simplified axioms would go in a ⁄-primitive formulation of C1. I’ve put in a reference to you and Vickers on 2.6.2; but tell me whether you and he approve of it. I have a problem: there are some who think that the distribution of duplicated stuff is tantamount to publication, and there are some who think that the fundamental purpose of bibliographical references is to make sure that credit goes where it is due and the record of priorities is kept straight. There are others who think that a man should not be saddled with responsibility for ephemeral material that he has not yet chosen to publish, or who think that the main point of bibliographical references is to direct one’s readers to works they can get hold of and ought to read. I have no strong views; I’m glad to comply with the wishes of those of either persuasion, but I have to know what your preferences are. I don’t think of my counterfactuals as weak implications but rather as strong ones; I call them ‘variably strict conditionals’, thinking of them as varying in a range between material conditionals and (logical) strict conditionals. A counterfactual is as strict as it must be to escape vacuity (impossibility of the antecedent) and no stricter. I know you can get a weak conditional by not imposing conditions on the selection function; this is exactly equivalent to having a family of sententially or propositionally indexed accessibility relations. Brian Chellas has studied this; there’s a reference in my stuff to his duplicated paper.2 It was suggested in 1967 by Montague and recently by Kit Fine that my systems of spheres ($-systems) looked like neighborhood systems in topology. I think this is not a good idea. In topology, you’re interested in a concept of distance that is not only non-quantitative but also non-comparative. Is j right next to i (= in every neighborhood of i) or is it some distance away? Topological neighborhood systems don’t distinguish more and less distant among points that are some distance away from i.   ‘Completeness and Decidability of Three Logics of Counterfactual Conditionals’ (Lewis 1971b).   ‘Basic Conditional Logic’ (Chellas 1975).

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Formally, this is because any superset of a neighborhood of i is a neighborhood of i; so if j and k are some distance from i, then always there is a neighborhood that reaches j but not k and another that reaches k but not j. My requirement of nesting of each $1 is what makes my systems more than topological – what gives me comparative, not only qualitative, distance. I have hitherto taken no interest whatever in Pittsburgh entailment. It may be that I will have to change my mind when I hear what Meyer has done. (Also I hear that Dana has done interesting work on entailment this year; but though I’ve read some duplicated ephemera of his, I haven’t grasped the intuitive idea.) But I have yet to find out whether Meyer’s semantics answers my intuitions about entailment (as Kripke semantics does for strict implication) or whether it only works technically. I don’t know what you’re referring to as Dana’s ‘three-place causal relation’; I look forward to finding out. My own tentative view, expounded in a section of Counterfactuals, is that if c and e are two events such that e occurred after c occurred, then c is a cause of e iff c did not occur ⁄ e did not occur. This makes for trouble, how serious I don’t know, about overdetermination. Sometimes I’ve thought that we wanted explanatory connectives like ‘___ rather than _ _ because . . .’ where commonly, but not always, the second argument would be the negation of the first. I’ve never worked this out. I have a new, rather non-technical piece on counterpart theory in a recent JΦ.3 Sorry I can’t enclose an offprint; I won’t be able to get at my offprints until I reach Princeton in September. The original version of counterpart theory looks rather artificial and complicated; Dana complains of this in ‘Advice . . .’.4 Here’s a way to make it less so, with no real change. (1) As in my ‘General Semantics’ (latest Synthese)5 the assignment of values to variables is included as a coordinate of the indices, along with the world, time, speaker and so on. Let’s forget time, speaker and so on; an index is then a pair of a world and an infinite sequence of possible individuals. (2) Fundamental semantic relation is truth of a formula at an index. The formula may have free variables; so this is what you might also call satisfaction of the formula by the assignment-­ coordinate of an index at the world-coordinate of the same index. (3) Accessibility of worlds and counterpart relations among things are lumped together into accessibility of indices. Index is to be accessible from index iff wʹ is accessible from w and aʹ is a counterpart in wʹ of a and bʹ is a counterpart in wʹ of b and so on. (4) □Φ is true at an index iff Φ is true at every index accessible from that index.   ‘Counterparts of Persons and Their Bodies’ (Lewis 1971c).   ‘Advice on Modal Logic’ (Scott 1970).    5  (Lewis 1970b).

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20.  To Peter Woodruff, 2 June 1971

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It’s been unpopular that because of the possibility that one thing might have two counterparts, it comes out that in counterpart theory you don’t get equivalent translations for Φ(x, x) and for x = y & Φ(x, y), Φ being a formula that has occurrences of its variables inside a modal operator. Most simply: ◇x ≠ x is, but x = y & x ≠ y isn’t, a contradiction. If you dislike this (which I don’t especially), change (3) above so that any identities among the terms of the assignment-coordinate of an index reappear in all indices accessible from it. For instance, let a = b. Then is ac­cess­ ible from only if in addition to the conditions above, also aʹ = bʹ. [. . .] Best, David

20.  To Peter Woodruff, 2 June 1971 Headington Hill Oxford, England Dear Peter, In my last letter I think I said this address was good until 19 July. Not so: until 19 June. Anything sent here after that will be forwarded at least twice. Glad the footnote is OK with both you and Vickers. Thank you for his 1968 circular letter on the subject. Yes: certainly we could have a sequence-of-sets-selection function, giving the sequence of diminishing nonempty members of {⟦Φ⟧ ∩ S: S ∈ $i}. Seems to me not very well motivated, though; doesn’t have the simplicity of the set-selection function, nor the close connection with the underlying comparative similarity relation of the beta- or gamma-semantics. The idea of treating assignments in the same way as worlds, times, ­speakers, . . . goes back to Montague, ‘Logical Necessity, Physical Necessity, Ethics, and Quantifiers’, Inquiry 3 (1960): 259–269.1 However, he there treats alternative interpretations also in a parallel way, something he wouldn’t have wanted to defend later. Assignments are treated parallel with worlds as coordinates of indices also in some of Montague’s recent work – for instance, the version of ‘Universal Grammar’ that will appear in the Prior memorial issue of Theoria.2

 (Montague 1960).   2  (Montague 1970).

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I’m unfamiliar with uniform spaces; however, I remember that Montague also made a connection between them and something like my counterfactuals. It went like this (I’m more or less copying from duplicated material dated 19 November 1967 from Montague’s seminar; I rewrite to make it self-contained). is a similarity space iff 1) Ɛ is a nonempty set of reflexive and symmetric relations having I as field, 2) ∀R, S ∈ Ɛ  R ∩ S ∈ Ɛ, 3) ∀R ∈ Ɛ  ∃S ∈ Ɛ  S|S ⊆ R. Remark: If is a similarity space and ℑ = {R: ∃S ∈ Ɛ S ⊆ R ⊆ I × I} then is a uniform*3 space; and if is a uniform space and Ɛ = {R ∈ ℑ: R is symmetric} then is a similarity space.

Intuition: each R ∈ Ɛ is a relation of similarity in respect of a certain feature. An interpretation over a set of worlds I of language ℒ is 24-standard iff ∃Ɛ such that 1) is a similarity space, 2) ⊨i Φ ⁄ Ψ iff   3) ⊨i Φ ¡ Ψ iff ∀i Φ ⁄ ¬Ψ ∃R ∈ Ɛ ∃j ∈ ⟦Φ⟧jRi  ⊃ ∃R ∈ Ɛ ∃j ∈ ⟦Φ⟧(jRi & ∀k ∈ ⟦Φ⟧(kRi ⊃ k ∈ ⟦Ψ⟧))

Intuitively: either (1) no Φ-world is similar to i in any respect, or (2) there is a respect R such that some Φ-world is similar to i in respect R, and such that Ψ holds at all Φ-worlds similar to i in respect R. Yours, David

21.  To Ken Kress, 7 November 1972 [Princeton, NJ] Dear Ken, Many thanks for the port! Very good, and not easy to come by here. Such things are among the amenities of California that we miss. I have heard that Einstein’s Straus is the UCLA Straus; but it’s possible that my source didn’t really know. * 

In sense of Kelley p. 176   

  General Topology (Kelley 1955, 176).

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21.  To Ken Kress, 7 November 1972

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I only know from rumor what’s in Ayn Rand; but if my impressions are right, there’s something better on the market that appeals to the same inclinations. See if you can get hold of one of the many prepublication copies of Robert Nozick, Anarchy, The State and Utopia and try your brother – for that matter, yourself – on that. It’s wild stuff. Very clever. I think he gets away with some arguments that could be stopped, however. We’re much the same. Steffi is teaching half-time at Princeton this year; supervising some junior and senior independent studies and teaching some sections in the spring. Nice while it lasts, but it is only for the year. The long run depends on the dissertation, of course. I’m teaching beginning logic out of Jeffrey, as often before at UCLA – boring, since I can’t think of new ways to improve the course. The only fun would be the honors precepts – extra topics for those who find the main material too easy to be interesting – and I foolishly gave those away to my assistants. Just as well though, in view of shortage of time. I’m also teaching a course on time travel, which is great fun. Really it’s a pretext for a survey course in metaphysics – except for God and mindbody, all the standard topics turn up. You heard the whole business in its early stages; it has since been my lecture series in Adelaide, and should someday be a book. Not that I’m writing that book, or any other. Since I sent the final version of Counterfactuals to the publisher in July, I haven’t been able to write much of anything. Maybe the struggle to finish Counterfactuals in time – late nights for weeks on end – was enough negative reinforcement for trying to write that I now know better than to do so! Can’t escape it though: I’ve set lots of deadlines for myself in the next few months. It’s bad to have more-or-less-done things to polish or rewrite, rather than new things to start! The biggest thing in the works will be a paper on causation, to the effect that c causes e iff if c had not occurred e would not have, or something similar. (In view of problems about a cause that preempts what would otherwise have caused the same effect, though, I think maybe the thing to do is to take the ancestral of the relation just defined.) I really want this paper to be good, and want to get it off my back, because it’s my oldest piece of unfinished business: it began as a Phil. 1 term paper at Swarthmore in 1958!1 This has been a very busy term. Heavy teaching (though not by the standards of most of the world); lots of miscellaneous work. Many of my friends (and others) are giving me as a reference for promotions to tenure; I’ve been writing one difficult letter after another trying to be favorable, convincing (too favorable isn’t convincing), informative and even truthful. Thanks to our election break (so that those who wish can go out and campaign), and no thanks to a long cold, I’m almost caught up. There remain a batch of time travel term papers and some reading matter from Barbara’s 1   David Lewis. 1958. ‘On Causality and Natural Laws’. Swarthmore College, Papers; 1957–62; David Lewis Papers, C1520, Box B-000696 Folder 3, Princeton University Library.

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seminar on Montague. (Time travel term papers have nice titles: ‘To Be or Not Two Beings’, on personal identity, is best.) I disbelieve two things. First: that your choice of a profession will have much influence one way or the other on the improvement of your character. Second: that any alternative, seen from close up, will be much of an improvement on academic philosophy, seen from close up. Yours,

22.  To Bas van Fraassen, 28 March 1973 [Princeton, NJ] Dear Bas, I’m surprised and distressed by the tone you detect in my final footnote on page 83 of Counterfactuals – it is very far from my intention to suggest that ‘it is not possible to say of an opponent that his theory contains a “core of truth”, or that it might not be correct to say that, although one’s opponent gives an incorrect account of the phenomena, the phenomena are real and need an account’. I can’t detect this bad tone; if you can, that means that I’ve done very badly in putting my thoughts on paper. Indeed, who are supposed to be my ‘opponents’ here? Certainly not Stalnaker and Thomason, either when they put forth their theory in its original version or when they suggested using supervaluations to permit ties in closeness! Still less someone – you, or the then-hypothetical theorist I mentioned in the footnote – who brings the Stalnaker-plus-supervaluations theory even closer to mine by adding a truth predicate to define my ‘would’ and ‘might’. I take it that all of us agree on very much more than a ‘core’; we should rather speak of mere fringes of disagreement (on the Limit Assumption, the ‘might’ counterfactual, and Conditional Excluded Middle). On a more pleasant topic: I haven’t yet really thought through the reason why probabilities of conditionals equal the conditional probabilities in causal cases, if not in general, but I certainly agree with you that the key has to do with independence between the conditional – or something else – and the antecedent. In many cases, at least, what we have is as follows. Some precondition B is independent of A; necessarily (or, throughout a set of worlds of probability close to 1) we have a counterfactual – hence causal, in my view – dependence of C on A iff B. A: I look in my wallet for a penny. B: there is a penny there. C: I find a penny. A ⁄ C holds iff B, except in

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23.  To Jaegwon Kim, 11 August 1973

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bizarre worlds with negligible probability. Also ABC holds iff AB, and iff AC. Then P(A ⁄ C) and P(C/A) are equal because both equal P(B). But how many of the cases are like this? Yours, David Lewis

23.  To Jaegwon Kim, 11 August 1973 as from: Princeton University Princeton, NJ [Oxford, England] Dear Jaegwon, Thank you for your comments. Although I have revised the paper1 to meet Alston’s length limits, nothing in your comments is obsolete except for a little bit of notation and terminology, as follows. I now speak of ‘nomic’ rather than ‘deductive-nomological’ dependence; and I speak of it as holding in virtue of premise-sets ℒ and ℱ (respectively of true lawpropositions and true particular-fact propositions) rather than in virtue of the argument 𝔇 that has those premises. Also I refer to a family now by a list A1, A2, . . . (without corner-brackets) and I refer to it for short as ‘the A’s’. You’ll get my revised version and see what I mean. Your counterexamples will make for an interesting discussion, closely related to several recent discussions of individuation of events. My reply will probably be that in each case we do have counterfactual dependence that is not causal dependence; however, in no case do we have counterfactual dependence between distinct events. In each case, we have counterfactual dependence between distinct entities (property-exemplifications, we may call them) which you but not I would consider to be events. Also we have entities which I would consider to be events; but I would not grant the distinctness of these entities. I think the connection between laws and counterfactuals and causation has been greatly exaggerated for many years by almost everyone. All there is to it is that we find laws important; so we treat them as weighty respects of similarity; so laws have some tendency to be counterfactually independent of not-too-diverse ranges of alternatives. The lemma you mention on page 3 does indeed go for arguments from any counterfactually independent premise set, whether or not it consists partly of laws.   ‘Causation’ (Lewis 1973a).

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My attitude toward your last point is that while it would certainly be nice to go from an analysis of causation to an explanation of why we make causal statements, the first order of business is to find out which analyses are at least adequate against apparent counterexamples. But if the outcome is that every analysis can be defended against counterexamples at a price, and none deals with them in a completely satisfying way, then I suppose that other sorts of comparative merit might be more important. I like the whole set of comments, which raise important points on which ser­ ious differences of opinion are likely. The discussion at Atlanta should be good, and I look forward to it.2 Yours, David Lewis

24.  To John Pollock, 15 April 1974 Princeton University Princeton, NJ Dear John, Many thanks for your new paper on counterfactuals.1 The problem you state for my analysis is one that often has bothered people, so it’s good to have it so clearly set out. I certainly agree that failure of the Generalized Consequence Principle is unintuitive and surprising – but to me it still seems not enough so to refute the analysis. It’s worth noting that if you have quantification, you can put the thing in a less metalinguistic way: given my analysis without the limit assumption, you can have something of this form true, surprisingly.

∀x (A

Fx) & ¬(A

∀x Fx)

even when the domain of quantification is the same at all worlds

A: the line is more than one inch. F: the line is less than___inches. Domain of discourse: all reals greater than 1. 2   Lewis presented ‘Causation’ at an APA Symposium, American Philosophical Association Eastern Division, Atlanta, December 1973. Kim commented on ‘Causation’ in that same session. Kim’s comments were published as (Kim 1973).

  ‘The “Possible Worlds” Analysis of Counterfactuals’ (Pollock 1976).

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24.  To John Pollock, 15 April 1974

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What do you make of the temporal analogue with ‘when next’ (or ‘when last’)? It’s quite clear that whatever may be the case with order of similarity or of minimal change, the order of time is a dense simple order. So you will not find it easy to give an otherwise acceptable semantics for ‘when next’ that respects the Generalized Consequence Principle. What time will it be when next it is (strictly) between midnight and sunrise? For any time t after midnight, it will be between midnight and t; for if it were after t, by what right could we ignore the intervening time and say ‘when next’? But then by the Generalized Consequence Principle we get the false conclusion that when next it is between midnight and sunrise it will be no later than midnight; wherefore the Principle is refuted. But the Principle is just as unintuitive and surprising here as in the counterfactual case! So if we can stand to abandon it here, why not in the counterfactual case as well? I think there may be Gricean effects casting a bit of fog over the whole matter: maybe it’s conversationally inappropriate to use counterfactuals (or ‘when next’) in certain sorts of peculiar cases, and maybe these peculiar cases are the very ones where failure of the Generalized Consequence Principle (or failure of Conditional Excluded Middle) may arise. Thus it seems that I have some leeway to explain away intuitions in favor of the Principle. But why not adopt your treatment? It seems to me to restore the Principle at a very excessive price. Take your page 9, lines 5–6: ‘It might also be three inches long, or four inches long, etc’. Three and four don’t sound bad, but what does the ‘etcetera’ cover? 1000 miles? No! I want to insist that even if that line were over an inch, it wouldn’t be more than a very few inches. Given your partial ordering on the basis of containment of changes, I don’t see how you can account for that. Or rather, I think that you can account for it only in a way you’d find unacceptable: namely, by saying that the change of making the line at least x inches long is contained in the change of making the line at least y inches long whenever y is greater than x. That brings you right back to the conclusions you don’t want. (And incidentally it leaves me puzzled about why your semantics does validate the Generalized Consequence Principle when mine doesn’t. Did you really claim that? I thought you did, since your treatment was meant to set right the problem you found with mine. But now I see that mine is a special case of yours, so yours can’t validate more than mine does.) I’m sympathetic to using a partial ordering of some sort; though presumably one based on similarity rather than your ‘containment of changes’ which seems to me either to come to the same thing or to be quite puzzling. An indeterminate simple order comes to the same thing as a partial order. Formally, if we have an in­de­ter­min­ate similarity order and a class of alternative ways of resolving the indeterminacy, then ‘__ is closer than . . . (to world i) no matter how the indeterminacy is resolved’ should be a partial order; and if we have a partial order, then we can think of the result of

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extending it arbitrarily to a simple order as an indeterminate simple order, in­de­ter­ min­ate and arbitrary to the extent that there are many ways to make the extension. I’ve always thought that there was a lot of indeterminacy and blur; even if we worked with a partial order we’d still have the indeterminacy and blur, though, so I’m not clear that we gain much. (Even a partial order ought to be considered indeterminate – (1) to account for our intuition that some counterfactuals have indeterminate truth conditions, and (2) to leave some vagueness for contextual factors to resolve.) Maybe this is the strategy: we have a coarse simple order, with thresholds, that obeys the limit assumption; thus we validate the Generalized Consequence Principle. But we make the position of the thresholds quite indeterminate; thus we do not make true, except at one arbitrary resolution of indeterminacy among others, such absurd counterfactuals as: ‘If the line were longer than an inch, it might be any length up to 2.89674ʹʹ, but it would be no longer than that’. However, we more or less rule out some of the more extreme resolutions of the indeterminacy, so that we do make true (true on all resolutions of indeterminacy within reason) such counterfactuals as ‘If the line were longer than an inch, it wouldn’t be more than a foot or so’. This strategy seems to give me a lot of what I want – how far does it satisfy you? Hoping you’ve sent Bob Stalnaker a copy of your paper, I’m sending him also a copy of this letter. Yours, David PS Trivia: [. . .]

25.  To John Bigelow, 8 November 1974 [Princeton, NJ] Dear John Bigelow, I agree with you that your sentences ‘London’ and ‘Lemon’1 are, in all probability, false. But I needn’t go to such lengths as you suggest to account for their falsehood. A much simpler hypothesis is close at hand; it requires no change at all in my original theory, and it is independently motivated. Now read the clipping.2 (The clipping announced the discovery of another moon of Jupiter.)3 1   London: If London is a large city, then Jupiter has twelve moons. Lemon: If my lemon had been 6 cm long, then Jupiter would have had twelve moons (Bigelow 1976a, 216–17). 2   ‘New Moon Over Jupiter: No. 13’, Science News 106 (1974), p. 195. 3   Parenthetical remark added to Lewis’s copy of the letter after it was sent.

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25.  To John Bigelow, 8 November 1974

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Joking aside, thanks very much for your interesting paper4 and letter. I’m sorry not to have answered you sooner. I gave priority to some less pleasant chores with deadlines attached. My reaction, I think, is that I still am not persuaded that there is any problem with (corrected versions of) ‘London’ and ‘Lemon’. But if there is a problem, it is beyond the reach of your remedy. Still, I like the idea of looking at truth of my coun­ ter­fac­tuals not at our actual world only, but throughout a sphere of resonance around it. I think this should be part of the whole story about counterfactuals, but I think its place in the story is not what you say. Second things first: let me say why your remedy doesn’t cure the problem if there is a problem. You say, and I agree, that there are conditionals just as fishy – and fishy in the same way – as ‘London’ and ‘Lemon’ in which the antecedent and consequent are both true as a matter of natural law. You conclude that the sphere of res­on­ ance should not be fixed once and for all; we should take it to be at least large enough to include some worlds in which both the antecedent and consequent are false. Since we sometimes know very well that the antecedent and consequent are true, this seems to me to subvert your original epistemic motivation for the sphere of res­on­ ance; but let that pass. The real point is that sometimes there’s no way to get a big enough sphere to do the trick. Surely there are conditionals just as fishy – and fishy in the same way – as ‘London’ and ‘Lemon’ in which the antecedent and consequent are both true as a matter of mathematics or logic or whatever is your favorite sort of absolute necessity. No way to choose the sphere of resonance (unless you go for impossible – sometimes blatantly impossible – worlds) will make the conditionals false on your theory. I conclude that whether or not ‘London’ and ‘Lemon’ are false, what makes them fishy is something that’s capable of conferring fishiness even on the true conditionals we’ve just considered. Don’t you think there are special contexts that make ‘London’ and ‘Lemon’ seem neither false nor in any way fishy? Some fool claims that in some mysterious way the number of Jupiter’s moons depends on the size of London or the length of your lemon. You disagree in these words: ‘If London were a small city, a large city, a middle-sized city, a tiny hamlet, indeed whatever you like, still Jupiter would have 13 moons!’ ‘If my lemon where 2cm., 3cm., 5cm., 91/4cm., 8,137cm., or any length you like, still Jupiter would have 13 moons!’ Good and true replies; and I take it that they are abbreviated conjunctions of true counterfactuals, and that the true coun­ter­fac­ tuals ‘London’ and ‘Lemon’ are among the conjuncts. So what makes ‘London’ and ‘Lemon’ fishy seems to have disappeared in this context. That seems to point to pragmatic fishiness, not falsehood. I know it’s not a decisive reason – you could say that   ‘If-Then Meets the Possible Worlds’ (Bigelow 1976a).

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this special context shrinks the sphere of resonance enough to restore the truth of ‘London’ and ‘Lemon’, or alternatively you could say that these ‘even if’ conditionals differ semantically from ordinary counterfactuals. Only to the extent that you find these two strategies ad hoc will you take this special context as evidence that ‘London’ and ‘Lemon’ are true. My feeling is that although I can detect fishiness without the aid of theory, I cannot always discriminate without the aid of theory between falsehood of what has been said and other sorts of fishiness. Other sorts of fishiness can indeed be matters of falsehood, so even the reaction that some sort of false message has been conveyed isn’t conclusive. Suppose you say to me, in an urgent tone of warning: ‘You won’t eat those mushrooms and live!’ And it’s true; for I take warning, I don’t eat those mushrooms, a fortiori I don’t eat them and live, just as you said I wouldn’t. But something was wrong with what you said; for I thought that you believed and said what you did because you believed the mushrooms were poisonous, and since I thought you knew mushrooms I came to believe that they were poisonous, and yet in truth those mushrooms were not poisonous. A truth was said, but a falsehood was conveyed – the falsehood that the mushrooms were poisonous. Perhaps you even meant to convey a falsehood – having kept me from the mushrooms by getting me to think they were poisonous, you return at leisure and take them for yourself, for you knew all along that they were good. There was deception; falsehood was conveyed; there was something very fishy about what you said – but according to theory (the theory of truthfunctional connectives) what you said was nevertheless true. Approached naively, I  think there’s no saying whether it was true or not; only when we make a theory, rudimentary or sophisticated, do we go reliably beyond our first reaction that the affair was somehow fishy and deceptive. I think it’s so also with counterfactuals, and indeed with conditionals generally. In uttering a counterfactual in normal circumstances, I certainly suggest that it holds (on my semantics) not only at our actual world but also throughout some sphere of resonance. In the first place, I’m not expected to say what’s true only by accident but rather to make (more or less) certain that I’m truthful; so I should say only those things that are true in all the leading open epistemic possibilities, which will include many worlds that differ from ours in various not-immediately-detectable ways. In the second place, I shouldn’t utter a conditional with a true antecedent and consequent unless I’m surer of the conditional than I am of the antecedent and consequent; else it would be more efficient and informative to give the antecedent and consequent themselves. That will be so only if the conditional holds in some significant open epistemic possibilities in which the antecedent doesn’t. This leads me to think that although the ordinary counterfactual has my truth conditions, yet normally

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25.  To John Bigelow, 8 November 1974

45

when it is asserted a stronger proposition also will be suggested and conveyed; and this stronger proposition may be something rather like your conditional. In consigning something – the fishiness of ‘Lemon’ and ‘London’ – to pragmatics, I don’t mean to consign it to the wastebasket. It is possible that consigning something to pragmatics will yield a better explanation – as formal and precise as you could wish – than leaving it in semantics. A case in point is Bob Stalnaker’s elegant explanation, in terms of the kinematics of pragmatic presupposition, of the fishiness of ‘All John’s children are asleep and John has children’ but not of the same conjunction with the conjuncts in the opposite order. Semantic explanations of the same fact had been given, but they looked very ad hoc. I would take the key idea of your paper as an insufficiently general semantic explanation of the fishiness of ‘London’ and ‘Lemon’, but simultaneously as part of a good pragmatic explanation. I find the idea interesting also in a different connection. The generative semanticists find it plausible that ‘kill’ means ‘cause to become not alive’. But that isn’t right. I really don’t think I’ve ever killed anyone. But I think that I, or anyone my age, must have caused a great many deaths, although by roundabout and unforeseen causal chains. I’ve often made appointments with people, causing them to be at various places when and where they wouldn’t have been otherwise. And they in turn have planned their meetings with other people accordingly, causing many more people to be at various places when and where they wouldn’t have been otherwise. And so on; the ramifying causal chains I have in mind have many links per day, and some of them have been running for years now. I’m sure I’ve caused many people to be in the path of a drunken driver, to travel on a plane that crashed, and so forth. (Of course, in the same way I suppose that I’ve also prevented many deaths.) So if killing is anything like causing to die, it must be a special kind of causing. By a short causal chain? I think not; I could kill someone by means of an arbitrarily complicated clockwork, with arbitrarily many steps in the inexorable causal chain of gear movements, pendulum swings, ratchet releases, . . ., leading from my pushing a button to his becoming not alive. Or is it a foreseen or foreseeable causal chain that’s required for killing? I think not that either. I can kill someone negligently, by a causal chain I failed to foresee; or inadvertently, by a causal chain nobody could have foreseen because nobody had any way to know that he had a fatal allergy to the combination of papaya, venison, and kirschwasser. What might be true, I think, is that killing is non-fortuitous causing to die, where a causal chain is fortuitous if it has links that hold at our actual world but not throughout a suitable sphere of resonance. That is: the special kind of causation is stable causation, causation that persists despite various minor changes in the way the world is. That’s as far as I’ve thought it out, but I think it may have some chance of working. As is, it’s too vague to test.

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Turning now to the idea in your letter: that we might go from comparative similarity to probability measure in logical space in a way analogous to the way in which we go from distance to volume in Euclidean space. It’s interesting: and worth pursuing, but I don’t believe it will work. Even when you go from my 3-place comparative relation to your more informative 4-place relation, still you have a structure so unspecified that a standard metric space is a special case. And even if you have a metric space, I don’t know of any uniquely natural way to go from a metric to a measure. We know the constructions that work in Euclidean n-spaces (different constructions for different n, notice) but do you even know a way to build a measure from the natural metric for Euclidean ω-space? It’s trivial just to establish existence of a measure defined from a metric, I suppose (no, on second thought I don’t see how to have even that in general), but you need more. You need to show that your measure is, in some sense, uniquely natural. For instance, you’d like to make sure that various alternative constructions of measures that yield the same measure in Euclidean n-space for fixed n will not disagree with one another in the general case. Consult a good math­em­at­ ician, which I’m not. My guess is that the thing can’t be done in general, but maybe can be done if you pile on a lot of extra constraints on the comparative relation you start with. Then your job is to defend the constraints; and maybe that can be done. I do have a hunch that more formal constraints can be imposed on comparative simi­ lar­ity than I’ve thought of. Again, thanks very much. I hope you’ll send me anything more you do on these (or other) topics. Please give my best to Max. Yours, David Lewis

26.  To Kit Fine, 3 February 1975 [Princeton, NJ] Dear Kit, We’re soon off to Oxford once again, I to spend a term of leave finishing up several old odd jobs, and Steffi to finish her dissertation for UCLA. We leave in 2 1/2 weeks, though with some miscellaneous travel in the US between now and then. We’ll rent Philippa Foot’s house (15 Walton Street) for most of our stay, starting 22 March; it shouldn’t be hard to find something temporary to fill the gap before that.

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26.  To Kit Fine, 3 February 1975

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We return early in June and set out immediately for California, where I’ll be participating in some sort of workshop on linguistics and computer science that George Lakoff is arranging. Many thanks for your pleasant and interesting review of Counterfactuals.1 I have a little to say about some of the points you discuss. (1) You say there’s nothing essentially metalinguistic about the alternative account. OK; but there’s something to add. One reason – not the only one – to like the alternative account better than mine is that you believe in sentences and you don’t believe in possible worlds. But in that case you probably won’t believe in pro­ posi­tions either – from propositions to worlds or back again is no big step. So one sort of motivation for the alternative, ontological parsimony, favors only the metalinguistic version and not the propositional version. (2) If Nixon had pressed the button there would have been a nuclear holocaust. (I think this is false for irrelevant reasons; it’s a bit harder to cause a nuclear holocaust than people think. But never mind that.) The point is that it looks as if we could stick close to actuality by making the future as well as the past similar, thereby having a hypothetical cause without its effects; whereas what’s true is that if the cause had occurred, its effects would have followed. My reply is not, I think, that future similarities don’t count simply because they’re future. For I do want future similarities to count in special cases – say, inside a time machine where all the or­din­ ary de facto differences between the past and future directions of time are locally reversed. Instead, I will say that approximate similarities of particular fact throughout a spatio-temporal region count for little or nothing, although perfect similarity throughout a region counts for a lot. The bigger the region of perfect match, the better. Suppose Nixon had pressed the button (antecedent A). We have several sorts of A-worlds. (1) A-worlds that perfectly match the actual world until just before the fatal moment, in which some small miracle permits A to happen nevertheless, in which no further miracles occur, and in which particular facts afterward diverge greatly from actuality. (2) A-worlds that perfectly match the actual world before, in which a small miracle permits A, and in which another small miracle averts the holocaust and brings us back to something fairly close to the actual future. Not a perfect match: there are traces. The button bears a fingerprint, Nixon has his memories, light waves going out in all directions carry the image of the button-pressing, the wire remains broken, and so forth.   (Fine 1975).

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(3) A-worlds that perfectly match the actual world before, in which a small miracle permits A, and in which another large bundle of miracles wipes out not only the holocaust itself but also traces of Nixon’s button-pressing, thus permitting not only approximate similarity but renewed perfect match. (There are still further sorts of A-worlds which we don’t need to consider.) Now the result had better be that the (1)-worlds are closer to actuality than the (2)-worlds and the (3)-worlds. Else the wrong counterfactuals end up being true according to the theory. Why do the (1)-worlds beat the (2)-worlds? Because a region of approximate similarity of particular fact isn’t worth enough to outweigh a mir­ acle, even if it’s only a little miracle and there’s already one miracle. Why do the (1)-worlds beat the (3)-worlds? Because the much larger bunch of miracles needed to wipe out all the traces and produce a perfect reconvergence to the actual future is a very serious departure from actuality, serious enough to outweigh the admittedly weighty perfect match of particular facts throughout the future. The hypothesis is that (a) given the de facto asymmetries of time that normally prevail hereabouts, reconvergence takes a very much bigger miracle than divergence; (b) approximate similarity of particular facts has little weight; (c) exact similarity of particular facts throughout the entire past or the entire future outweighs a small divergence miracle but not a big reconvergence miracle. And why believe this rather complicated hypothesis? Simply because, together with the rest of the theory, it seems to predict correctly which counterfactuals are true; but it does it in a way that leaves open the possibility of exceptional cases in which if the present had been different its past ‘effects’ would have been different also via reversed causation. (3) On true antecedents. You say, not knowing if Jones has worked hard, that if he’d worked hard he would have passed. In truth he worked hard and passed, but he passed by cheating and his hard work didn’t give him the wherewithal to pass. You say your conditional is false, and I just don’t agree. There were plenty of falsehoods in the offing: you believed them, they were the premises that led you to assert the conditional, thus your hearer inferred and came to know that you believed them. It’s uncontroversial that you were mistaken and (if your hearer trusted you) that you led your hearer to share your errors. In such a case, it’s hard to tell if what you said, taken literally and by itself, was false. I cannot distinguish my feeling that the whole affair involves error (which is true on any view) from a trustworthy naïve opinion that your conditional was false, which is the datum you need for your point. (4) On disjunctive antecedents: I accept the first solution you mention, that of saying that English ‘or’ often is not truth-functional disjunction. As you note, this is so not only for antecedents of conditionals but in many other contexts also. I don’t

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27.  To Thomas McKay and Peter van Inwagen, 9 February 1976

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have a theory of ‘or’ that explains in a natural way why it sometimes is truthfunctional and sometimes acts like a comma in a list, but I think that – and not some fancy business in the theory of counterfactuals, permission, ability, etc – is what’s needed. (5) On similarity in respect of counterfactual propositions. I like your distinction between impredicativity and circularity; it explains why I thought there was something wrong with objections that my account might be circular because coun­ ter­fac­tuals themselves contributed to similarity. I have been inclined to accept some thesis to the effect that worlds alike in non-counterfactual respects were alike in counterfactual respects also, though I didn’t think my theory depended on it. But now I’m a bit puzzled. I know how a sentence is indicative or not, or at least I understand this roughly in a sufficiently impoverished language. But if a proposition is not sentence-like but is simply a set of worlds, how can a proposition be indicative or not? It’s like distinguishing, say, the conjunctive or negative propositions, which I take to be clearly futile. Presumably any proposition could be expressed by conjunctive or by non-conjunctive sentences, or by negative or by non-negative sentences, or by counterfactual or non-counterfactual sentences, if the language is rich enough. To transplant such distinctions from sentences of a fixed language to propositions, it seems you must find a reasonable way of limiting yourself to far less than all possible languages. The final part of the review, on questions of definability, was quite interesting, but I have nothing helpful to add to what you say. Again, many thanks for the review – it’s helpful, interesting, generous, fair in its criticisms. Yours, David

27.  To Thomas McKay and Peter van Inwagen, 9 February 1976 Princeton University Princeton, NJ Dear Profs. McKay and van Inwagen, Many thanks for your paper on disjunctive antecedents,1 if such they be. I’m in complete agreement with your solution. That’s not to say I’m very happy with it. It

  (McKay and van Inwagen 1977).

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would be terribly ad hoc to say that seeming narrow-scope disjunction is really widescope conjunction, if the phenomenon were confined to counterfactual antecedents. It’s much more widespread, however. Probably your Axiom of Choice example is a genuine instance of it, though I think an example where the two formalizations are equivalent isn’t going to convince anyone who isn’t convinced already. Other ex­amples include: You may have your coffee with cream or without. The law allows you to count this either as a deduction or as an adjustment. I can fly or take the train. Tell me whether you’ll fly or take the train. Whether I fly or take the train, I still won’t be on time. So the phenomenon exists, and I’m free to appeal to it to get out of trouble. But I wish I understood it, and I don’t. A similar phenomenon exists with seeming existential quantification. It’s kind of you to look for something nice to say about Nute and to speak of his ‘valuable discovery of sentences like S’; but you’ve inadvertently slighted quite a few people who made the discovery earlier or discussed it more sensibly or both. I don’t think I can give a complete list of people who have made the discovery. One excellent discussion is in Kit Fine’s review of Counterfactuals in Mind;2 he discusses three solutions, including the one we prefer and the one Nute prefers. Another good discussion is in another review by Creary and Hill, published or forthcoming in Philosophy of Science;3 they give a solution like Nute’s4 and point out that interchange of equivalents will fail. The first to notice the point was Mike Slote, around 1969. I think I’m forgetting someone else. John Pollock has come close to it; he looks at examples of a somewhat mild sort (the seeming disjuncts aren’t mutually exclusive, and one is not obviously more far-fetched than the other) and takes them to prove that we need a partial ordering of worlds, in which worlds that depart from actuality in different ways are incomparable. I’ll be replying to Pollock in Phil. Studies,5 and will take the opportunity to comment on seemingly disjunctive antecedents. I think that one of your two counterfactuals about Goldbach is vacuously true; in calling it false, you were responding not to the unknown truth value of the conditional but rather to the obvious falsity of the implicature that Goldbach claimed that ~G. I don’t think we can always take judgments of truth value as linguistic data: we judge that there’s something very wrong, and we may even say loosely that the ­sentence is false. But an interpretation that makes the sentence false is only one

 (Fine 1975).   3  (Creary and Hill 1975).   

2

4

 (Nute 1975).   5  (Pollock 1976).

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28.  To Thomas McKay, 17 February 1976

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explanatory hypothesis among others to explain why we find it bad. To explain our judgment of ‘falsity’ – or, to speak more cautiously, of some sort of wrongness – by the hypothesis that the sentence is indeed false would be nice if it could be done. But it’s not obligatory. Yours, David Lewis

28.  To Thomas McKay, 17 February 1976 [Princeton, NJ] Dear Professor McKay, That’s the sort of hypothesis that would make me happier with the solution we prefer. But I don’t think the phenomenon can be quite so simple. Consider these. (1) Someone once told me that snow is white and someone once told me that grass is green. (2) Someone once told me that snow is white and grass is green. (3) Someone once told me that snow is white or grass is green. Since (1) and (2) differ in meaning, the hypothesis predicts that (3) might mean the same as (1); but although (3) is ambiguous, I can’t get (1) as a meaning for it. My hunch is that you’ve given a necessary condition for the phenomenon, but not a sufficient one. Also, it’s not clear to me that telling you whether I’ll fly or take the train is the same as both telling you whether I’ll fly and telling you whether I’ll take the train. If I say ‘I’ll fly’ (and we’re presupposing that I’ll do exactly one) then I’ve told you whether I’ll fly or take the train, and I’ve told you whether I’ll fly, and perhaps I’ve informed you whether I’ll take the train; but it seems to me that I haven’t exactly told you whether I’ll take the train. Yours, David Lewis

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29.  To C.B. Daniels, 8 April 1976 Princeton University Princeton, NJ Dear Danny, Once upon a time I wanted to take the bus downtown. Just as I was finally getting on, I discovered to my annoyance that the bus only took exact change and I had only big bills in my wallet. But afterward the thought came to me that I’d been stupid; I was wearing my coat, and sometimes when I wear my coat I put change in my coat pocket instead of my wallet. What would have happened, I wonder, if I’d looked in my coat pocket (L)? Would I then have been able to take the bus (B)? Is this conditional true: if it were true that L, it would be that B? I utter this conditional; whether truthfully (and truly) remains to be seen. You say that the conditional is true iff X & □(XL ⊃ B) (first version); or perhaps simply iff □(XL ⊃ B) (second version).1 Here □ is an ordinary necessity operator governed by reflexive accessibility; and X is a suppressed sentence representing all that I, the speaker, have in mind as points of similarity that count in the evaluation of what I am saying. I say that the conditional is true iff there was sufficient change in my coat pocket (C). No general theory of the truth conditions of conditionals is any good unless it comes out that way in the present case. Case 1. I haven’t worn the coat since that day, so whatever change was there at the time must be there still. I check, and conclude correctly that C. Having C in mind as a point of similarity, I utter the conditional truthfully. Doubtless you’d say that X = C in this context. (Let’s stuff some other fixed background into the accessibility relation; that won’t matter to the argument.) Then the conditional is true, as it should be, according to both versions of your theory. Good. Case 2. Like case 1, except that when I check I conclude correctly that ¬C. Having ¬C in mind as a point of similarity, I utter the conditional untruthfully (I have my reason for lying). Doubtless X = ¬C; so the conditional is false, as it should be, on both versions. Good again. Case 3. My pocket was picked after I failed to take the bus but before I checked and before I uttered the conditional. I check and conclude that ¬C but I’m wrong; actually C. However, what I have in mind in this case is no different from what I had   Cf. ‘An Analysis of the Subjunctive Conditional’ (Daniels and Freeman 1980).

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29.  To C.B. Daniels, 8 April 1976

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in mind in Case 2. So if X = ¬C in Case 2 then likewise X = ¬C in Case 3, making the conditional false in both versions. Bad; it’s clearly true. Thanks to the pickpocket I believe that the conditional is false, but that’s one of the things I’m wrong about. Case 4. It’s too late to check; I’ve worn the coat often since and much change has come and gone from the pocket. I have no opinion about whether C or ¬C. I am in no position to have either one of them in mind as a point of similarity of other worlds to our world, since I have no idea which sort of world ours is. Yet it’s not too late to wonder about the truth value of the conditional. And it’s not too late to reason hypothetically about it, as when I think that if it’s true that there’s been at least some time when my stupidity has got me into trouble whereas if it’s false then it may yet be that my stupidity is completely harmless. I don’t think it will do to say that X is determined by what the speaker has in mind as a point of similarity. That gives the wrong answer (on both versions) in Case 3; and I don’t see how it applies to Case 4 at all. Maybe the best I can do is this: since in Case 4 I have neither C nor ¬C in mind as a point of similarity, X = (C ∨ ¬C) so that the conditional is false. But no: it’s true if C is. Or maybe X is indeterminate between C and ¬C, making the conditional indeterminate in truth value. But no; maybe some conditionals are indeterminate in truth value, but this one isn’t. All I have in mind in Case 4 (except irrelevancies) and part of what I have in mind in the other cases also is a question: the question whether C or ¬C. This question by itself doesn’t determine a point of similarity to actuality; which point of similarity is it? That depends on whether our world is a C-world or a ¬C-world. But the question by itself does determine a respect of similarity: the respect in which all C-worlds are similar to one another and in which all ¬C-worlds are similar to one another. And this respect of similarity is something I had in mind in each case. You can think of a question as a propositional concept: the concept whose value at a world is whichever answer is true there. I commend you to a theory that is just like the second version of yours except that X is jointly determined by the truth and by what the speaker has in mind: it is the true answer to the most comprehensive question the speaker has in mind as giving the respects of similarity that count in evaluating what he says. X is the actual value of the concept. I’d have little quarrel with such a theory so far as it goes. Technically, it would fit my machinery. (You’d want a system of double indexing, as in 2.8 of Counterfactuals.) I’d only object that it’s too individualistic in taking what the speaker has in mind, rather than what’s relevant according to the shared understanding of speaker and audience. What if my conditional is true, filling in the question I had in mind; but

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false, filling in the question conventionally relevant in the context? However, it’s of no great importance whether you agree with me in judging that conditional false; you’d agree with me that it was deceptive and that’s good enough. Yours, David cc: Bob Stalnaker

30.  To Richard J. Hall, 12 May 1976 [Princeton, NJ] Dear Professor Hall, Many thanks for your note about counterfactuals to the effect that things would have been very different if. . . . The point is interesting, and new to me.1 (The closest thing to it is a parallel point Feldman once made against counterpart theory: how can it be true, according to me, that someone might have been very different from the way he actually was?)2 To begin with data, certainly both of the following strike me offhand as true; I couldn’t accept a theory that flatly denied either one. (C) If Oswald had not shot Kennedy, things would be very different. (P) It is logically possible that Oswald did not shoot Kennedy yet things were not very different. I hope I have always conceded – nay, insisted – that similarity is a vague matter, and that different resolutions of the vagueness are appropriate to different contexts. In considering (C) and (P), out of the blue without special contexts, I think I’m resolving the vagueness in a way that stresses approximate similarity of particular facts – notably, of newsworthy events throughout the 60s. I had in mind something close to (C*) If Oswald had not shot Kennedy, the headlines would be very different. (P*) It is logically possible that Oswald did not shoot Kennedy yet the headlines were not very different. The resolution of vagueness appropriate to evaluating counterfactuals may be different. Indeed, I think it is almost opposite, at least for many counterfactuals in many contexts. Approximate similarity of particular facts is played down; perfect   Cf. ‘Counterfactual Dependence and Time’s Arrow’ (Lewis 1979b, 466–7).   (Feldman 1971). See also Letter 135. To Fred Feldman, 7 March 1972, Volume 1: Part 2: Modality.

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30.  To Richard J. Hall, 12 May 1976

55

match of particular facts through limited spatiotemporal regions and conformity (perhaps imperfect) to the actual laws of nature are played up. These different em­phases give something that is every bit as much a comparative similarity relation as the one I had in mind when I said that the world would have been very different but could have been not very different. But the similarity relations are not the same, and they can disagree. Let S1 be the similarity relation appropriate to explicit discussions of things being very different in the natural context where we have foremost in mind the approximate similarity of the newsworthy events of the next few years. Let S2 be the similarity relation appropriate to evaluating many counter- true together, we need a situation like this. We have the antecedent-worlds: worlds where Oswald did not shoot Kennedy (or better, where Oswald’s counterpart didn’t shoot Kennedy’s; but let’s ignore this modification). Let us sort these worlds into three classes. (1) Most of them are grossly different from actuality: the earth is populated entirely by turtles or what-not. These antecedent-worlds we shall ignore. (2) Some of them are closest to ours according to S2. There is no departure from the actual course of events until the time of the shooting, and minimum lawviolation thereafter. In these worlds events take their course in the way you’d expect after the non-shooting; you have the actual laws and most of the actual initial conditions but not the shooting. Consequently, these are worlds where the newsworthy events rapidly diverge from those of our world. They are not very close to our world according to S1. Hence (C) is true. (3) Still others are closer to our world according to S1. Somehow the nonshooting is followed by events very like those that actually followed the shooting. Perhaps Kennedy is struck down by a miraculous bullet from heaven. Perhaps he has a heart attack just then, of such a sort as to cause people to suspect foul play. Perhaps someone else shoots him. But to provide for these substitutes for the shooting, we need either miracles or else differences in initial conditions. We pay for S1-similarity by gratuitous S2-dissimilarity. Hence these worlds, although they are what we need to make (P) true, do nothing to make (C) false, and all is well. You might reply that maybe, if things were just right, you could have S1similarity without paying for it by S2-dissimilarity. Maybe someone else was on the point of shooting. But I doubt it. And only because I doubt it do I believe (C). If you could show me a way, given the facts, to get an Sl-similar antecedent world without paying for it, I would take this as a reason why I was wrong to believe (C). You would persuade me that if Oswald had not shot Kennedy, things might after all be not very different. You might reply – in the note you do take this route – that by stipulation when you speak of ‘things being very different’ this is to be understood with respect to the same similarity relation, whatever it may be, that is appropriate to evaluating

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c­ oun­ter­fac­tuals. But then you undermine the data you need. (C) and (P), taken in an offhand and normal way, and judged using what I take to be the facts about our world, are surely undeniable. But (C) and (P), taken in accordance with this special stipulation, are by no means undeniable. I have no offhand opinion about whether they are true, and your argument shows me that one of them must be false. That is: you cannot both appeal as you do to the opinion of the ‘many Kennedy admirers’ and use the definition at the bottom of page 2 (with the understanding that by ‘Lewis’s . . . simi­lar­ity relation’ you mean the similarity relation with a resolution of vagueness appropriate to evaluating counterfactuals).

31.  To Peter Gärdenfors, 7 October 1976 [Princeton, NJ] Dear Peter, Our greetings to your son, and congratulations to both of you! I will indeed lecture in Uppsala on causal explanations, most likely in late May or early June, just before Uppsala’s anniversary celebration. Most likely Steffi also will be able to come with me. I hope we’ll see you then. Not having an unstable table to support, I used your paper for reading matter instead,1 and found it quite interesting. I partly agree and partly don’t. Certainly one important thing that can be wrong with an attempt at explanation is that it adds nothing to the explanatory information that the recipient already possesses. Whether this makes it a non-explanation or an unsatisfactory explanation is a difficult question, but I think one that we need not solve. Anyway, I agree with you that in characterizing good explanation we have to consider what gets added to the previous knowledge situation. But I don’t agree with your equally important point that the explanatory information should make the explanandum less surprising than it was before. Often that is so, but sometimes the opposite is true. I throw ten successive heads with a coin some stranger has given me. Since I know that he is a salesman for a company that manufactures two-headed trick coins, I’m not very surprised; I think perhaps I’m getting a demonstration of his wares. But now I acquire some correct explanatory information: the coin was fair, and the run of heads was entirely a chance phenomenon after all!   Possibly ‘A Pragmatic Approach to Explanations’ (Gärdenfors 1980).

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32.  To Alvin Plantinga, 22 October 1976

57

Now that I have this explanatory information, the explanandum fact seems very much more surprising than it did before. The reason is that my new explanatory information has ruled out an alternative hypothesis which I assigned some medium degree of belief, and which if true would have made the explanandum unsurprising. Another case: initially I have no idea at all of how the run of heads is to be explained. Having failed to consider that maybe I have just seen a very improbable chance phenomenon, I find the event unsurprising. But when I learn the explanation – as before, that the run of heads took place by chance – then I begin to find the explanandum very surprising. Your paper stimulated me to produce a brief outline or manifesto of my notions about explanation – not at all a full exposition or defense – which I enclose.2 That should give you some idea of what the Uppsala lectures will be about. Yours, David Lewis

32.  To Alvin Plantinga, 22 October 1976 Princeton University Princeton, NJ Dear Al, I’ve recently been trying harder than before to figure out what I think of Leibniz’s lapse – if such it be – and your refutation of it. I thought for some while, partly as a result of a conversation with Saul Kripke, that there had to be something wrong somewhere. Counterfactuals are contingent, for the most part; if the coun­ter­ fac­tuals of our world cramp God’s style, why didn’t He actualize a world with different counterfactuals? I dare say you’ve heard this worry from others before now. But a worry and a hunch are no answer to a proof. When I checked your refutation of Leibniz’s lapse line by line, though I got lost in the details and didn’t grasp the strategy of the proof intuitively, I could find nothing wrong. (At least not in the NON version.1 GF&E is another story;2 the proof there looks like a simpler proof that commits the counterfactual fallacy of transitivity, though perhaps it can be construed 2   An outline or manifesto that Lewis incorporated into his Hagerstrom lectures at Uppsala, 1977. See his ‘Causal Explanation’ (1986d, 214–40).

  The Nature of Necessity (Plantinga 1974b).   God, Freedom, and Evil (Plantinga 1974a).

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instead as a simplified sketch of the NON proof.) But now I think I’ve understood better what you are doing. I’ve reorganized and streamlined the proof, but I hope without departing from your strategy of argument. If I have departed, I hope you’ll at least find my proof interesting as an alternative to yours. As a result, I think I’ve been able to sharpen my vague worry into a real objection. You have a choice to make about how to construe your definition of weak ac­tual­iza­tion. One way makes your proof valid; but unfortunately it seems to me that this way makes the definition seem peculiar and unmotivated. The other way is better motivated, but it makes the proof fail. In fact, far from leading to a refutation of Leibniz’s lapse, it leads to a proof of the opposite! And now to get down to business. Preliminaries. I shall not distinguish between sets of worlds, propositions, and states of affairs; and I shall use capital letters to stand for them. I shall also use letters in the vicinity of ‘W’ to stand ambiguously for worlds and for their unit sets, or in other words for propositions or states of affairs of the sort that hold at one world only. ‘A ⊆ B’ can therefore be read as meaning that proposition A implies proposition B, or that state of affairs A includes state of affairs B. I shall write ‘A ⁄ B’ to mean that if the proposition A held the proposition B would hold; though this notation will later turn out to be not quite satisfactory. When I speak of ‘counterfactual logic’ I shall mean the system VC of Counterfactuals, my favorite system.3 Stalnaker’s stronger system would do as well. But some of the uses I will make of counterfactual logic would fail in the systems some other authors have proposed. Strong Actualization. If God strongly actualizes any state of affairs whatever at world W, then let us call W a normal world (the term comes from modal logic) and let T(W) be the largest state of affairs that God strongly actualizes at W. Then for any state of affairs A, God strongly actualizes A at W iff T(W) ⊆ A. If W is non-normal, then let T(W) be undefined. For any state of affairs A, let GA be the proposition that God strongly actualizes A, or in other words the set of all normal worlds W such that T(W) ⊆ A. We shall need three premises about strong actualization. (1) Whenever W is normal, W ∈ T(W). (2) Whenever W is normal and V ∈ T(W), then V is normal and T(V) = T(W). (3) W is normal iff God exists at W.



Premise (1) is obvious enough. Premise (2) is less obvious. You use it in NON at the bottom of page 181 and the top of page 182, and I hope the following defence of it will capture what you had in mind. One proposition that God strongly actualizes at W is what we may call His record at W: the proposition that specifies, for every

  (Lewis 1973b).

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32.  To Alvin Plantinga, 22 October 1976

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­ ossible deed of strong actualization, whether or not He performs that deed. This p proposition holds at W and V alike. But the record suffices to determine exactly what God does and doesn’t strongly actualize, hence T(V) = T(W). The same line of thought justifies (3), which I don’t think you use but which I shall need: if God exists, then He strongly actualizes a record of total idleness if nothing else. (Not for nothing does ‘G’ look boxy. It’s like an S5 necessity operator except that GA always is false at non-normal worlds. Modalities like this have been studied by Lemmon, Kripke, and others.) Weak Actualization. Presumably it is a contingent matter which world, if any, God weakly actualizes. And presumably it is never the case at a world W that God weakly actualizes some world different from W; only W is actual at W, so only W can in any case be actualized at W. Therefore when you introduce weak actualization, on page 173 of NON, I take it that your definition can be understood this way: (4) It is the case at W that God weakly actualizes W iff, for some X, God strongly actualizes X at W and GX ⁄ W. (At this point the big problem arises, but let it pass for a little longer.) At present we’re interested not so much in asking which worlds God does weakly actualize – answer: ours, if any – but rather in asking which worlds God can weakly actualize. God can weakly actualize W iff it is the case at some world that He does weakly actualize W; but that world could only be W itself. So God can weakly actualize W iff it is the case at W that God weakly actualizes W; that is, iff the right-hand side of (4) is true. Weak Actualization Redefined. Now we have a lemma, provable from counterfactual logic plus assumptions (1) and (2) about strong actualization. You prove it, in effect, in the course of your refutation. But it does wonders for perspicuity to sep­ar­ ate it from the rest of the proof.

(5) The following are equivalent: (a) For some X, T(W) ⊆ X and GX ⁄ W; (b) T(W) ⁄ W.

Proof of (b) given (a). First, if V ∈ T(W), then by (2) V is normal and T(V) = T(W), so T(V) ⊆ X by substitution into the hypothesis that T(W) ⊆ X, so V ∈GX; this shows that T(W) ⊆ GX, and therefore by counterfactual logic T(W) ⁄ GX. Second, GX ⁄ W by hypothesis and W ∈ T(W) by (1), and therefore by counterfactual logic GX ⁄ T(W). Third, we are given that GX ⁄ T(W). From these three premises (b) follows by counterfactual logic. Proof of (a) given (b). If V ∈ T(W), then T(V) = T(W) by (2), so T(V) ⊆ T(W), so V ∈ GT(W); conversely, if V ∈GT(W), then T(V) ⊆ T(W), so since V ∈ T(V) by (1) it

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­follows that V ∈ T(W). Hence T(W) = GT(W). By substitution into (b) we have that GT(W) ⁄ W. Also T(W) ⊆ T(W). Taking X as T(W), (a) follows by existential generalization. This completes the proof of (5). Our lemma (5) yields a simpler definition of weak actualization, equivalent to the original definition, as follows.

(6) God can weakly actualize W (and it is the case at W that God does weakly actualize W) iff T(W)⁄ W.

The Refutation of Leibniz’s Lapse. With the simplified definition under our belt, the hard work is done. We proceed with the refutation. It is safe to say that there is a possible world W that meets three conditions. First, God strongly actualizes something at W, so W is normal. Second, God does not strongly actualize at W every state of affairs that holds at W, so T(W) contains more worlds than just W itself. Third, W is not only possible but entertainable (in the sense of Counterfactuals, page 16), so that A ⁄ B and A ⁄ C are never both true when A holds at W and when B and C are incompatible. One example of such a world W might be a world where God leaves one of His creatures free in the incompatibilist sense that you favor. Then we have:

(7) T(W) contains at least two different worlds, V and U;



(8) Not both T(W) ⁄ V and T(W) ⁄ U;



(9) Both V and U are normal, and T(V) = T(W) = T(U) (by (2));



(10) Not both T(V) ⁄ V and T(U) ⁄ U (from (8) and (9)).

Now suppose by way of reductio that God can weakly actualize just any world, or at least that He can weakly actualize just any normal world. Then He can weakly actualize V and He can weakly actualize U. By (6), that means

(11) T(V) ⁄ V and T(U) ⁄ U, which contradicts (10). This refutes Leibniz’s lapse. So far, so good.

The Dilemma. If we bear in mind that counterfactuals may be contingent, and that we are reasoning partly about worlds other than our own, we should not be content to speak simply of the truth of counterfactuals. We should rather speak of their truth at specified worlds. Let us write ‘A ⁄ B at W’: it is the case at W that if A held B would hold. This will help us to keep track of whether we are talking about the counterfactuals of our own world, @, or about the counterfactuals of other worlds. Let me ask you whether you construe (4) as (4A), which fixes on the counterfactuals of our world, or as (4S), which shifts consideration to the counterfactuals that hold elsewhere.

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32.  To Alvin Plantinga, 22 October 1976

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(4A) It is the case at W that God weakly actualizes W iff, for some X, God strongly actualizes X at W and GX ⁄ W at @. (4S) It is the case at W that God weakly actualizes W iff, for some X, God strongly actualizes X at W and GX ⁄ W at W. What if you choose (4A)? Then the refutation goes through just as before. The only difference is that all the counterfactuals in (4)–(11) are tagged ‘at @’. Technically, all is well. But I complain that this is a peculiar and unmotivated way of defining weak actualization. Why should the counterfactuals of one world, ours, have any relevance to what God does at some other world W, and to what God can do? This is my original worry: if the counterfactuals of our world cramp God’s style, why didn’t He actualize a world with different counterfactuals? But note it reappears not as a hunch that something is wrong somewhere, but rather as an objection directed specifically against definition (4A). What reason can you give for preferring (4A) instead of (4S)? What if you choose (4S), which I take to be the better-motivated version of (4)? Then the refutation fails. (Strictly speaking, I should say that my reorganized version fails, but I’m sure your original version fails in the same way.) All is well with (4)–(10); the only difference is that all the counterfactuals are tagged ‘at W’. But when you get to the reductio, you need substitution instances of (6) with V and U in place of W. That means the correctly tagged versions of (10) and (11) will not comprise a contradiction. They will be: (10S) Not both T(V) ⁄ V at W and T(U) ⁄ U at W; (11S) T(V) ⁄ V at V and T(U) ⁄ U at U. Not only does the reductio fail; we can prove the opposite, given definition (4S). Let W be any normal world whatever. W ∈ T(W) by (1). It is a principle of counterfactual logic – though one that some have disputed – that whenever the antecedent and consequent of a counterfactual both hold at a world, so does the counterfactual. So T(W) ⁄ W at W. This means, by (6) correctly tagged according to (4S), that God can weakly actualize W. God can weakly actualize any normal world; that is, according to (3), any world whatever except one where he does not exist. The counterfactual element has dropped out. According to (4S), weak actualization is nothing more than actuality-cum-normality. You might say that Leibniz is vindicated. Or you might say that even on the better-motivated definition (4S), the idea of weak actualization has proved to be unhelpful. I prefer the latter. Yours, David

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33.  To Frank Jackson, 3 December 1976 [Princeton, NJ] Dear Frank, Many thanks for your paper.1 You’re right that I’d looked briefly at Jack’s copy; but I’m very glad to be able to read it at more leisure, and to know where it will appear. You’re right that I’m not convinced, but I nevertheless like the paper very much. I won’t comment on major issues; mostly you can predict my responses by looking at ‘Counterfactual Dependence and Time’s Arrow’.2 (Did I give you a copy? I forget; but certainly Jack has one, and I think also Brian. Let me know if you’d like me to make a copy for you.) I do have a few small comments. Page 5: sometime I’d like to see someone make the case that there is such a possible world as the Hume world – that is, that laws are independent of the complete history of particular facts. I don’t believe it: see Counterfactuals, pages 73–4. Your paper hints at an argument, but you rightly don’t commit yourself to it, that runs as follows. (1) Suppose I hold that regularity R could not be true without being a law (or, more realistically, suppose I hold that a certain system of regularities couldn’t all be true without all being laws; but let’s stick to the simple case). Suppose R says that all A’s are B’s. (2) You ask me: isn’t it possible that it’s a matter of chance whether A’s are B’s? (3) I reply: yes; for instance W is a possible world where B-hood of A’s is a chance matter and every A has 50% propensity to be a B. (4) You say: well then, there’s a certain small probability, .5n where n is the number of A’s, of all the A’s being B’s. So let Wʹ be a world where that happens: a world that conforms to the probabilistic laws of W in which all A’s are B’s. (5) I agree that there is such a world Wʹ. (6) But isn’t Wʹ a world where R is true but not a law, contrary to supposition? I don’t agree with that. Wʹ conforms to the laws of W, but has an extra law that W lacks, namely R. The question seems to me to concern this assumption. (*) Whenever one world is possible relative to the laws of another, the two worlds have exactly the same laws; the relation of physical possibility between worlds is an equivalence relation. Assumption (*) would give you an argument for the existence of a Hume world, along the lines suggested at the top of your page 5. I reject (*). The account of lawhood in Counterfactuals 73–4, sketchy though it is, is at least enough to explain how (*) could fail. Page 7: try as I may, your Chappell-Gilmour counterfactual3 sounds as if it should be a standard sequential counterfactual. Presumably Chappell did hit the   ‘A Causal Theory of Counterfactuals’ (Jackson 1977).    2  (Lewis 1979b).   viz., If Chappell had not hit the winning run, then Gilmour would have (Jackson 1977, 12–14).

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33.  To Frank Jackson, 3 December 1976

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winning run, say at time t. What if he hadn’t hit the winning run? I can’t hear that as anything except the supposition that, after going as it actually did until t or just before, the course of the game diverged in such a way that neither at t nor later did but got nowhere – he thought my problem was that I didn’t know anything about sport! I don’t but I don’t think that was my problem.) Now there is a sentence (H) ‘However the game had gone, if Chappell had not hit the winning run, Gilmour would have’. I think you think of your original counterfactual as having the same meaning as (H); I’m unable to hear it with that meaning. But it scarcely matters; the question is what to make of (H). I think of it as a sort of tacit quantification, the instances of which are sequential: for any W, if W is a way the game might have gone without too much departure from actuality, and if Chappell didn’t hit the winning run in W, if W had come to pass then Gilmour would have hit the winning run. It’s a more complicated version of this case. There’s a gadget with ten buttons, a switch, and a bulb; you push button four, I flip the switch, the bulb lights. Whichever button you pushed, if I’d flipped the switch, the bulb would have lighted. That is, for each button b it is the case that if you’d pushed b and I’d flipped the switch the button would have lighted. Some think you can say that in English, if not in this case at least in some parallel ones, just by saying ‘If I’d flipped the switch the button would have lighted’. For instance, Martin Tweedale claims that the counterfactuals found in books that ­analyze bridge games normally work like that, and for all I know he may be right. Page 7, bottom. You misrepresent me slightly. In Counterfactuals 75–6 I state the problem of future similarities, mention two alternative solutions to it, but suspend judgement between the two. ‘Perhaps [first solution]. But perhaps [second solution]’. You write as if I’d endorsed the first solution, but I didn’t. Nowadays, as you know, I’ve decided in favor of an expanded version of the second solution. So I then only entertained the possibility, and now definitely disbelieve that ‘we put more weight on earlier similarities of particular fact than on later ones’. Page 11. People do sometimes indulge in back-tracking counterfactuals; though we agree the usual thing is to hold the past fixed. Why do you think that one who backtracks must be confusing counterfactuals with indicatives? Why couldn’t he be using counterfactuals, without confusion, in one of their legitimate senses (or under one of the legitimate resolutions of their vagueness) though not in the most standard way? Pages 13–14. Thomson couldn’t have bowled faster throughout the stretch unless either the laws were violated sometime during the stretch or his adrenalin level had been higher at the beginning; let’s suppose that’s true. You rule out the first alternative. Then you’re stuck with the counterfactual ‘If he’s bowled faster his

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adrenalin level would have been higher at the beginning’. That sounds to me like a typical back-tracker; the sort of thing that I call a legitimate deviant usage and that you call a confusion of counterfactuals with indicatives. And we can apply my test: it permits the paraphrase ‘. . . his adrenalin level would have had to be higher . . .’ or the like. Pages 14–15. What’s the difference between the reversed sequentials which you treat as legitimate counterfactuals of a special kind, and the counterfactual you’d stigmatize as confused ‘If Frank had jumped, he’d ’? Page 22.4 I’ll be OK if I construe (G) If I had been greater, then O would have been less than O* as tacitly quantified, so that it means (G-U) For any x (within broad limits), if I had been greater by x then O would have been less than O* since (G-U) is straightforwardly false on my analysis. Note by way of support that you might as well have paraphrased (G) as ‘If I had been any greater . . .’. It won’t do to confine the quantifier to the antecedent and make it existential, though; (G-E) if it had been that (for some x (within broad limits) I was greater by x) then O would have been less than O* isn’t equivalent to (G-U), presumably is true, and hence won’t do as a construal of (G). You might think, then, that I’m in trouble over a version of (G) that clearly does contain an existential quantifier, namely (G-S) If I had been greater by some amount, then O would have been less than O*. I take it that (G-S) is just as false as (G-U) and (G), and is indeed equivalent to them. So why does it have the existential ‘some’ that suggests (G-E)? I suggest, because it’s derived from (G-S*U) For any x (within broad limits), if x is some amount, then (if I had been greater by x then O would have been less than O*). Out of the blue, this last claim should seem shockingly ad hoc. To make it seem less so, read ‘Adverbs of Quantification’ in Edward Keenan, Formal Semantics of Natural Language.5 4   In the following example, we are to consider a system such that I is the energy input to a system, O is the output, and O* is any value greater than that O takes in the actual world (see Jackson 1977, 16). 5   (Lewis 1975a).

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34.  To Hector-Neri Castañeda, 21 December 1976

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Page 26. If I were interested in doing a reduction to sets of sentences, I don’t see why similarity couldn’t be taken as primitive. I would say to you: to understand what this relation is, it could have been defined if there were possible worlds. Somehow, this dodge would serve to transmit understanding of similarity, from one nonbeliever in possible worlds to another. Page 28. See ‘Counterfactuals and Comparative Possibility’, Journal of Philosophical Logic 2 (1973): 418–446, section 8. Page 29. I’d say the resolution of vagueness switches in the middle of the argument, so no wonder it’s fallacious. Believing in a multitude of resolutions of vagueness is not too different from believing as you do in many kinds of counterfactuals ‘each reflecting a different facet of the one central . . . notion’. Again, many thanks! Yours,

34.  To Hector-Neri Castañeda, 21 December 1976 as from: Princeton University Princeton, NJ [Oberlin, OH] Dear Hector, I must apologize that I have waited until the vacation, when I am away from daily chores at Princeton (and unfortunately also from my typewriter), before sitting down to answer your most interesting letter of 27 October. I do hope this reply will be not too late to continue the discussion begun at my visit. You principally ask what linguistic data I seek to explain. There is no one answer. (For one thing, I would like to explain how a counterfactual analysis of caus­ ation can respect the asymmetry of causation, and this is not a linguistic matter at all.) But I did indeed begin the paper with a linguistic explanandum, and it is not among the pieces of data you mention. Since Downing was the first to observe it, as I noted in the paper,1 let me illustrate it with Downing’s example:2 Father and Son quarrelled yesterday, and today Father is still in a rage. So plainly (1) If Son had asked Father for money today, Father would have refused to give him any.   ‘Counterfactual Dependence and Time’s Arrow’ (Lewis 1979b).   (Downing 1959).

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Philosophical Letters of David K. Lewis But wait. Son is a prideful fellow. The breach in relations prevents him from asking as surely as it would prevent Father from giving. Son would not have asked unless their quarrel had not taken place. But for the quarrel, Father would have been generous as usual. So it seems, after all, that (2) If Son had asked Father for money today, .

I take it that we have two pieces of linguistic data about this example. First, it seems that, while both (1) and (2) are legitimate things to say, (1) is much more clearly and straightforwardly true than (2); (2), unlike (1), requires a suitable context to make it acceptable. Second, it is unacceptable to combine (1) and (2), for instance in arguing from both together. How may we explain why (1) is more acceptable than (2), although (2) is not clearly and straightforwardly false? How may we explain why they cannot be combined? I put forward a hypothesis which, if true, would explain these data. Suppose that counterfactuals are vague, and that (1) and (2) are true under alternative le­git­im­ ate resolutions of the vagueness. That explains why each is somewhat acceptable, since each is true under some resolution. That explains why their combination is totally unacceptable, since no resolution makes both true. Suppose further that one of the alternative resolutions is favored over the other – it is the one that governs our judgements of acceptability except in certain special contexts – and that this favored resolution of vagueness (or, as I call it, the standard resolution) is the one that makes (1) true and (2) false. That explains why (1) is more clearly acceptable than (2) and why (2) is acceptable only in a special context such as the one I gave in stating Downing’s example. I accept this hypothesis, but that is only preliminary to my real interest: the semantics of counterfactuals under the resolution of vagueness that, for example, favors (1) over (2). You ask by what criteria I distinguish standard from deviant resolutions of vagueness. By statistical investigation? No – it might turn out that the deviant reso­ lution is more frequent, though that would surprise me. Rather, the differences between the resolution that governs judgements of acceptability and special contexts only and the one that governs judgements out of context. Nothing turns on my choice of the names ‘standard’ and ‘deviant’ for the two resolutions which, if my hypothesis is right, favor such counterfactuals as (1) or such as (2). Neutral names would have had the advantage of avoiding side issues, but would have had the disadvantage of being less mnemonic. *** I turn now to the question of contraposition. Your suggestions about ‘only if’ conditionals are indeed interesting, though I must say that I find some of your

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35.  To Holly Goldman, 26 December 1976

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ex­amples, especially (14), (15c), and (16c),3 somewhat unidiomatic and consequently hard to grasp. But I think they do not bear directly on the question of contraposition as I, and at least some other writers on conditionals, understand it. This question concerns the properties of the function which is the semantic value (under any one fixed resolution of vagueness) of the conditional construction ‘If it were that . . . then it would be that . . .’. Let this function be f and the negation function on propositions be n; then I take it that f(p, q) = f(nq, np) does not hold in general. Of course there is another function f ʹ such that f(p, q) = f ʹ(nq, np), and it may be that f ʹ is expressed by your ‘only if’ conditional construction. But this is not to say that the original conditional construction obeys contraposition. I hope our disagreement about this is only terminological. Sincerely, David

35.  To Holly Goldman, 26 December 1976 [Oberlin, OH] Dear Holly, Many thanks for letting me have a copy of your paper on deontic logic;1 I’ve now read it. I have mixed reactions. I disagree almost not at all with your philosophical and linguistic points. But as a piece of criticism, I think the paper misses the ­target badly. In recent times, what goes on in deontic logic is that the deontic modalities (socalled obligation and permission, in conditional and unconditional versions) are introduced semantically and their properties are studied. There are various reasons why one might be interested in the deontic modalities. (1) One might be interested in the analysis of ordinary language, and hope that the deontic modalities exactly match the deontic constructions of ordinary language. You and I agree that this is implausible for various reasons. What’s more, I think our view has become almost universal among those deontic logicians who have any interest in ordinary language.

3   (14) Only if the light did not go on, then Jones did not flip the switch. (15c) Only if Jones were not to jump, he would not jump ten feet. (16c) Only if Peter does not come, do not give him the book. (Letter from Hector-Neri Castañeda to David Lewis, 27 October 1976, pp. 3–4.)

  ‘David Lewis’s Semantics for Deontic Logic’ (Goldman 1977).

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In earlier days it was otherwise, maybe; I’m not sure. (2) One might think that the complications of ordinary language have little point, and that the language of de­ontic logic is a better medium for systematic ethical thought. I guess this may be the most important stimulus for the study of deontic logic; I have some sympathy with it. (3) One might be interested in the analysis of ordinary language, think of the deontic modalities as rough approximations to the ordinary deontic constructions, but also hope that the ordinary constructions might be analyzed in some roundabout way using deontic modalities. At the time I wrote Counterfactuals I’d have found this plaus­ ible; now I’d tend to doubt it. (4) One might take a technical interest in the deontic modalities independent of any use they might have in ethical theory or the analysis of ordinary language. This last, though not my only reason for interest in deontic logic, was my only reason for discussing it in Counterfactuals. As noted at the beginning of Section 5.1, I was interested in pointing out analogies between the conditional deontic modalities and counterfactuals. You say that Lewis has proposed a theory, and the theory you mean seems to be that the deontic modalities exactly match the deontic constructions of ordinary language – that is, the hope I just mentioned as the first of many possible reasons to take an interest in the deontic modalities. You correctly say that this theory ‘goes astray’. It does, for the reasons you give and more besides. But why did you think I proposed the incorrect linguistic theory about the deontic constructions of ordinary language? The claim I find on page 100, at the crucial point, doesn’t mention them. What is said is that operators with certain truth conditions ‘may be regarded as versions of the conditional obligation operator of deontic logic, commonly written as O(…/…)’. Then it is said that they may be given certain English readings, these being the customary English readings of the operator O(…/…). Much the same is said for conditional permission, and for unconditional obligation and permission. It would have been a digression, given my purposes, to talk about the match or mismatch between the deontic modalities and the constructions of ordinary language. Consequently I did so only in two brief footnotes, on pages 100 and 102, in both of which I noted discrepancies (but far from all the discrepancies that should have been mentioned if my topic had been the deontic constructions of ordinary language). The trouble is with the terminology that has become standard: the names ‘obligation’ and ‘permission’, and also the standard English readings with ‘ought’ for the so-called obligation operators. I see that one might regard this terminology as tied to the linguistic theory we reject, and not to be used without incurring a commitment to that theory. I don’t regard it that way. I think the situation nowadays (though it was otherwise in the early days of deontic logic) is that these terms have legitimately come to be understood as having a technical use (or cluster of uses) somewhat

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35.  To Holly Goldman, 26 December 1976

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­ ifferent from their ordinary usage, in which they stand for various versions of the d deontic modalities. (It is much like the mathematical use of such terms as ‘computable’, which differs in at least two ways from a more ordinary use.) If the point of deontic logic were mainly to put forth an analysis of ordinary language, it would of course be mischievous to call the deontic modalities by such names as ‘obligation’ when the very point at issue is whether they are exactly the same as what we ordinarily call by these names. But that’s not the main point of deontic logic and scarcely even part of the point any more. If the technical usage and the ordinary usage had nothing much in common, then also I think that the technical usage would be misleading (as if ‘computability’ had become the word for the property of having as values only integers). But I don’t think that’s the case either. The match is imperfect for quite a few different reasons, but it’s good enough to be interesting. In particular, it’s good enough so that many of the same phenomena that crop up in connection with the ordinary deontic constructions turn up also in the simplified approximations which are various versions of the deontic modalities; and good enough so that the refinement of the technical concept of, e.g., conditional obligation may usefully be guided by some of the things we say in ordinary language about what Jesse ought to do given that he’s already robbed the bank. In short, the opposition between free stipulation and accurate analysis of ordinary language is too simple. Simplified ­models have their own interest. And why not name them after their prototypes, if that is the prevailing custom in the field? With the aid of hindsight, it seems to me that I should have put a warning footnote on page 100 much stronger than the one I actually had: ‘Obligation’ is here used in accordance with the usage customary in deontic logic. This so-called obligation differs in various ways from what we call obligation in ordinary language. For one thing . . . That would certainly have avoided misunderstandings. But also it would, I think, have been an unjustified complaint against what I take to be an entirely le­git­ im­ate stretching of ordinary usage, in accordance with tradition, within a project for which I have a considerable sympathy. *** [. . .] I’m sure you’re thinking that both the book and this letter are very wishywashy about what, if anything, is claimed about ordinary language. But why not be wishy-washy? That just wasn’t the topic. The point was that certain deontic mo­dal­ ities, which may or may not have anything to do with ordinary language but which are familiar (modulo slight variations) from the work of some deontic logicians, are formally analogous to counterfactuals. Yours, David Lewis

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36.  To Terence Horgan, 18 April 1977 [Princeton, NJ] Dear Prof. Horgan, Many thanks for your paper on ‘could’-statements.1 I like it very much. I find little to disagree with or object to, apart from your use of the personal pronouns. My own treatment (see the marked parts of the enclosed paper)2 would be in terms of compatibility with facts of a sort determined, or perhaps not perfectly well determined, by context. But that’s equivalent to yours, at least if your accessibility relation is reflexive: let j be accessible from i iff it shares the facts of the selected sort. There’s an excellent paper by Angelika Kratzer arguing for unambiguous but heavily context-dependent ‘can’ and ‘must’. It’s called ‘What “Can” and “Must” Can and Must Mean’.3 It’s unpublished but Kratzer would probably gladly send you a copy. Her address is: Sonderforschungsbereich 99 ‘Linguistik’, Universitat Konstanz, Konstanz, Germany. (There’s a published version in German, but it has a mistake which is corrected in the English version.) I thought at first that I doubted your thesis that there’s a special moral sense of ‘could’. But on re-reading I think you don’t hold that thesis; rather, you talk of the sorts of resolution of vagueness that standardly arise in certain sorts of moral context. So there’s no disagreement. But you might emphasize more than you do the difference between your view and one that multiplies senses. I do think there’s a morally relevant distinction that you leave unmentioned: between ‘could at will’ and ‘could with luck’. Robin Hood could hit the bullseye at will; in no world accessible according to the contextually appropriate relation does he try and fail. Not I; but I could hit it with luck, and do hit it in some accessible worlds. If we both miss, it’s true of both of us in some sense that we could have hit. But Robin Hood is responsible for missing in a way I’m not, because he could have hit it at will. This is why we go for counterfactuals about trying, to capture the ‘could at will’ sense; though I’m also unsatisfied with those counterfactual analyses. There’s a way to get this distinction in your terms, but it seems artificial: Robin Hood, unlike me, could hit the bullseye at will because he hits it in an accessible world where only worlds where his luck is as bad as possible count as accessible. Yours, David Lewis

  ‘Lehrer on “Could”-Statements’ (Horgan 1977).      (Kratzer 1977).

1 3

2

  ‘The Paradoxes of Time Travel’ (Lewis 1976a).

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37.  To Pavel Tichý, 12 September 1977

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37.  To Pavel Tichý, 12 September 1977 [Princeton, NJ] Dear Pavel, Many thanks for your paper on counterfactuals,1 which I’ve read with interest. Let me not comment on your positive treatment; I feel that while I can follow step by step, I don’t have any real grasp of what’s going on. Details apart, the idea of starting with connection as primitive certainly seems a worthwhile approach, and a strangely neglected one. In the critical part of the paper, beginning with the very first sentence, you use a notion which many philosophers seem to understand, but which I do not – the notion of logical priority. Consequently I also don’t understand your conception of vicious circularity. It seems to me commonplace that we come to understand both A and B better when we discover that they are interdefinable: that A is analyzable in terms of B and vice versa. For instance, Quine’s ‘Two Dogmas’ gives us definitions of analyticity from synonymy and of synonymy from analyticity and thereby (though that wasn’t Quine’s intention) helps us understand both. But if that is so, it cannot be that there is some priority ordering such that the only illuminating analyses are those in which the analysis is prior to the analysandum. In the case at hand, if I had a counterfactual analysis of causation (as I think I do) and also a causal analysis of coun­ter­ fac­tuals, I would not fuss about the order of priority; rather I would regard them as two equally useful pieces of knowledge about causation and counterfactuals! Similarly, I don’t understand the thesis that causation is a primitive . . . relation. To me, ‘primitive’ is relational: X is primitive in definitional system Y. It’s like ‘starting point’; Dunedin is a starting point for some journeys and not for others, and I wouldn’t understand you if you said, simply, that it was a starting point. The argument on page 2 seems to make a bit of a jump. Certainly the simi­lar­ ity theory needs to appeal to dissimilarities between our world and worlds that violate its laws. But similarities in respect of laws are not the same as similarities in respect of causal facts as you conceive of them. It’s a non-trivial step from lawful connection to causal connection – consider the lawful connection between two effects of one cause – and your argument only illustrates the similarity theorist’s use of the former. The criticism of the similarity theory on 16–17 seems to me another form of the criticisms we discussed a year ago. So you can predict my reply: intuitions aren’t a reliable guide to the relative importance of respects of comparison, and there are   ‘A New Theory of Subjunctive Conditionals’ (Tichý 1978).

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similarity relations on which w1 is the closest A-world to w0. It is possible that your choice of ‘intensional base’ may impose The criticism of the argument-form at the top of page 27 is very interesting. If it works, it endangers the similarity analysis as much as more direct attacks would do. But I’m not sure it does. I wonder if the counterfactuals A⁄B A⁄C are clearly true after all. Or are we misled by the clear truth of something a little bit different: A* ⁄ B A* ⁄ C where A* means that at some time or other r21 goes on spontaneously? You couldn’t replace A by A* throughout, of course, because you don’t have B ⁄ A*. If you had a case for A ⁄ A* that would bridge the gap and restore the problem; but I don’t think that is either intuitively true or supported by considerations of similarity. What is true is At ⁄ At* where At means that r21 goes on at t and At* means that r21 goes on spontaneously at t; but that also won’t help because it’s essential to the example that you not fix the time but leave it existentially quantified. (I’m not very sure of any of this; it’s a fas­cin­ at­ing problem.) Let us know of your plans if you will be travelling east. It is also possible that we may see you next year in New Zealand; I’m to be in Canberra in June–August 1978, and it’s likely that we can manage time for some travel – but I don’t know how much – in New Zealand on our way to or from Australia. Our best to Jindra. Yours,

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38.  To Robert C. Stalnaker, 13 September 1977

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38.  To Robert C. Stalnaker, 13 September 1977 Princeton University Princeton, NJ Dear Bob, Pavel Tichý has sent me a paper on counterfactuals.1 Along with much else of less interest (but some interest) he gives a plausible counterexample to the inference pattern α

A⁄B B⁄A A⁄C _________ ∴B⁄C

We’re both committed to that pattern, so we need a way out. (I don’t know if Pollock’s treatment is; that might be a line of retreat.) Here’s a circuit made out of relays; I’ve redrawn it from Tichý’s paper in a simpler notation. The square things are relays. They’re bi-stable: that is, they have two states ‘on’ and ‘off’ and they stay in whatever state they’re in until something happens to send them to the other state. Wires with forward arrowheads carry turning-on signals, which operate with a one-second delay; so for instance if b is on now, a will receive a turning-on signal which will cause it to be on a second hence. Likewise wires with backward arrowheads carry turning-off signals, which also operate with a one-second delay; so for instance if b is on now, x will receive a turning-off signal which will cause it to be off a second hence. The triangular thing marked with an ampersand is an ‘and’ gate; it sends a signal iff it receives turning-on signals from both its inputs. (It operates without delay.)

  ‘A New Theory of Subjunctive Conditionals’ (Tichý 1978).

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The actual history of the system is that it has always existed and always will, and at all times x is on and the other relays stay off. Let A mean that a is on at some time or other; let B mean that b is on at some time or other; let C mean that c is on at some time or other. Then Pavel reckons that the premises of our inference pattern α are clearly true, but the conclusion false. Suppose a were on at some time or other, say t. Also x would be on at t; so the gate would operate; so b and c would receive turning-on signals; so they would be on at t+1. There you have the first and third premises. Suppose b were on at some time or other, say t. Then a would get a signal and hence be on at t+1. Second premise. But also x would get a turning-off signal and be off at t+1, so the gate wouldn’t operate at t+1, so c wouldn’t get turned on. Denial of conclusion. Now you’ll see that the arguments I just gave aren’t watertight, but they’re awfully plausible. Can we explain away their plausibility? Maybe like this. Let Aʹ mean that a comes on spontaneously at some time or another; likewise let Bʹ mean that b comes on spontaneously at some time or another. Then certainly we believe, because of the arguments given, that: β

Aʹ ⁄ B Bʹ ⁄ A Aʹ ⁄ C not(Bʹ ⁄ C)

(And this will be OK on the similarity analysis, given my monkey business with perfect match and little miracles.) Is it perhaps so that the original premises and the denial of the original conclusion get their plausibility because we confuse A and B with Aʹ and Bʹ? Of course Pavel has no hope of restoring the counterexample by priming throughout; the A and B on the consequent side have to stay unprimed. The acceptable versions β by themselves aren’t counterexamples to anything we believe. What would restore the counterexample is one of two things. (1) To establish that the original unprimed versions don’t steal their plausibility from the primed versions, but enjoy plausibility in their own right; or (2) to make a case for γ

A ⁄ Aʹ B ⁄ Bʹ

which (since the primed versions imply the unprimed) would give us back the problem using β and three applications of pattern α. I think the two alternatives come to the same thing: what gives the example its plausibility is that we tacitly assume γ all along.

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39.  To Donald Nute, 27 September 1977

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What do you think of the intuitive plausibility of γ? They sound fishy when you focus on them (maybe because A and B, as opposed to Aʹ and Bʹ, are peculiar things to have as counterfactual antecedents at all). On the other hand, if they aren’t plausible why does Pavel’s argument have as much persuasive force as it does? For what it’s worth, I don’t see how a similarity analysis with my favorite sort of simi­lar­ity relation would support γ. To sum up. I’m inclined to hold out; to deny the alleged data; to claim that the example gets its plausibility either by confusing A and B with Aʹ and Bʹ or by tacitly assuming the false premises γ. But I’m not as content with this defense as I’d like to be. Can you see any way to make matters better? Or worse? See you next month. I meant to tell you what I’m going to talk about, but I haven’t time now. I’d better tell you soon (or better, write the paper) because I hope you’ll comment. Yours, David

39.  To Donald Nute, 27 September 1977 [Princeton, NJ] Dear Professor Nute, Thank you for the two papers. One I believe I’ve seen in a previous version, but the other – the one about probability – I have not seen.1 It’s quite interesting. I agree with you that there’s such a thing as a subjunctive probability (of B given A) which is not the same as various other things: not an or­din­ ary conditional probability, not a probability of a conditional (either material or counterfactual), and also not a probability about which we have a conditional. (We might have a conditional: if it were that A, it would be that B has a probability of .5; but that’s not the same as a .5 subjunctive probability of B given A, though they might agree in some cases.) The only thing I’ve written about subjunctive probabilities is very brief: section 8 of a paper called ‘Counterfactuals and Comparative Possibility’, Journal of Philosophical Logic 2 (1973): 437–8. The notion there is world-relative, so it’s more like your

1   The first paper is ‘Simplification and Substitution of Counterfactual Antecedents’ (Nute 1978). The second paper (that is, ‘the one about probability’) is Chapter 6: ‘Subjunctive Probabilities’ (Nute 1980b, 109–27).

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plausw(B/ /A) than like your ‘subjunctive probability’ proper; the latter is of course the (subjectively) expected value of the former, and I’m not sure which notion is more important. What’s the difference? Our usual disagreements about how to describe the structure intuitively – similarity, plausibility, or what? – and corresponding difference about what constraints to place on it. In particular, my avoidance of the limit assumption makes my definition complicated because there’s need for a procedure of taking a limit as the selective structure (spheres, ordering, s-function) tightens down more and more. Also, I let the subjective probability measure do duty also for the measure you call M; I think that’s ok in the example I describe (since I took a case in which the agent remained uncertain) but it’s not ok in general. There’s another thing I wanted to comment on. Throughout your paper, you sum probabilities of worlds instead of integrating probability densities. This certainly makes the mathematics neater – but are you serious about it? It seems to me that surely here the probability is spread over far too many worlds to permit worldby-world summation, in any ordinary case. I wrote ‘It will be convenient to pretend, from this point on, that there are only finitely many possible worlds. That will trivialize the mathematics but not distort our conclusions’ (P of C and CP, page 310).2 In discussing my paper, I wish you’d made clear that I was working under this pretence; I’d hate to have anyone think I didn’t know a sum from an integral, or didn’t know you couldn’t spread probability around with positive shares for uncountably many worlds (or with shares greater than some positive lower bound for infinitely many worlds), or didn’t believe there were many worlds. As for your own work: it seems to me sensible to adopt the pretence (who wants to fuss with integrals, and the math­ em­at­ic­al complication would just obscure the underlying idea). But at one point you do get some mileage out of the fact that you’re summing rather than integrating dens­ities: top of page 15. I think that’s unfortunate. Unless the summations are more than a simplifying fiction, you don’t have a real difference but only an artifact of the simplification. But maybe the point is that you’re relying on the FMP;3 and if so, this reflects a difference of approach. I’m primarily interested in the intended models – the models where W is the set of possible worlds itself, not some other set acting in the role of the set of worlds. So I have to worry about W being uncountably infinite. But to the extent that you’re after completeness theorems and the like, you don’t have to care about the intended models – rather, about all models. Then if you have the FMP you can indeed go ahead as if the worlds were finite in number. That’s fine if it’s the logic   ‘Probabilities of Conditionals and Conditional Probabilities’ (Lewis 1976b).   FMP means ‘finite model property’.

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40.  To Frederick Kroon, 22 February 1978

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you’re after but not, I think, if you also want to say things about the intended ­interpretation. [. . .] See you at Ohio State. Sincerely, David Lewis

40.  To Frederick Kroon, 22 February 1978 Princeton University Princeton, NJ Dear Fred, Your review1 of Plantinga’s GFE2 has been on my desk half a year, I’m afraid. I’m very sorry to have kept you waiting so long. The end of the annual admissions rush, which is today, makes it a good time to get around to other things at last! But I still have no critical reactions – I liked your piece and have nothing to object to. I agree with you that Plantinga gets away with too much in distinguishing consistency proof from theodicy. When he writes that the free will defense ‘solves the main philosophical problem of evil’ I think he’s claiming more than he has any right to. The steepest thing he uses, I think, is not the hypothesis of transworld depravity or the hypothesis that demons cause the natural evil, but rather the notion that a wholly good God might value uncausedness so much that he wouldn’t lift a finger to rescue us from the evil schemes of a Hitler or Satan so long as those schemes were uncaused. It’s not good enough, as you rightly say, to say that he can mean what he chooses by ‘freedom’. The free will defender has a problem explaining why, unless in self-defense, anybody should worship this Fanatic who’s wild about uncaused spontaneity at any price! It’s fun to play around with Leibniz’s lapse and all that, but I suppose the ser­ ious believer should look elsewhere – perhaps combining the consideration you discuss that there might not be a best with Bob Adams’ view that choosing the best is not necessarily required by perfect goodness even if there is a best (ΦR ’72).3 Plantinga would accept the option you offer on page 13 of rejecting the analysis of what God can do in terms of what He does at some world. I enclose a copy of a  (Kroon 1981).   2  God, Freedom, and Evil (Plantinga 1974a).   ‘Must God Create the Best?’ (Adams 1972).

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letter I once wrote to Plantinga.4 His answer to the choice I gave him between the A and S disambiguations was that if the analysandum is something about what God does at some other world, then he takes the S version but if it’s something about what is in God’s power to do, then he takes the A version. In brief: what’s in God’s power is contingent, just as (and indeed because) counterfactuals are contingent. If we ask why God didn’t weakly actualize some world where everyone freely chooses the good, the answer is that it’s not in his power (at the actual world) to do so. That he has the logical possibility of doing so is considered irrelevant. I know that for me, what’s logically possible exceeds what’s in my power; but I don’t claim to be omnipotent. Plantinga claims that God also lacks the power to actualize some of his possibilities; nevertheless there is a sense – and Plantinga claims a sense with historical precedent – in which God is nevertheless omnipotent. Still it seems to me that Plantinga’s solution to Leibniz’s lapse amounts to: omnipotence amounts to less than you might think. The difference I’ve spotted between the GFE and the NON5 versions of the argument about L’s lapse is that in GFE there’s a fallacy of counterfactual transitivity, and in NON that’s bypassed by a rather complicated (and valid) argument. We’ll see you in Auckland early in June; exact dates not certain yet. Yours, David

41.  To Hans Herzberger, 18 August 1978 [Princeton, NJ] Dear Hans, Many thanks for letting me read ‘Counterfactuals and Consistency’.1 I’ve read it with interest, but I’m afraid I’ve ended with very mixed feelings. The point you have in mind surely does have merit. Yes, inconsistent counterfactual theories are counterintuitive; refusal to make the Limit Assumption is tantamount to a tolerant attitude toward inconsistent counterfactual theories; and that’s a demerit of my treatment. Ceteris paribus, it’s better to guarantee the consistency of counterfactual theories. But at what price if ceteris aren’t paribus? Here we probably disagree – you apparently think it’s intolerable to tolerate ‘counterfactual i­ nconsistency’,

  Letter 32. To Alvin Plantinga, 22 October 1976.   

4

  (Herzberger 1979).

1

  The Nature of Necessity (Plantinga 1974b).

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41.  To Hans Herzberger, 18 August 1978

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whereas I think it’s merely unwelcome. I don’t know how to settle such a dis­agree­ ment. I’ll get back to this later. [. . .] Your final sentence, on the other hand, is just right. You can indeed argue for  the Limit Assumption from a plausible premise. It needn’t remain a mere assumption. But how conclusive is the argument? How authoritative is our intuition in favor of ‘counterfactual consistency’? I put it to you that this intuition is suspiciously akin to others, others which we rightly reject though they seemed plausible at first blush. When I was in high school, I read of an infinite hotel: even if every room was full, it still could take infinitely many more guests! Just move the man in #1 to #2, the man in #2 to #4, . . ., and put the new guests in the odd-numbered rooms. Severely counter-intuitive! I was taught that this just goes to show that our intuitions are made for finitude, and can’t be trusted in the infinite case. That still seems to me the right response. Later, in college, I learned something closer to our present problem: you can have a nested sequence of nonempty open intervals with empty intersection. That also seemed very severely counter-intuitive. But I think what I was taught was right. Again my intuitions, shaped as they were by the finite case, were wrong and needed reeducation. Now come closer still to our topic. Consider the ‘when next . . .’ operator. The when-next theory of A is the set of all B such that ‘when-next A, then B’ is true. Doesn’t it seem to stand to reason that when-next theories should be consistent? (Modally, not just formally.) I think it does. This intuition seems just as strong as any intuition I can conjure up that counterfactual theories should be consistent! And yet all the following seem plainly true (and also they come out true under the only natural semantics for ‘when next . . .’). When next it is afternoon, then it will be after 12:00 When next it is afternoon, then it will be before 12:30 When next it is afternoon, then it will be before 12:15 When next it is afternoon, then it will be before 12:07 1/2 So much the worse for the intuition, say I. Yet it seemed just as convincing, offhand, as the one you take as your premise. So isn’t that one also at least a bit suspect? I think so. Still, I’d like to respect ‘counterfactual consistency’ – if the price is right! Sincerely, David Lewis

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42.  To D.M. Armstrong, 23 January 1979 [Princeton, NJ] Dear David, My appointment at Monash runs from the day of my arrival – 2 June, most likely – to the day of my departure immediately after the AAP. Frank Jackson offered me ‘lots of opportunity to travel around’, and we mean to take him up on that to the greatest possible extent. However all my efforts so far to get him to tell me just what my duties at Monash will be have failed. So I presume one or more visits to Sydney will be possible – but when, how long, how many, I can’t say until Frank tells me something more definite. Maybe he will soon: I asked him again two weeks ago in connection with the possibility of a trip to Perth, for which the sooner we book the train the better. I’ve been thinking lately, under the stimulus of a course by Saul Kripke, about spinning balls of homogeneous matter. I’d like to have a go at adapting your treatment to a broadly Humean view as follows: if two possible worlds are alike as regards their distribution of qualities over space-time, then also they’re alike in all other ways – laws, counterfactual dependence, causation, persistence of matter. But I don’t have a copy of your talk (I think it was at the 1976 AAP) about the subject. I’d much appreciate either a reference or a copy.1 (So, I think, would Saul.) All I’ve ever written about what makes a regularity into a law of nature is in Section 3.3 of Counterfactuals. I enclose a copy of the section. Since I don’t think it’s a good idea to explain lawhood in terms of counterfactuals, the treatment of lawhood is independent of the theory of counterfactuals. I don’t think the theory of lawhood is especially dependent on possible worlds either, though I do think that if it correctly selects the laws of this world then also it correctly selects the laws of other worlds. I want to respect the broadly Humean view mentioned above: laws are supervenient on matters of particular fact (distribution of qualities) so no two worlds have different laws but are exactly alike in matters of particular fact. I also want to respect the contingency of laws. Indeed, a twofold contingency: a law of world i (our world, as it might be) might be a non-law of another world j because false at j, but also might be a non-law of yet another world k by being true at k as an accidental generalization. It should be clear from Section 3.3 how that might happen. Incidentally, let me warn you against a misunderstanding that has befallen some readers, e.g. your ex-colleague Molnar if reports I’ve heard are true. Contrary to 1   ‘Identity Through Time’, presented at the 1976 Australasian Association of Philosophy (AAP) conference. See (Armstrong 1980).

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43.  To D.M. Armstrong, 13 March 1980

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what is suggested by the quote from Ramsey, the Concise Encyclopedia of Unified Science is not expected to be a deductive system with all truths as theorems! I think Ramsey never meant to suggest that; but if he did (in which case his view doesn’t make sense) nevertheless I don’t. See you soon. Yours, David Lewis

43.  To D.M. Armstrong, 13 March 1980 Princeton University Princeton, NJ Dear David, You say that what makes it a law that all A’s are B’s, if law it is, is that a certain relation holds between universals; perhaps between A and B, perhaps between A1 and B1, A2 and B2, . . . where all A’s have A1 or A2 or . . . and likewise for the B’s. You call the law-making relation necessitation (or involving) but I think those names premature, so for now I’ll just call it Solon. That’s a mere proper name, meant to be without descriptive content. Maybe there’s another relation between universals: the relation of constant conjunction, whether lawful or accidental. I name it: Constance. Necessarily, all A’s are B’s if and only if A bears the relation Constance to B (where A and B are universals). No mystery about how that can be so: Constance just is the relation such that it’s so. I realize that you may doubt that there is any such relation as Constance; but let that pass. I think what I will say presupposing the existence of Constance could be put neutrally, and I don’t think it will matter to what follows, except as noted. If you thought that Constance was the law-making relation, you’d be a regularity theorist; for Constance is merely the regularity-making relation. You’re not a regularity theorist. So I can ask you what you take to be the connection between the two relations Solon and Constance. You’re committed to the truth of (*) For any universals A and B, if A bears Solon to B then also A bears Constance to B. But what is the status of (*)? In effect, this is the question you raise in the next-to-last paragraph of your Russellian Society paper.1 But I’m puzzled by your answer. ‘If   ‘Laws of Nature’ (Armstrong 1979).

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[Solon] holds, however, then, of logical necessity, the corresponding uniformity holds. For [Solon] is the relation which is manifested in particulars in this way’. No; Constance is essentially the relation which is manifested in particulars in this way, and on pain of falling into a regularity analysis you must grant me that Solon isn’t Constance. Solon is manifested in particulars in this way – by uniformities – because Solon always is accompanied by Constance. That is, because (*) holds. But if it’s to be ‘of logical necessity’ that there’s uniformity if Solon holds, then (*) must not only hold but also hold of logical necessity. Is (*) necessary in the strictest sense, logically or metaphysically or absolutely necessary? How can it be? A’s bearing Solon to B and A’s bearing Constance to B look like two different states of affairs of which one could occur without the other, distinct existences. They’re on a par with x’s being a conductor of heat and x’s being a conductor of electricity, which you agree are contingently, though lawfully, conjoined. Perhaps (*) is necessary because, although Solon and Constance are not the same, Constance is part of Solon. But then I ask what you take to be the connection between the rest of Solon and Constance. Does the rest of Solon necessitate Constance? If so, how? Having subtracted Constance from Solon, we should have distinct existences now if we didn’t before. Henceforth, when I speak of Solon, I think what I say will still be right if instead I said ‘Solon, or the rest of Solon if Constance is part of Solon’ but I won’t bother to say it. It might be analytic that if A necessitates (or involves) B, then also A bears Constance to B. But (*) certainly isn’t analytic in the same way. That’s why I thought it premature to give Solon a name with descriptive content, a name he wouldn’t deserve unless (*) held. It clouds the question of the modal status of (*). Is (*) necessary not in the strictest sense but in some weaker sense – naturally or physically or causally or nomically necessary? Maybe so, but I think that gives up the point of your proposal. You might as well have been content at the start to say that laws are regularities that are naturally (or whatever) necessary. More generally, is (*) a law, where lawhood in the case of (*) is to be explained in some other way than yours, or not explained at all? Then again I say that you might as well have used the alternative explanation, or non-explanation, from the start, not only for (*) but for all laws. Or is (*) a law, where the lawhood of (*) is to be explained in your way? You could say that (*) is a law because Solon (or is it Solon’s big brother?) holds between Solon and Constance. But that starts a regress. Besides, at this point it does matter if there’s no such universal as Constance. What’s left? Is (*) a mere regularity, not a law and in no way necessary? Or is it a regularity distinguished only by earning a place in some nice theory? Certainly a

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44.  To D.M. Armstrong, 10 April 1980

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regularity like (*) in form, but with some other relation of universals in place of Solon, could hold as nothing but another cosmic coincidence. Why not? But if (*) is a mere regularity (or even one that earns a place in theory) and if, as you think, such regularities aren’t explanatory, then (*) isn’t explanatory. It’s no good saying that this A is a B because A bears Solon to B, if it’s a mere accident that Solon is accompanied by Constance. And it’s little better to say that this A is a B because A bears Constance to B and also A bears the rest of Solon to B, if it’s a mere accident that the rest of Solon is accompanied by Constance; if so, the rest of Solon does no explanatory work and you might as well have said, as the regularist does, that this A is a B because A bears Constance to B. In either case, Solon does not deserve the name of necessitation; so although it might indeed be explanatory to say that this A is B because A necessitates B, you’re not entitled to say that, if (*) is accidental. I admit that there’s something a bit unsatisfying about the Regularity view of laws, even in the fancy versions Smart and I favor. Your first critical heading, ‘lack of an inner necessity’, indeed seems to be a way in which any Regularity view, however fancy, will remain a bit counterintuitive. (Your other points seem to me either to come back to that or to be remedied by fancy versions.) But if I’m right, you’re no better off. The problem is only postponed, and returns when I ask you how there can be any inner necessity to (*). Yours, David cc: Smart, Tooley, Railton

44.  To D.M. Armstrong, 10 April 1980 Princeton University Princeton, NJ Dear David, We reach Canberra 1 July, you and Jenny leave 9 July. So I’m of two minds. We’d like very much to see you, and could easily come up to Sydney for a brief visit any time in 2–8 July. But if you’re like us, the time just before going away is pretty hectic and the last thing you’d need is visitors on your hands! Right; I think your best answer to me is that (*) is necessary in the strictest sense; Solon necessitates Constance more in the way that redness necessitates color than in the way that decapitation necessitates death. I find it mysterious how that can be so. Mysterious, but no worse; I haven’t a knock-down argument that it couldn’t be so.

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I didn’t mean to make it definitional of ‘distinct existences’ that there can’t be necessary connections between them. I mean that to be a substantive thesis, which I believe but can’t do much to defend. I don’t want to argue from distinct existence to separability in thought to possibility of one without the other, because I think that conceivability is a poor guide to possibility. (To some extent it seems to me that I can imagine impossible things, and to some extent it seems to me that I can’t imagine some actual things, e.g. curved space-time.) But if conceivability is a poor guide to possibility and I haven’t a better guide to put in its place, then I’m not in a good pos­ ition to argue for theses about possibility, though of course I still believe some. When can universal X necessitate universal Y, so that it’s strictly necessary that whatever has X has Y? Two cases seem clear to me, but I think only the first should suit you. (1) When X is conjunctive, and is the combination YZ. I argued that this might be the case of Solon and Constance, but if so the original problem returns as a problem about the relation of Z and Y, (Solon-Constance) and Constance. (2) When Y is disjunctive, and X is one of the disjuncts. That seems to me the case of Red and Colored, or the case of P and Cʹ, where P is a complex property and Cʹ is the property of having some or other complex property. (Perhaps that’s not a fair rendering of your ‘. . . is in some degree complex in nature’, but I’m not sure how else to render it.) However, it seems to me that your rejection of disjunctive universals goes far enough to eliminate all candidates for necessary connection of the second kind. In particular, II 1171 seems to commit you to the denial that the universal Red necessitates the universal Colored (or even that some fully determinate shade of red necessitates Colored) on the grounds that there is no such universal as Colored. True, the discussion of II 120–72 suggests that there may be common parts to at least some of the determinates under a determinable; but if this leads to necessary connections of universals, they are of kind (1). How about color and extension? Rather, a fully determinate shade and extension, so that at least the universal doing the necessitating is one that exists according to you. I take it that a color turns out, a posteriori, to be a shape – not just a shape of a hunk of matter, but a shape of fields and a distribution of charge – still, a shape. (Of course we’re not aware of it as a shape, but you and I agree that it still might be one.) So the question is: how does having a certain determinate shape necessitate being extended? And that seems to me yet another determinate-determinable case. So long as you oppose disjunctive universals, it seems to me that you cannot provide cases of necessary connection of kind (2): which might possibly – though I don’t quite see how – serve as the model for the necessitation of Constance by Solon.   Universals and Scientific Realism II: A Theory of Universals (Armstrong 1978b, 117).   (Armstrong 1978b, 120–7).

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45.  To Jonathan Bennett, 7 November 1980

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If on the other hand you admit disjunctive universals freely (and negative ones, which seem to me to pose the same issues) you then provide me with a general means of subtraction, thus enabling me to push my question about Constance and (SolonConstance) without any special assumption that Solon is conjunctive. The formula is: A – B = not-B or A. --------------The problem about the law connecting two quantities, of which only finitely many values are instantiated in the history of the universe, seems to me to go only against a simple regularity theory; not against one that requires laws to earn a place in a good total theory. Best to Jenny, and from Steffi to both. Yours, David

45.  To Jonathan Bennett, 7 November 1980 [Princeton, NJ] Dear Jonathan, Ginet’s account of explaining why A rather than B (which you’re inclined to take as correct on one disambiguation, though not on all) is something like this: I can explain why A rather than B by producing something common to (more generally, by giving information about the common part of) the causal histories of A and of not-B.  Does that seem right? When A and not-B result from a choice, as in the ex­ample we mostly discussed, it seems that an appropriate belief or desire of mine (or something that caused me to have some belief and desire, e.g. the sending of an invitation) might be the requisite thing common to the two causal histories. The invitation from Monash, and beliefs and desires caused thereby, belong to the causal history of my going to Melbourne and also to the causal history of my not going to, say, Oxford. My worry about this proposal is that the condition is too easily met. I think anything in the causal history of A will also be in the causal history of not-B; even something which would equally have been in the causal history of B if that had happened. Thus I think my desire to escape the Princeton hot, muggy summer belongs to the causal history of my not going to Oxford – it’s among the causes of my decision to go to Melbourne, which in turn is a cause of my not going to Oxford – despite the fact that Oxford is just as good an escape from the Princeton summer, and hence

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my desire to escape the summer doesn’t explain why I went to Melbourne rather than Oxford. Perhaps, but this I’m less sure of, the point can be reinforced by asking what kind of thing a not-doing is. Suppose a particular occurrence of not-Φing is taken as the complex of (i) the occurrence which is my doing whatever I did instead of Φing, and (ii) the facts, occurrences, or whatnot in virtue of which whatever I did instead is incompatible with my Φing. Thus my not going to Oxford – the particular not-goingto-Oxford which in fact took place – consists of my going to Melbourne together with the facts of geography, transport, finance . . . in virtue of which I couldn’t do both. If not-B is the complex of A and C, then of course the causal history of A is included in the causal history of not-B. But I don’t want to rely on this, being uncertain whether not-doings ought to be analyzed as complexes in this way; so I think it’s good that in such cases as the previous paragraph’s, it seems directly plausible that enough of the causal history of A is included in the causal history of not-B to defeat the Ginet proposal. Yours,

46.  To Elliott Sober, 23 February 1981 Princeton University Princeton, NJ Dear Elliott Sober, Thank you for your note on ‘Equilibrium Explanation’.1 I am sorry; for the present, I do not give you permission to quote or refer to ‘Causal Explanation’, since it is both unpublished and not in final form. But I hope you won’t have to wait long. Why don’t you write me again in early May – I might be able to give you the go-ahead (and a revised, final version) then.2 Why ‘arctic penguins aside’ (page 5)? I thought penguins in the wild were strictly southern hemisphere, the nearest approximation in the arctic being auks and puffins. In view of your address I assume you know whereof you speak, but tell me more. On the case of Walt, I differ with the step you take after ‘presumably’ toward the bottom of page 3. Walt’s supply of antibodies is Walt’s immunity. Yes. Then is  Walt’s being immune the same as his possessing those antibodies? No. It’s a  (Sober 1983).   2  See (Lewis 1986d, 214–40).

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47.  To Thomas Nagel, 4 April 1981

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­ roperty-instance which still would exist even if Walt were protected by other antip bodies, or by something that wasn’t an antibody at all. Walt’s immunity therefore isn’t the same thing as Walt’s being immune. Now admittedly there’s a bit of linguistic regimentation here; perhaps either English phrase could denote either thing. But, call them what you will, the point is that there are two different entities. One is a particular occurrence, but isn’t causally explained by his supply of antibodies because it is his supply of antibodies. The other isn’t his supply of antibodies – it could exist if he had no antibodies but were otherwise protected – but that one isn’t causally explained by his supply of antibodies because it isn’t a particular occurrence. In fact I don’t think it has any causes or effects. The second thing is, as you put it, constitutively explained by the first; further, it’s partly-causally-partly-constitutively explained by whatever causally explains the first. I have some idea what more to say about this, but I think I’d better save that for another paper and try to get this one out – none too soon, I think you’ll agree. It will come as no surprise that I think your equilibrium explanations are causal, though indeed no definite causal history is produced. I set a lower standard than you wish for what is to count as information about the causal history, but I don’t think it’s a standard so low as to ‘utterly trivialize’ my main thesis. The test is: does this information eliminate any possible causal histories? (An alleged explanation that would eliminate no causal histories would be, for instance, the deduction of height of tower from length of shadow.) An equilibrium explanation does eliminate some possible causal histories, though the remaining ones are many and varied. Yours, David

47.  To Thomas Nagel, 4 April 1981 [Princeton, NJ] Dear Tom, Unlike some compatibilists, I don’t want to commit myself to analyzing ‘could have’ as ‘would have if I’d had suitably different motives and beliefs’. So I say that I could have raised my hand, but I needn’t say that I would have done if my motives and beliefs had been different. Let me also say that my motives and beliefs could have been different; I needn’t say that they would have been if some earlier motives and beliefs had been different, though that also might be true.

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You ask what about: ‘It could have happened that I raised my hand’. I find that ambiguous and unidiomatic enough not to be subject to decisive intuitions as it stands. Does it mean ‘I could have raised my hand’? Then it’s true. Does it mean ‘My raising my hand was consistent with the history and the laws’? Then it’s false. On the second reading, a compatibilist is indeed committed both to ‘I could have raised my hand’ and to ‘It could not have happened that I raised my hand’, but shouldn’t find this at all surprising. It’s scarcely even a consequence of compatibilism – just a restatement of it. I think you probably had in mind a third reading, perhaps something conditional of the sort considered earlier in the letter: ‘I would have if I’d wanted to’, or something of the sort. I question whether that’s a reading of ‘It could have happened . . .’, but I do think it’s something not settled one way or the other by the facts that I could have raised my hand and that I was predetermined not to. Yours,

48.  To Peter van Inwagen, 7 April 1981 Princeton University Princeton, NJ Dear Peter, Many thanks for your letter, paper, and book ms. pages.1 The speed-of-light law (soll, henceforth) is a poor candidate for something that one can weakly render false, for a couple of reasons. One is that it doesn’t have much to do with the way the brain works; so it seems implausible that a tiny, localized divergence miracle in the brain – which seems the right place for a divergence mir­ acle that might have happened if I’d done something I was predetermined not to do – would violate soll. More likely it would violate laws having to do with the biochemistry of neuron firings. The second reason is that soll isn’t a very comprehensive law; even if violating soll is one way to get a minimal divergence miracle, it’s unlikely to be the only way; and if it isn’t we’ll get at most a might-counterfactual from my doing the thing I was predetermined not to do to the violation of soll, not a wouldcounterfactual. I don’t know if these considerations make it such a poor candidate that, necessarily, nobody ever is able to render false soll in the weak sense; or if a case of this   From a book manuscript of An Essay on Free Will (van Inwagen 1983).

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48.  To Peter van Inwagen, 7 April 1981

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ability could be devised under suitably fictitious physics and brain physiology. I’ve some notion how to get around the first consideration: imagine the Velocitarians, who store information in the brain by setting little particles rotating very, very fast. Thus soll has more to do with the way their brains work than with the way ours do, making it plausible at least that if a Velocitarian who was predetermined not to raise his hand nevertheless did raise it, then it might be that the divergence miracle violated soll. That doesn’t help you get around the second consideration and promote the ‘might’ to a ‘would’. Three truths: (0) There never was a time when you could have arranged matters so that you visited Arcturus IV yesterday. (1) Your not visiting Arcturus IV yesterday is entailed by soll and the state of affairs before your birth (for short: history). (2) Soll is a law. You say that (0) follows from (1) and (2); I doubt that, but don’t deny it. I suggest that more premises are needed to make the thing formally valid; if the extra premises are necessary it’s fair to leave them out, if they’re merely true it’s no fair. Of course many additions of premises would do the job, but the ones that look to me to be of interest are these. (3) For anything you ever could have done, if you’d done it the state of affairs before your birth would have been just the same. (4) If soll is a law, then there never was a time when you could have rendered soll false in the weak sense. As for (3): I grant its truth, doubt its necessity, but don’t want to press the issue. I don’t want to stake my compatibilism on my views about the possibility of time travel and the like. As for (4): I grant its truth and doubt its necessity; for the reasons above, I only doubt and don’t deny its necessity. Probably it’s obvious how the argument from (1)–(4) to (0) goes, but let me just write it down. H: history. V: you visit Arcturus IV yesterday. L: soll. Can: there was a time at which you were able to arrange matters so that. Cwrf: you could at some time have rendered false in the weak sense. Law: it is a law that. (1) ¬◇(HLV) Premise (2) Law L " (3) ∀X(Can X ⊃ (X ⁄ H)) " (4) Law L ⊃ ¬Cwrf L " (5) Can V Hypothesis for reductio (6) V ⁄ H 3, 5 (7) V ⁄ ¬L 1, 6, uncontroversial logic of conditionals (8) ¬∃X(Can X & X ⁄ ¬L) 2, 4, definition of Cwrf (9) ¬(V ⁄ ¬L) 5, 8 (0) ¬Can V 7 and 9 complete the reductio

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You pass to the * case, in which soll gets replaced by the conjunction of laws, and then to the ** case, in which visiting Arcturus IV gets replaced by an arbitrary action. Formally, of course, no change. What does change is the status of the auxiliary premises. (4) is clearly true, and perhaps also necessary, whereas I think (4*) is false. No change in (3), of course, since the substitutions don’t affect it. If the second step, * to **, makes a difference, I suppose it’s a difference to the prospect of finding some other auxiliary premises to do the job instead of the ones I’ve been considering; it can’t make a difference in any other way. So to the dilemma at the bottom of your ms. page 3–29, I reply in the first way. There is a difference between soll and the conjunction of all laws, namely that the latter is more vulnerable to minimal divergence miracles than the former; because of this difference, my objections to the First Argument don’t carry over to the Arcturus Argument. *** I don’t think your move of ‘building the past into’ the definition of ‘can render false’ is a good idea. Let’s speak of the weak version, the strong version, and the official version of the First Argument, according as ‘can render false’ is understood in my weak sense, my strong sense, or the sense of your official definition on 3–20. I think the official version begs the question in a way that the weak and strong versions don’t. To beg the question isn’t to argue from premises; to argue from premises that fail to be neutral with respect to the conclusion; to argue from premises that your opponent is free to deny; or to argue from premises that your opponent probably would deny. (It isn’t a fallacy to argue, or to argue validly, or to argue with a free man, or to argue with a stubborn man.) The most promising account of begging the question supposes that there’s a dialogue going on and doesn’t directly apply to a monologue (or -graph): there’s a status of being under challenge, there are ways for a participant to give something that status, and there’s a rule against using challenged premises, the point of which rule presumably is to avoid going on and on in a deadlocked condition. We imagine the dialogue your text would be part of, if it were part of a dialogue; and in that dialogue it seems that Premise 6 of the official version, unlike the premises of the weak and strong versions, would automatically come under challenge as soon as compatibilism itself was in dispute. To put the point more simply, official Premise 6 is awfully close to an explicit denial of compatibilism. (To be precise, it denies the sort of ability the compatibilist thinks possible, for a case in which that ability would exist if it ever could.) The official version of the argument covers very little distance, and much of its structure seems superfluous. For what does official Premise 6 mean? Note that we can define ‘It is determined that X’ as ‘It is not possible in the broadly logical sense that not-X and that the

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past have been exactly as it is in fact was and the conjunction of (actual) laws be true’. That’s instantaneously equivalent to the alternative definition: ‘some true historical proposition and some conjunction of laws jointly imply X’. So official Premise 6 can be put this way: ‘it is not within J’s power to arrange . . . in some way such that it is determined that he not arrange . . . in that way’. Whichever version you give him, the compatibilist denies a premise. Premise 6 for the weak version, Premise 5 for the strong version, Premise 6 again for the official version. But when he has to deny weak Premise 6, we discover something interesting, and something advantageous to you; for weak Premise 6 has some intuitive plausibility, and it wasn’t altogether obvious that the compatibilist would have to deny it. So the weak version has some bite to it. And when the compatibilist has to deny strong Premise 5, we again discover something interesting and to your advantage: that the compatibilist has a problem explaining why he wouldn’t be reversedly causing a divergence miracle. So the strong version also has some bite. But when the compatibilist has to deny official Premise 6, we only discover that he is indeed a compatibilist. Nothing gained, either for your cause or for our understanding of what’s at stake. No bite. What the official definition of ‘can render false’ does for you, I think, is to make Premise 5 completely safe and focus the issue on 6. I take it that 1–4 are safe in any case, though I take it you’ve had some flak on 4. But the defence of 6, once the issue is focussed on it, is no different from the defence of incompatibilism itself. The rest of the argument looks like idle wheels. The problems for compatibilism that the weak and strong versions reveal – inconclusive, but still problems – aren’t revealed by the official version unless they recur within the defence of 6. Finally, I think your reason for ‘building in the past’ on 3–19 and 3–20 isn’t strong. First, I was surprised to find you appealing to linguistic intuition about the notion of being able to render false; I thought this was introduced terminology and it didn’t matter whether one respected its meaning in ordinary language, if any. More important, the desired conclusion that Anwar could have rendered it false that the prophecies were correct could also be obtained by taking the weak sense instead of the official one. You imply that such counterexamples could be dealt with in more ways than one; right, and I think another way – the weak version – leads in a more interesting direction. (Still another way is to deny that Anwar, by himself, could have rendered it false that the prophecies were correct; what’s true is that Anwar and Nostradamus could have rendered it false together, Nostradamus doing his part by making the prophecies he did and Anwar then doing his part by smashing the Sphinx.) *** I agree with you that the weakest link in the separate argument for incompatibility of responsibility and determinism is (B), the rule that distributes N over ⊃. I can

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simplify the choice of counterinstances you offer me, eliminating the uncertainty about which is the counterinstance. For I think it’s clear that N(SL); and if determinism is true, then □(SL ⊃ US nuked Japan), so N(SL ⊃ US nuked Japan); but not N(US nuked Japan). My first thought was that this was the same old stuff and got the same old reply, mutatis mutandis, since N could be defined as ‘no person, and no group, ever could have rendered it false that . . .’. But that’s wrong. In fact, the definition fails both ways (and not for reasons that force us to fuss over the senses of ‘can render false’). Left to right: N(SL), but I myself could have rendered SL false by raising my hand, if indeed I was predetermined not to, in all the senses we’ve considered. Right to left: we can become morally responsible for consequences we could not have prevented by stepping in and doing what some preempted alternative potential cause would otherwise have done. Come what may, Satan would see to it that M: there is a certain high level of misery in the world. But he prefers to stand idly by and let cruel people do his work for him, relishing the cruelty and the leisure as well as the misery itself. Still, the dirty work will be done one way or another, there’s nothing anyone (any person – Satan’s not a person) can do, or ever could have done, about that. Fortunately for Satan, there are plenty of cruel people and he needn’t do a thing. Then not N(M), although no person, and no group, ever could have rendered M false. The case of Satan gives us another counterinstance to (B). Let S specify enough about Satan’s intention, the laws he operates under, his powers, his circumstances, to entail that M: given S, necessarily the specified level of misery is going to be reached one way or other. Then □(S ⊃ M), hence N(S ⊃ M). But also N(S): no human made Satan, no human ever failed to tame him, . . . . Yet not N(M), since the cruel people gratuitously took upon themselves the responsibility for the misery that would have come about in any case. I can hear someone say: no, strictly speaking the cruel people aren’t re­spon­ sible for M itself, for the fact that the misery is there; they’re really responsible for the different fact that they’re the ones who made the misery. But I think the ‘strict speech’ advocated is reformed language, not our ordinary language. (The second part is right in any case. Yes, they’re responsible for the fact that they made the misery, and that’s the issue.) I think the reformed conception of responsibility, which turns more on causal dependence and less on causation than our ordinary one, may indeed by a more enlightened, more just conception than our ordinary one; be that as it may, it’s different. Yours, David

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49.  To Allen P. Hazen, 8 April 1981

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49.  To Allen P. Hazen, 8 April 1981 Princeton University Princeton, NJ Dear Allen, I remember intending to send you ‘Causal Explanation’1 but I don’t remember if I ever did. Tell me if I didn’t. I think your array-of-automata example is convincing;2 I was indeed relying on the fact that the world isn’t (a credible deterministic world wouldn’t be) like that when I said that if I’d raised my hand I wouldn’t have reversedly-caused a divergence miracle, since there are many ways the divergence miracle might have been accomplished, no one way that it would have been. This suits me – as you know, I’ve been saying that the asymmetries of causation and counterfactuals are imposed by contingent global features of the world. Your point fits into that, though it’s different from what I’d been saying about the asymmetry of overdetermination. No worries for the defence of compatibilism, I think. Maybe the ‘logic of compatibilism’ had better be noncontingent, but that doesn’t mean that the compatibilist (or soft determinist) can’t rely on empirical features of the world. Say that compatibilist freedom occurs whenever someone can do something he’s predetermined not to do. The soft determinist says that it sometimes does occur – certainly that’s empirical. The compatibilist says at least that it’s logically possible for it to occur – that’s not empirical, but of course he can help himself to the most favourable possible world to be the world where it does occur. But the more important thing the compatibilist says is that it’s epistemically possible that compatibilist freedom occurs (taking it to be not yet known, despite some strong evidence, that the world is extremely indeterministic); or that it would occur in the closest deterministic world to ours. And for either of those claims, of course he can help himself to the empirical information that our world isn’t like the array of automata. However, a question arises about something else in my paper. Someone in the array-of-automata world is predetermined not to raise his hand. Had he raised it, a certain definite divergence miracle would have occurred. Does that mean that he – unlike a predetermined free agent closer to home – would have caused a miracle if he’d raised his hand? If so, should I retract my agreement that nobody could do   (Lewis 1986d, 214–40).   The example is of a world that consists of a finite (or infinite) array of automata. There are things with states characterized by machine tables but without inner structure such that, as Hazen writes, ‘the state one of the little buggers goes into at a given moment and the signal it emits at that moment are determined by the state it went into at the preceding moment and by the signals emitted at the preceding moment by its twelve (spherical close-packing) neighbors’ (Letter from Allen P. Hazen to David Lewis, 22 March 1981, p. 2). The Game of Life is a two-dimensional version of such a world. 1 2

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something that would cause a law-breaking event? Or should I grant that the incompatibilist argument shows that he couldn’t have raised his hand, although it doesn’t show the corresponding thing about the predetermined agent closer to home? I think probably the way to go is to deny that if he’d raised his hand (event h) he’d have caused the miracle (event m; o: occurs). Yes, -o(h)⁄-o(m) and o(h)⁄o(m); but the right question is whether o(h)⁄(h caused m), that is, roughly, whether o(h)⁄(o(h)⁄o(m)) and o(h)⁄(-o(h)⁄-o(m)).* And the second of the ­double counterfactuals looks doubtful (though your fictitious physics makes it more plausible than otherwise). That is, the paragraph ‘We do not have . . .’ on page 6 is beside the point; the real issue is the one addressed in the following paragraph. Yours,   David

50.  To Keith Lehrer, 9 April 1981 [Princeton, NJ] Dear Keith, Thank you very much for your two papers, which I’d missed and which I like.1 I take the point that my principal move in ‘Are We Free . . .’2 resembles yours of page 199 of ‘Preferences . . .’. (That’s what you meant, I think, though you used the number of the other paper.) The resemblance deserves a footnote.3 But though the moves start alike, we continue differently. That is, we agree in distinguishing: (1) I could have done so-and-so, and if I had, the laws (or history) would have been different, (2) I could have brought it about that the laws (or history) would have been different. We grant that (1) is true; but (2), the one that would embarrass us, is still false. (2) adds some false extra content. I say the false extra has to do with causation from my action to the law-breaking miracle (or the alternative past). But you make it a matter of conditionals, as witness your immediately following sentence – ‘On the contrary, it is false that if S had preferred that either the laws of nature not be as they are or that the state of the universe at t not be as it was, then one of these conditions would have been satisfied’. *  What’s at issue is whether ‘would have caused’ has the meaning generated from the meanings of ‘would have’ and ‘caused’; or whether, as is somewhat plausible, it should be analyzed whole in terms of dependence among unactualized events.

  One of which was: ‘Preferences, Conditionals and Freedom’ (Lehrer 1980).   ‘Are We Free to Break the Laws?’ (Lewis 1981).    3  See (Lewis 1981, 116, n. 3).

1 2

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51.  To Keith Lehrer, 10 April 1981

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I don’t think I buy that. I think the conditional you say is false might be true. The Guru has fuddled you into thinking that it makes sense to speak of violations of laws and changes of the past; and he’s even led you to think that you could bring these things about. You have only to raise your hand – right now! If you’d preferred a different past of different laws, you’d have raised your hand; but you were so well content with the past and laws as they are that you didn’t do it. In fact, you are determined to be content and leave your hand unraised. Had you preferred that the laws and past be otherwise, there’d have been a divergence miracle before you had that preference and acted on it, so the laws and past would have been different. (It’s just like any counterfactual about something happening that was determined not to.) But you still wouldn’t have, couldn’t have brought it about that the laws and past were different. I think we can leave aside matters of higher-order preference in this case; suppose them to be such as to make you free, and suppose they would have been so also in the counterfactual situation. The Guru isn’t much as a teacher of supernatural powers, but as a teacher of inner harmony and self-mastery he does a better job. Yours,

51.  To Keith Lehrer, 10 April 1981 [Princeton, NJ] Dear Keith, The Guru example in my letter to you yesterday can be improved. By trying to give it a superficial resemblance to a genuine case of ability, I made it vulnerable to the following objection: ‘By hypothesis, you suffer from conceptual confusion about what laws are. Then is it clear that your preferences concerning laws, in the counterfactual situation, are rightly so described?’ Maybe this isn’t much to worry about, but it still seems worth circumventing. Here’s a new version. I’m taking a poll by show of hands. I say ‘All who prefer that the laws or the past be different, raise your hands’. You are predetermined not to so prefer, and not to raise your hand. But you could have raised your hand, and if you had, the laws or the past would have been different. And if you had preferred that the laws or the past be different, you would have raised your hand and the laws or past would have been different. But it’s not so that you could have brought it about that the laws or the past would have been different.

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So what must be added to ‘I could have done something such that, if I’d done it, the laws or past would have been different’ to get ‘I could have brought it about that the laws or past would have been different’ is not the conditional saying that the laws or past would have been different if I’d so preferred. Indeed, the case can be simplified still further, taking away all connection between the thing I could have done and a preference for different laws or past. I am predetermined not to raise my hand now; had I done it, the laws or past would have been different. I am also predetermined to prefer that the laws and past be as they are; had I preferred otherwise, the laws and past would have been different. Yours, cc: van Inwagen

52.  To Jonathan Bennett, 21 April 1981 Princeton University Princeton, NJ Dear Jonathan, Many thanks for your extremely interesting draft, ‘Similarity and Law’.1 I have a number of comments, as you might expect. Pages 7–8. Even in the case where the antecedent is that Nixon presses the button, and where this takes a substantial part of a second, the miracle required for perfect reconvergence doesn’t have to be widely scattered in space. The reason is that we don’t have to wait for the button-pressing to be done before the reconvergence mir­ acle begins. Rather than miraculously cleaning up traces that have already spread, we can miraculously stop them from setting out in the first place. But I think the reconvergence miracle, even if not spatially dispersed, still will be quite in another league from this – or any – divergence miracle in the variety of miraculous processes that have to be part of it, to stop the variety of traces that there otherwise would be. And here I think that making the antecedent event more short and sudden wouldn’t change matters. (What would change matters would be setting the story in a world of simpler and more ‘digital’ physics.) Pages 9ff. I don’t see why it threatens the account of ‘time’s arrow’ to grant that we sometimes use a kind of conditional that licenses backtracking (other than the sort that occurs in the transition period or in cases of time travel or the like), so long   A descendant of this paper is: ‘Counterfactuals and Temporal Direction’ (Bennett 1984).

1

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52.  To Jonathan Bennett, 21 April 1981

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as it’s different from the kind that doesn’t. Just because both exist, it doesn’t follow that we do or we should give them equal roles in our thought. I think one main difference is that causal dependence is connected with the standard sort of counterfactual, not at all with the non-standard sort. Page 15. Right you are: the criterion of similarity that would give commonplace back-tracking isn’t the same as the one – inviolability of law – that gives backtracking unlimited. Frankly, I’ve given it little thought, thinking of the back-trackers as having little interest in their own right and getting their interest more from the way they pop up as distractions in our thinking about causation. But I suppose one thing to say is that we get the criterion that permits moderate back-tracking by slightly altering the trade-off between holding the divergence miracle off as late as possible and keeping it small – let it be earlier if we can thereby keep it smaller. Another hypothesis – I don’t think of a clear case to test between the two – is that divergence miracles are still permitted, on much the same terms as under the standard criterion, except that they should not be too close to the antecedent time. To get Jim to ask Jack for help today, without differences throughout the past, we still need a divergence miracle somewhere (under determinism); the back-tracking conditionals put it yesterday or before; and my first hypothesis says that’s to let it be a smaller miracle, whereas my second hypothesis says that’s because miracles near the present count as extra-bad. (The second strikes me as more ad hoc but more likely to work. It’s not ad hoc in the way I’d mind most, namely by having a built-in asymmetry of time.) Page 21. I think you can’t get ‘If Collett had ever designed a Pacific . . .’ right by taking it as a universal quantification (presumably restricted) of ‘If Collett had designed a Pacific at time t . . .’. The trouble is that one can sensibly ask and answer questions about when, if ever, he would have done it. Early in his regime, when they would have met an unfilled need and would have been something new to the credit of the new C.M.E.? Or later on, when the Kings were already available to do the job and when a Collett Pacific would have looked like mere imitation of Stanier and Gresley? *** So much for small points. Now to give my reaction to the theory you propose, in which the closest P-worlds are (1) worlds that do not at all violate the laws of this world, and (2) P-worlds that are in some sense similar to this world in the present, or more generally at antecedent-time. That is, we add the antecedent to the present, holding the present otherwise fixed so far as possible; and we provide this counterfactual present (or these counterfactual presents, if the previous step doesn’t give a unique answer) with a past and a future by applying the actual laws both backwards and forwards. I think this is an attractive theory. Also, I grant you that there is no reason to fear that the needed counterfactual presents will be physically impossible. I take it

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that any momentary configuration of particles falls on some lawful trajectory (and likewise mutatis mutandis in a field physics). I think there would be some problem if the kinematic laws weren’t differential equations of the sort we’re used to but rather difference equations of the sort that sometimes appear in economic models. Then the laws and a single slice might do very little to determine a history, though laws and a segment (a long enough segment), or laws and a set of slices, would do it. But if our evaluation of counterfactuals should turn out to presuppose something about the form of laws – something we do in fact believe – so that it would go haywire in a world where those presuppositions failed, I wouldn’t think that much objection. (I’d better not, since of course I too am relying on contingencies such as the abundance and variety of traces to get things to come out as they should.) The decisive objection seems to me to concern the problem you discuss on page 16. I think there are many cases of counterfactuals that follow this pattern: If P, given laws and present background, Q would ensue; but Q together with historical background implies S, where S specifies a pattern across time, consisting partly of historical events and partly of future events; so if P, it would be that S. In the case you discuss, S is the breaking of an athletic record; in a case I’ve usually used to illustrate the point, S is getting revenge, where by definition it isn’t revenge unless there really was a past injury to the revenger. On your theory, a counterfactua1 of this sort is right only if the requisite historical background would still be there in the alternative history (histories) derived by law from the counterfactual present(s). I think that in many cases where the counterfactual seems right, this will not be so; but I can rely on something safer: in many cases it will not be known to be so. Then in many cases, even if we do get the truth values right, it’s by undeserved luck. Put it this way. How can you account for the fact that we argue from historical background without even considering the question what history would have preceded the counterfactual present according to the laws? This is a very serious mistake that your theory imputes to us, regardless of how often we get away with it. I don’t think a theory that imputes that mistake can be right. *** Let me offer you a new theory. At a price, which you may or may not consider acceptable, it gives you a lot of what you want without imputing the mistake. No miracles, a fortiori no need for comparison of miracles; no arrow of time that emerges from counterfactuals, but only one that’s there because we’ve put it there. For the last reason, the theory won’t meet my needs, but you’re not trying to make coun­ter­fac­ tuals do all the work I’m trying to make them do. Let A be the antecedent, and for simplicity let antecedent-time be the present. Let H be a complete specification of the past, let P be a complete specification of the

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53.  To Robert Pargetter, 4 August 1981

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present, and let L be a complete specification of the laws (all as they actually are). Let PA be a complete specification of an alternative present, closest to the actual present among the A-presents, where similarity of past and future and laws don’t enter into the comparison. (Or let PA be an incomplete specification of what’s common to all the closest A-presents.) Let HA consist of all the consequences of L ∪ PA that are about the past; and let FA likewise consist of all the consequences of L ∪ PA that are about the future. Thus HA and FA specify (completely or incompletely) the alternative history and future that are derived by law from the closest A-present(s). Then A > C is true iff C follows either from L ∪ PA or from H ∪ PA ∪ FA. (But not if C follows from neither singly, but only from the inconsistent union of the two.) This makes it right to backtrack as you wish to; it makes it right to combine historical background freely with counterfactual future, as we do in fact insist on doing; but it doesn’t make it right to mix counterfactual and actual history and exploit their discrepancies. This is an instance of quarantine by fragmentation, as in ‘Logic for Equivocators’.2 The set of all consequents C such that A > C is true is an inconsistent set; the rule I’ve called ‘Deduction Within Conditionals’ doesn’t in general preserve truth. That’s the price. But we don’t get chaos. This inconsistent set is the union of two fragments, each consistent and logically closed (under perfectly classical logic), and the full set is closed under implications that don’t draw their premises from both fragments. Yours, David cc: Frank Jackson, Bob Stalnaker

53.  To Robert Pargetter, 4 August 1981 [Melbourne, Australia] Dear Robert, Many thanks for ‘Laws and Modal Realism’.1 I suppose I think that if it were settled that we had to have some non-Humean difference to account for laws – as would be true if there were Hume worlds – a primitive accessibility relation might be as good a candidate as any. It’s interesting, and an option I hadn’t thought seriously about.

  (Lewis 1982).

2

  (Pargetter 1984).

1

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I also like the idea of taking the kind of counterfactuals that require divergence miracles as nested; I think I’ve not seen anything like that suggested before. However, I wonder how strong the motivation really is. The point is to save ‘legal conservatism’ except when the antecedent is explicitly counterlegal as in the outer counterfactual of the nesting. And the point of that is that sometimes it seems right to hold the laws fixed and backtrack, as in the second rocket counterfactual. Yes – I grant that we have backtrackers, and I also want them to be a different kind of counterfactual. But are they legally conservative? I’m not convinced that there are linguistic intuitions, as opposed to some philosophers’ theoretical commitments, in favor of coun­ter­fac­ tuals that say that if the present were different, the whole of the past would be different. Yet that’s what it takes for legal conservatism if the laws are deterministic. If you get only a bit of backtracking – to maybe a few days ago when the rocket was inspected – without a difference to the whole past, there still will have to be a divergence miracle. In doing counterfactuals, you don’t really replace similarity fully with accessibility, do you? – there’s still the match of history. Maybe it’s better to say that the aspect of similarity that threatens to be non-Humean is replaced with accessibility, the rest of similarity is unproblematic. The first paragraph of section 3 puzzled me. Do you mean to say that any proposition is a law in w0 iff true in w0 and all worlds accessible from it? Or only any generalisation? Or do you doubt that there is a distinction between generalisations and non-generalisations for propositions (as opposed to sentences)? If the laws are supposed to be generalisations, as might be expected, how can there be incompatible ones, a possibility that seems to arise in the discussion on pages 5 and 6? E.g. if there is nothing at all, all generalisations, whatever are true together. More modestly, if there are no A’s, all generalisations about A’s are true together. Either I’m missing something, or the discussion of intransitivity on pages 5–6 could be simplified and the conclusion strengthened. I say that as you set things up, any world is at most two steps away from any other. Start with w0; let w1 be a Hume world that imitates w0, so that the laws of w0 are among the accidental regularities of w1; w1 is accessible from w0. But w1 is to be a compleat Hume world with no laws at all; so any world whatever is accessible from w1; for all the laws of w1, all none of them, are unviolated at all other worlds. My impression is that it’s fairly usual to think of physical accessibility in your way – the laws of one world are unviolated at the other – rather than in the way you think of as more standard – the worlds have the same laws. But I’m not prepared to back this up with citations. Yours, David

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54.  To Peter van Inwagen, 18 October 1981

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54.  To Peter van Inwagen, 18 October 1981 [Princeton, NJ] Dear Peter, Thank you for your letter of 7 July. I’m sorry to be so long answering – it has to do with my having been in Australia, hence not having a copy of your earlier letter available. No; I definitely am not asking you to produce Nozick arguments.1 Would I be so foolhardy? I think that your strategy of tightening up until the controversy is confined to a single premise is a strategy that fails to serve your own purpose. And I understood perfectly well that your purpose isn’t to coerce conversions. It is, in the first instance, to clarify what the spectrum of consistent positions is; and perhaps, as a side-effect, to make converts among those who were attracted only to inconsistent versions of compatibilism. (Actually, I should just say: the spectrum of positions. Even those who continue to accept positions they know to be inconsistent don’t automatically die. Several are alive and well in Australia. ‘Contradictions are not to be multiplied beyond necessity’ – Graham Priest.) You will teach people something (and maybe make converts in the process) just to the extent that you reveal the inconsistencies in subtly inconsistent versions of compatibilism. But how is that possible? How can one fail to notice an inconsistency? Uncontroversially, the answer often is (and I think the answer always is, but that’s very controversial) that one thinks in a fragmented way. My mental map for getting around town had Nassau street running east-west; my mental map for getting around the Northeast had the Pennsy main line2 running north-south; both maps had them parallel. By attending to the questions one at a time, I managed for some years to accept conflicting answers, and so to have an inconsistent total belief system. The remedy requires considering the two controversial questions together. It wouldn’t help to take one of the two conflicting beliefs and surround it with auxiliary premises true by definition. I think that if you leave more than one premise controversial, you may show people that they’ve been inclined to accept, one at a time, the different members of a jointly inconsistent set. I don’t see how you can do that if you concentrate the controversy – unless, of course, your official argument sets the reader to thinking of other

  Philosophical Explanations (Nozick 1981, 4–8).   

1

  Pennsylvania Railroad.

2

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interpretations of your words which aren’t your official argument and which disperse the controversy. *** Thank you for reminding me of ‘Ability & Responsibility’.3 I wonder why it didn’t stick in my memory – perhaps when I read it I agreed. I certainly don’t agree now. In fact, I’m happier with my example about Satan and the cruel people, now that I see so many other examples of the same sort! Take the case of Gunnar and Ridley, where the ‘factor F’ is Pistol; and where Pistol, if not preempted, would have killed Ridley at much the same time and in much the same manner as Gunnar actually did. Let k be the particular event of killing, an act by Gunnar, that took place. Let d be the particular event of Ridley’s death. Suppose (what may be to some extent a stipulative settling of an indeterminate matter) that k could not have been done by anyone but Gunnar – in particular, k itself couldn’t have been an act of Pistol’s – and that d could have been caused as well by Pistol’s act as by Gunnar’s. (With that last you will surely disagree.) I shall use the present tense tenselessly: ‘Ridley dies’ for ‘Ridley dies at some time or other’, etc. Now I think that Gunnar is responsible for all of the following: k d C(Ridley is killed) C(Ridley dies) C(either Pistol or Gunnar kills Ridley) although the only one that depends counterfactually on Gunnar’s conduct, the only one that didn’t lie at the end of all roads for him, is k. And I trust I’ve been clear enough that you don’t suspect me of confusing one thing with another! I don’t think Gunnar is responsible for C(Ridley is mortal); but I don’t think that’s the same as C(Ridley dies). I think that to be mortal is either to be doomed to die inevitably or to be capable of dying. If I remember rightly, the elves are vulnerable to death in battle, but they are not doomed to die; a lucky elf might live forever. I think that in a sense all elves are alike mortal, in a sense none are; but in no natural sense is it true that those who happen to die are mortal and the others aren’t. I don’t think Gunnar is responsible for C(Ridley dies or 2 + 2 = 4) or for C(Ridley dies or grass is green). The difference I see is this. If Gunnar is responsible for an event e, and e is the only occurrent event satisfying description Φ, then Gunnar is responsible for C(some event occurs that satisfies Φ). Interchanging equivalents within the

  (van Inwagen 1978).

3

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55.  To David Copp, 12 November 1981

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‘C’, that explains why Gunnar is responsible for C(Ridley is killed), C(Ridley dies), C(either Pistol or Gunnar kills Ridley). For Gunnar is responsible for an event (by doing it, or by causing it) and that event is the truth-making instance of the existential quantification. But C(Ridley dies or 2 + 2 = 4) and C(Ridley dies or grass is green) are not thus related to events for which Gunnar is responsible. I think that if you were right about these cases, language would do a better job than it actually does of marking morally significant distinctions in a simple way. Hence my remark about reformed versus ordinary language. But as for English as she is spoke, leaving hypothetical improvements out of it, I think you’re plain wrong. No; that’s too hard and fast. As happens so often, the meanings may not be altogether settled. So I’ll grant you two things. (1) You’re right about a language that would probably be an improvement on the one we mostly speak, and (2) this language is not entirely a fiction, but is a way we sometimes have some inclination to speak. But I don’t think you’re right about the predominant tendency. Yours,

55.  To David Copp, 12 November 1981 [Princeton, NJ] Dear David, Predictably, I say that your sets A and B cause nothing because, being sets of things other than spatiotemporal regions, they are not events.1 I should think that something analogous to the relation of causal dependence, except that it holds between suitable acts of things, might indeed be of interest to billiard players. Let p be the billiard player, f the man who is allegedly his father. Let P and F be the sets of counterparts of p and f respectively. Then p might well take an interest in the question whether, if the world had not contributed a member to F, it would not have contributed a member to P.  For this is the question whether p depends for his existence on the existence of f, which is (in part) the interesting question of whether his alleged father is his real father. – But is this relevant to anything? I put forward a view as to what concept we employ. Perhaps by engaging in speculation about the origins of language and the plasticity of mind I might venture a hypothesis about why we’ve picked on that one rather than some other. But I need not. It is no shortcoming of orthodox arithmetic that it fails to speculate about why 1

  A = {my jacket, my jacket’s counterpart in w1}. B = {my tie, my tie’s counterpart in w1}.

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we have no word for the relation that holds in two cases (1) between x, y, and z when they are numbers and the third is the sum of the first two, and (2) between m, w, and h when m and w are man and wife and h is the house they live in. Even if it would be easy to speculate about this matter – conceivably it would be – that’s not a required question for mathematics. As for your sets Aʹ and Bʹ.2 They’re disqualified on three counts from being events, hence from causing each other or anything else. They’re overly specific; they’re disjunctive; and they’re largely extrinsic. Let’s concentrate on the last. They’re related like the conference and its centennial in my example, necessarily connected and hence counterfactually dependent (in both directions). This is possible because the regions where the event occurs are characterized in a way that’s almost entirely extrinsic. In the case of the centennial: Whether the centennial of the conference occurs in region R of world W depends almost not at all on what goes on in R, almost entirely on whether the conference occurs 100 years earlier in R. In your case: Whether Aʹ occurs in R of W depends indeed on whether R contains a suitable jacket, but mostly it depends on whether W as a whole is one of the two specified worlds – this world and w1. Your C and D are not events,3 being disqualified because they are disjunctive. What makes them disjunctive? You say, intuitively: no one event goes on in all the regions that comprise C (or likewise D); or, as I might prefer if I joined you in distinguishing the events from the classes of regions, no one event has counterparts in all and only the regions that comprise C. The former version comes out true on my account, but of course it does nothing to explain why the regions in C do not comprise an event. The regions in C are not (sufficiently) alike – that’s why C is disjunctive, and no event. Regions are alike to the requisite extent iff some event goes on in all of them – true, but not explanatory. I see three main options. (1) Provide entities such that a class of things are alike iff (in some sense) they share one of these entities. That’s your choice, but generalized. If I were going to take this option, I’d want entities that could explain alikeness 2  Aʹ = {the region of spacetime that exactly encloses my jacket, the region that exactly encloses my jacket’s counterpart in w1}. Bʹ = {the region that exactly encloses my tie, the region that exactly encloses my tie’s counterpart in w1}. 3   C = {the region of spacetime in this world that exactly encloses my typing this description, a region of spacetime from another possible world iff the region exactly encloses the counterpart there of my dropping a glass of beer in Calgary on 25 Oct}. D = {the region of spacetime in this world that exactly encloses my drinking coffee now, a region of spacetime from another possible world iff the region exactly encloses the counterpart there of a beer stain’s appearing on a carpet in Calgary on 25 Oct}. All of these examples are from David Copp’s letter to David Lewis, 27 October 1981, pp. 1–2.

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more generally than just for the classes of regions that comprise events. That is, I’d want a serious theory of universals. (2) Take ‘alike’ as a primitive predicate of classes. (Pairwise resemblance comes out as a special case.) (3) Take ‘alike’ as a primitive relational predicate applying to regions inter alia – but it would have to have polyadicity, which seems to me not especially terrible. I haven’t much notion which of those programs I should prefer. But I do think that if I were going to go the first way – extra ontology rather than extra primitives – I’d want to buy entities that could serve more theoretical purposes than your unreduced events do. Yours, David Lewis

56.  To Terence Horgan, 2 November 1982 Princeton University Princeton, NJ Dear Terry, I was glad to hear of your plan for a conference on supervenience. Of course I agree on the importance of the topic, and it looks like a good list of participants. I’m afraid, however, that my own participation is not on. I’ve said my piece in ‘New Work’;1 I have other plans for next year; so don’t want to write anything new, either main paper or comment. If it weren’t for the tie-in with Southern Journal,2 I could give a talk based on parts of ‘New Work’; but (i) ‘New Work’ is long and not mainly on supervenience, so wouldn’t suit the special issue, (ii) it’s submitted elsewhere, and (iii) I do worry about visibility of a paper in Southern Journal, however widely they advertise their contents. I’m sorry. I’ve meant to write you a note about footnote 17 in your PΦQ paper:3 ‘Lewis’s formulation of determinism . . . should be modified in the same way’. At first sight I agreed with you, but on second thought I disagree. Let determinism mean that the prevailing laws are deterministic; let divergent worlds be worlds whose initial segments are duplicates but whose entire histories are not duplicates. I say that the system of laws L is deterministic iff no two divergent worlds both conform perfectly to L. I could also say that L is X-deterministic (X a class   ‘New Work for a Theory of Universals’ (Lewis 1983c).      ‘Supervenience and Microphysics’ (Horgan 1982).

1 3

  Southern Journal of Philosophy.

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of worlds) iff no two divergent X-worlds both conform perfectly to L. The proposed modification, I take it, is to consider the class X of worlds without beings (things or universals or instantiated natural properties) alien to our world, and take determinism to mean that the prevailing laws are X-deterministic. That is: no divergence of law-abiding worlds unless aliens are present.4 Is it a matter of law that the aliens are absent?* I think it well might be, given my theory that laws are regularities that make it into systems that optimize simplicitycum-strength. If it is a matter of law, the case in which the modification makes a difference doesn’t arise. So suppose it isn’t a matter of law. The aliens are absent (by definition) but not outlawed. Some law-abiding worlds have them. Suppose two lawabiding worlds diverge, but only with respect to the aliens. (The aliens are epiphenomenal, at least in the relevant world.) Counterexample to determinism? My definition, as it stands, says yes. And I think that’s OK. It is not predetermined whether or not aliens will show up, or what they’ll do if they do. Yours,   David

57.  To D.H. Mellor, 2 December 1982 Princeton University Princeton, NJ Dear Hugh, Thank you for ‘Fixed Past, Unfixed Future’.1 I read it yesterday, mostly agreeing and sometimes noting the reappearance of disagreements we’ve talked about before, and on the whole I liked it very much. But, I did get a bit of a shock at the top of page 4. I most certainly do take such truths – non-trivial counterfactuals about what chances would have been – to need this-worldly truth-makers! For I take such counterfactuals to be comparisons of similarity of worlds: our world is more like some world where the coin is tossed with equal chances than it is like any where the coin is tossed with unequal chances. So the truth-makers of coun­ ter­fac­tuals are the makers of similarities and dissimilarities of worlds, one of which   Cf. ‘New Work for a Theory of Universals’ (Lewis 1983c, 360–1).   PS Note telling difference: ‘laws of nature’ in (D), ‘microphysical laws’ in (S-1). Absence of aliens is more likely a ‘law’ than a ‘microphysical law’. 4 *

  (Mellor 1987).

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57.  To D.H. Mellor, 2 December 1982

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is ours. And what are those? – intrinsic features of the worlds in question, one of which is ours. It takes two to make a similarity (or dissimilarity): the way this world is, and the way the other world is. The this-worldly, contingent, truth-makers of counterfactuals (trivial cases apart) are the this-worldly halves of the matches and mismatches that settle the comparisons of similarity. I wish I did think that counterfactuals about chances needed no this-worldly truth-makers! For I’m much bothered about what those truth-makers might be. Up to a point, it’s easy: they are the manifest properties of the things involved – e.g. the microstructure of matter and fields. Or, what I take to be equivalent: the ­spatiotemporal distance relations of space-time points, together with the distribution of intrinsic properties over these points. Call such facts H: for ‘historical’, ‘Humean’, and ‘holographic’ (in roughly Kripke’s sense). What are the this-worldly truth-makers for: if this coin were tossed (in such and such way) it would have equal chances of heads and tails? In other words, what are the this-worldly halves of all the matches and mismatches across worlds that make it true? Up to a point, the answer is plain: they are H-facts, conceivably about the whole world up to now, but mostly about the present microstructure of the coin, the tosser, and the surroundings. But now imagine a complete, infinitely long specification of all the H-facts concerning a certain possible world W up to (a counterpart of) the present; or take the proposition such a specification would express. In calling it complete, I mean that every H-proposition about the appropriate initial segment of W is either implied by the complete specification or contradicted by it, according as it does or doesn’t hold at W. Call this proposition the history of W, or HW. What’s the truth-maker of HW⁄ equal chances? The H-facts of our world? Their role seems pre-empted by the completeness of Hw. Other facts about our world? First, I’d prefer not to believe in these other facts; second, I don’t see how they could do their alleged job of truth-making even if they existed. Maybe the best solution is that when we make the antecedent thus complete, we reach the trivial case where the antecedent strictly implies the consequent and no comparisons of similarity are needed. This seems to me im­plaus­ ible on the face of it, but maybe nevertheless the way to go. [. . .] Regards from Steffi. She’s having fun on Wall Street, in a rather hectic way. (Public finance at Kidder-Peabody: tax-free bond issues for subsidized housing and for MSW Resource Recovery. What’s that, you ask? High-tech garbology: you generate a bit of electricity or heat some buildings with steam from a boiler heated by your incinerator.) Yours, David

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58.  To Brian Skyrms, 13 June 1983 [Princeton, NJ] Dear Brian, Thank you for the note on Newcomb with mixed strategies, and for the paper on EPR and causation.1 I have a comment on the latter. Ad page 2: you say that on my view, we’ve got a closed causal loop between two events, ‘the measurement results down on left and up on right’. Maybe not; for remember that I’ve said that counterfactual dependence is causation when it’s between distinct events (and distinct means ‘nonoverlapping’, not just ‘nonidentical’), to deal with Kim’s example about the dependence between ‘Larry’ and writing ‘rr’. When you speak of the ‘the measurement result’ you might mean one of two things. (1) You might mean the reduction of the wave function in the down-left-upright way. Call this R. If one takes nonlocality seriously, perhaps the thing to say is that R is a big, nonlocalized event; and there simply isn’t any smaller event which is the part of R involving the particle that went off left, nor one which is the part of R involving the particle that went off right. Then there’s no closed causal loop between these two parts of R. Because there are no such two parts of R. (2) You might instead mean the triggering of detectors. Here we do seem to have a left-hand event, in which the down detector is triggered; and a right-hand event, in which the up detector is triggered. But I needn’t say that either of these causes the other; they’re two effects of the nonlocalized common cause R. If the down detector on the left hadn’t been triggered, then . . .? Shall we say that then R wouldn’t have occurred, so that then the up detector on the right wouldn’t have been triggered? No, that’s backtracking, just as in a commonplace classical case. Rather, if the down detector on the left hadn’t been triggered, something would have gone wrong with the detecting on the left; but R would have happened, and the up detector on the right would have been triggered, all the same. Yours,

  ‘EPR: Lessons for Metaphysics’ (Skyrms 1984).

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59.  P.N. Johnson-Laird, 10 October 1983

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59.  P.N. Johnson-Laird, 10 October 1983 Princeton University Princeton, NJ Dear Philip, Thank you for your ‘Models of Conditionals’.1 Let me comment a bit on the critical part – mostly trivia, but a brief remark also on the main argument. First the trivia. [. . .] Page 22, lines 1–2. There’s supposedly a disagreement between me and everyone else: I supposedly think possible worlds are concrete, everyone else who believes in them at all thinks they’re abstract. Formerly I agreed that there was such a dis­ agree­ment; but now, I ask what ‘abstract’ is supposed to mean. I think the term is covered in confusion: many different things are said, which conflict with one another. What you say is especially surprising. One strand in the meaning connects abstraction with lack of specificity: an abstract idea of a triangle is of a triangle, but not a triangle of any specific size or shape. Economic man is an abstraction: all there is to him is a bundle of preferences. . . . So the last thing a highly abstract entity would do is to settle the truth value of every proposition. If you want highly abstract worlds, you want the sort advocated for instance in Saul Kripke’s new preface to Naming & Necessity: ‘The thirty-six possible states of the dice are literally thirty-six “possible worlds”, as long as we (fictively) ignore everything about the world except the two dice and what they show . . .’. He calls them ‘miniworlds’; and he calls them ‘abstract’, though without explanation. Abstract they surely are, in the traditional sense in which an abstraction is what you get by ignoring specific detail – but I’m not sure that’s the sense he meant. My worlds are not miniworlds. Maybe we think about them by manipulating mental representations of small numbers of miniworlds; but if so, that’s where the abstraction comes in. The main disagreement between us is on the question whether an account of the meaning of counterfactuals can be expected to double as a reasonable account of  comprehension. We agree, of course, that a psychological theory according to which the mind surveys an uncountable infinity of complex structures, each of them infinite in size, is hopeless. Even if counterfactuals mean what I say they mean, we’d still better be able to comprehend them in a way that traffics in worlds wholesale rather than retail – somehow letting one miniworld stand for countless big worlds. 1  Cf. Mental Models: Towards a Cognitive Science of Language, Inference, and Consciousness (Johnson-Laird 1983, 54–62).

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There isn’t much room for conjecture in thinking about what a mathematician’s sentences mean: the mathematicians tell us, very explicitly, that they are talking about enormously complex infinite structures. (Sometimes structures so big that the infinity of possible worlds looks puny in comparison.) Representations of the structure the mathematician is talking about would go far beyond what can fit into even a mathematician’s mind. So either (1) what the mathematician means is very different from what he explicitly claims to mean, or (2) cognitive science should proceed on the assumption that mathematicians don’t exist, or aren’t really human, or (3) we have to recognise that somehow finite minds can comprehend sentences whose meanings involve structures much too big to fit into the mind. Of these alternatives, I think (3) is right for mathematical sentences about infinite structures; and right also for the sentences I give as analyses of ordinary-language counterfactuals and right for the counterfactuals themselves. To put the point another way: your reductio on pages 23–4 is precisely parallel to an argument that (except for some finite combinatorial bits) no one can ever grasp or evaluate sentences of mathematics. That argument too is a reductio; but not against mathematics! And also not, I trust, against a mental-model approach to comprehension. Rather, against the hope to merge accounts of comprehension and of meaning. More trivia. [. . .] Page 44, lines 1–5. There’s a problem with this, which Bob Stalnaker has illustrated with ‘If I’d asked the boss for a raise, he’d have granted it’, and I’ve illustrated with ‘If I’d looked in my pocket for a penny, I’d have found one’. The background of relevant beliefs takes you this far: the first is true iff the boss was in a generous mood; the second is true iff I had a penny in my pocket. But I have no idea whether, and hence wonder whether, the boss was in a generous mood or there was a penny in my pocket; hence, further, I wonder whether the counterfactuals are true. The conditional has unknown truth value. But on your proposal it comes out definitely false. For my mental models leave it open whether the boss was in a generous mood, or whether there was a penny in my pocket. So the consequent is not true with respect to the relevant model; or if I keep two models which differ on whether the boss was in a generous mood, or on whether I had a penny, then the consequent is true in one but not all of the relevant models. The cure might be this. Where there’s some sort of explicit focus on one’s ignorance about whether A, there are two mental models, one with A, one with not-A; the counterfactual is true if A and the consequent is true in the relevant A-model, or if not-A and the consequent is true in the relevant not-Amodel. Here the relevant A-model is jointly determined by the antecedent, background beliefs, and the supposition that A; and likewise for the relevant not-A-model. Of course, you don’t want to double up mental models whenever something is unknown; that proliferation would go against the whole idea of keeping things small

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60.  To Louis Loeb, 21 February 1984

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so as to get a plausible account of comprehension. But in the special case where wondering whether the counterfactual is true is tantamount to wondering whether A, maybe the doubling is acceptable. (A premise semantics can be made equivalent to mine, or to a generalisation of mine in which the orderings of worlds are partial. I’ll send you an offprint about that. The question is, though, whether this can be done while keeping the premises down to a manageable finite number. I think that question might be independent of whether the premises are held in mind as sentences, mental models, or whatnot.) Could I have page 17? It was missing from the copy. Thanks. Sincerely, David

60.  To Louis Loeb, 21 February 1984 [Princeton, NJ] Dear Louis, These pages are out of a draft that was turning out much too long and tangled; it remains that they give my view, but I probably won’t say most of this in the final version because it’s got to get much shorter.1 I’m curious about whether your student (Tesca?) was worried about the same problem that most worries me. That’s the kind of preemption where the chain from the alternate cause gets cut off not by a signal from part way along the chain from the preempting cause, but by a signal from the final effect. Like this, where the things are idealized neurons, forward arrowheads are stimulatory, backward arrowheads are inhibitory, firing of c is the preempting cause, simultaneous firing of cʹ is the preempted alternative, and firing of e is the effect.

1   From an early version of Section E. Redundant Causation of ‘Postscripts to “Causation” ’ (Lewis 1986d, 193–212).

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It’s true that without the firing of c, the firing of e would have been slightly later; I think that’s why I didn’t pay enough attention to this kind of case; and as far as I can now see, that would be the only way to deal with the case short of some major change. But it’s hard to see how to solve it in this way; because I accept Ken Kress’s point that not everything that makes some difference to time and manner of an event is a cause of it. So events can’t generally be fragile; that is, it can’t always be that a small difference in time or manner would have made it a different event. Somehow there has to be a double standard of fragility; in these cases, but not in others, we need to say that if E had fired a little later, that would not have been the same event. You and others have long asked how I knew there would be an intermediate in preemption cases; but the counterexamples I had in mind involved causation over gaps, backward causation, or preemption with infinitely many preempted alternatives. Those all seemed artificial enough not to worry about. But the case where the chain from the alternative gets cut off only by a signal from the effect itself isn’t artificial at all. Yours,

61.  To Louis Loeb, 13 March 1984 [Princeton, NJ] Dear Louis, If I took a really hard line about asymmetry of counterfactuals, I could answer Pesca in the way you suggest. But I don’t; I feel I have to allow a ‘transition period’, to avoid crazy counterfactuals like ‘If I were in ’79 Hall now . . .’ – I’m not, still the same room in McCosh – ‘I would just have gone several hundred feet at infinite velocity’. This reduces the gap where the intermediate can go, as my friend LeCatt has noticed1 (offprint, marked bits on 160 and 162) and I also had noticed. What Pesca does is to use this to get a case of late preemption without postponing the effect. But since I don’t think postponing the effects gets me out of the soup, it’s no worse trouble than I was in already. I hope my new manoeuvre for late preemption cures all the cases. It’s rather in the spirit of what you’re now proposing: take seriously that causation comes in chains, and look not just at the least excerpt from a chain that gives stepwise dependence but at the whole of what is intuitively the causal process.

  ‘Censored Vision’ (LeCatt 1982). This paper was written pseudonymously by Lewis.

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62.  To Hugh Rice, 5 June 1984

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I gave up on the draft I had, and rewrote it from scratch. I was in danger of abusing the word processor to hitch up a jumble of paragraphs written in the grip of many different views, so as to put together something barely coherent. One cas­ ual­ty is the extensive discussion of your paper2 that I sent you before – not because I don’t believe what I then said, but because that doesn’t fit in. I take the point that you said some things that commit you to not wanting preempted alternatives to C-conditions; it’s just that I thought that for your main purpose (and here I may have had in mind the dissertation more than the paper) maybe it would be just as well if they were. Thanks very much for your help. I hope I’m done this now, but that remains to be seen. Yours,

62.  To Hugh Rice, 5 June 1984 as from: Princeton University Princeton, NJ [Oxford, England] Dear Hugh, Thank you for your comments, which I found helpful and interesting. If you are willing, I’d like to add some material to ‘Redundant Causation’1 that mentions one of your suggestions. Draft enclosed. May I? Do you find my brief summary accurate? [. . .] Another matter. I take your point that my solution using quasi-dependence seems to give a second-grade sort of causation, causation only by courtesy. But tu quoque. In fact, I suggest that the same goes for any way of doctoring a counterfactual analysis of causation to make it let in some cases of causation without direct counterfactual dependence – the cases let in by the doctoring will seem second-grade. I think one might complain – I think Mellor might, for one – that when I let in causation by stepwise dependence, those aren’t proper cases of causation. Since there is causation without dependence, I think we have to tolerate a theory that seems to make some cases second-grade – or else give up on a counterfactual analysis ­altogether.   ‘Causal Theories and Causal Overdetermination’ (Loeb 1974).

2

  Section E. Redundant Causation of ‘Postscripts to “Causation” ’ (Lewis 1986d, 193–212).

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I’m sorry I haven’t been quicker in writing. It would be nice to talk further, but I’m afraid my visit is almost over. My normal address is above, though I’ll be traveling much of the summer. Again: thank you for your comments. Yours, David

63.  To Terence Horgan, 7 July 1984 [Sydney, Australia] Dear Terry, I’ve looked at your compatibilism paper and I have a lot to say about it.1 1) Typo: p 10, & 13: Nasser’s Nostradamus’s. 2) Can Nasser render false N2, that being a rigidification of ‘All of Nostradamus’s predictions come true’? Three different answers. A) Yes, in my original weak sense. Nasser is able to do something, namely order the destruction, such that, if he did it, there would occur an event e such that e’s occurrence is incompatible with the truth of N2, /that is,/ strictly implies the falsity of N2. But that event is not just d, the destruction of the sphinx; it’s d + f, f being a chunk of the continuing human history following the destruction. (If you like, let it be the destruction plus the outrage that follows when the news gets out.) Doesn’t that answer your point about the Martians? It does require a controversial premise about events, namely that at least some limited mereological summation of them over time is OK. There’s some inconclusive discussion of this in ‘Events’,2 in my Φ Papers II which I’ve sent you. B) Alternatively, let me introduce a new sense of ‘can render false’, weaker than even my ‘weak sense’ and simpler than any of the others. Nasser can render N2 false in the simple sense iff he is able to do something such that, if he did it, N2 would be false. And so he is, viz. order the destruction. Whether the weak sense differs from the simple depends on how sparse a theory of events you hold. If you’re quite tolerant of events of omission and the like (some description of this in Postscript to ‘Causation’, Φ Papers II)3 maybe any empirical

  ‘Compatibilism and the Consequence Argument’ (Horgan 1985).   (Lewis 1986d, 241–69).    3  (Lewis 1986d, 172–213).

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63.  To Terence Horgan, 7 July 1984

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falsehood is falsified (my narrow sense) by some genuine event. If not, not – for instance how do you find an event that falsifies a positive existential? I can’t remember why I picked on the weak rather than the simple sense in ‘Are We Free . . .?’4 I don’t think it was a considered choice. The weak sense is anyway probably equivalent to the simple for the special case that what’s being rendered false is a law. I probably never asked myself whether they’re equivalent in general, and that was before I’d written about events. C) Anyway, why care about whether Nasser can render N2 false? This ‘render false’ stuff isn’t ordinary language anyway, who needs linguistic intuitions about it, define it as you will and then see what you think about the incompatibilist argument. (Thus I agree with your conclusion – I think the definitional maneuvering is all a bit of a side show, can’t really change anything.) 3) I found it quite hard to get a grasp of your broad senses, and I think that some simplification is possible and helpful. First the preliminary notion. I’ll equivocate in notation between an event and the proposition that it occurs, OK? E broad-falsifies     Q) & EQ ⥽ ¬P). I say E broad-falsifies P iff E⁄      ¬P. Proof (→): We P = df ∃Q (Q & (E⁄  have E  ⁄      Q, E ⁄E, so E⁄EQ, so E⁄      ¬P. (←): We have E⁄      ¬P. I say we can take Q as E ⊃ ¬P. For then Q follows from E⁄    ¬P; so does E⁄    Q; and EQ ⥽ ¬P comes from truth-functional and modal logic. So henceforth I’ll simply write E⁄      ¬P where you have broad-falsification. Now let’s say that an agent can render P false in the extra-strong and broad sense iff he is able to do something such that, if he did it, P would be broad-falsified by his act itself. Extra-strong and broad is a special case of strong and broad, which is a special case in turn of weak and broad. Next, weak and broad ought to imply my simple sense, above. It’s minimal – any reasonable sense of ‘can render false’ should at least imply the simple sense. Let’s suppose I could show that simple implies extra strong and broad. That would seem to close a circle, showing that all three of the broad senses reduce to simple, hence are equivalent to one another. That almost is what happens. I need auxiliary premises, which I hope you’ll find uncontroversial. Also I need to foist on you a correction which I claim has independent motivation. I’ll equivocate some more in notation, this time between an act-description and the proposition that the agent does an act of that description. OK? And I’ll restrict the variable ‘A’ to act-descriptions that the agent is able to do. So the simple sense is just (S) $A A   (Lewis 1981).

4

¬P

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I’ll write ECA (‘E constitutes A’) to mean that event E occurs and is the agent’s very act of A’ing. So we have trivial analytic premises (Aux 1) ECA

E

( Aux 2 ) ECA

A

The third auxiliary premise is a substantive thesis about events, less trivial but still safe ( Aux 3 ) "A $E ( A

ECA )

Now I can write down the extra-strong and broad sense, and then the thing I want to foist on you as a correction of it. ( B) $A $E ( A ( B+ ) $A $E ( A

ECA & E

ØP )

ECA & ECA

ØP )

(S) and (B+) are equivalent. (→) For some A, we have A⁄ ¬P. By (Aux 3) also for some E we have A ⁄ ECA. By (Aux 2) we can strengthen this to a counterfactual biconditional, A ←“→ ECA. That licenses substitution of antecedents, so we have ECA⁄ ¬P, giving us (B+). (←) We have A⁄ ECA and ECA⁄ ¬P. Again, use (Aux 2) to strengthen the former to a biconditional whereby we can substitute ante­cedents in the latter. So we have A ⁄ ¬P, giving us (S). The only catch is that (B+) isn’t (B). But when you see why, I think you’ll agree that (B+) is the one you really wanted. Similarly with the other broad senses. You are able to twitch your finger voluntarily, but you very much don’t want to; however you have a tic and it sometimes twitches involuntarily. In fact, it does not twitch. Let E be the nonoccurrent event of its twitching, voluntarily or not; let A be the act-description: twitching it. A ⁄ ECA; but E ⁄ ¬ECA, since if there were a twitch it would be involuntary. Let P be the proposition that your finger twitches voluntarily or not at all. ECA ⁄ P but E ⁄ ¬P. So un der (B) you can render P false, which seems wrong; whereas under (B +), and equivalently under (S) you cannot – or cannot unless by means of some different act-description al­together – which seems right. The case illustrates intransitivity of counterfactuals from ECA ⁄ E and E ⁄ ¬P, ECA ⁄ ¬P doesn’t follow. So even when you have A ←“→ ECA still A ⁄ ¬P doesn’t follow. Intuitively, indeed, it seems to me that in the story as I told it, you cannot render false the proposition that you twitch voluntarily or not at all. By failing to imply the simple sense, (B) – and a fortiori, your strong broad and weak broad senses – are made suspect as being senses of ‘can render false’ at all. All this on

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64.  To David Sanford, 16 February 1987

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the s­ upposition – which I question – that it’s a good idea to have linguistic intuitions about ‘can render false’. If you believe, as van Inwagen does and I don’t, that events have their causal origins essentially, then the difference between (B) and (B+) would go away, and both would reduce to (S). For then we’d have more auxiliary premises ECA A

AE

ECA

ECA ECA

and we could get the biconditional E ←“→ ECA which allows substitution of E for ECA, getting you from ECA ⁄ ¬P to E ⁄ ¬P and vice versa. 4) My last comment is diplomatic rather than philosophical. You represent the order of things as: van Inwagen paper, then Lewis paper, then van Inwagen book. And you say it’s unfortunate that van Inwagen doesn’t discuss my rejoinder. This might be read as a reproach to van Inwagen, though I imagine you didn’t intend it so. If it were so read, the reproach would be undeserved; because the timing is not what the publication dates would suggest. Roughly what’s true is that the book came out before my paper, but took longer to publish. (More precisely, van Inwagen got his first look at my paper when he was only days away from submitting his final manuscript to OUP. And even if he’d wanted to make last-minute changes, he couldn’t in propriety have done so; because the draft I sent him was marked ‘Preliminary draft – don’t cite’. By the time he was at liberty to discuss it, his book had been in press for months.) Yours, David cc: van Inwagen

64.  To David Sanford, 16 February 1987 [Princeton, NJ] Dear David, A belated reply to your 12 December letter about super-realism.1 I’m sorry it’s been so long! Let me try to reconstruct the argument about variation of laws from one part of the super-world to another.   For Sanford’s discussion of super-realism, see If P, Then Q (Sanford 1989, Ch. 10).

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First, they must vary; else the laws would not be contingent. This means that a simple regularity theory – laws are regularities that hold without exception throughout the super-world, or they are those among such regularities that earn a place in an ideal system – is not on, since it permits no variation. What sort of theory would permit variation? There is a range of alternatives. At one extreme is the local theory: the laws prevailing at any point of the superworld are somehow determined by intrinsic properties of that point itself, or of whatever occupies that point. Other theories are regional theories: the laws prevailing at any point are determined by intrinsic properties of regions surrounding that point, or of whatever occupies those regions. Regional theories vary according to what they say about the size of the relevant regions. A large-regional theory could be a regularity theory: the laws of a point are regularities that have no exceptions within the neighbouring region, whatever exceptions they may have elsewhere; and they are those among such regularities that earn a place in an ideal system. A local or small-regional theory had better be a theory of non-Humean lawmakers – Armstrong’s N(F, G) or the like – since at a point or a sufficiently small region almost any candidate regularity will be apt to hold vacuously. According to a principle of recombination, anything and anything else – that is, a duplicate of anything and of anything else – can coexist side by side. Given a local or small-region theory, this is sufficient to make for abrupt change of laws. Given a large-region theory, this makes for lawless regions – regions of law-making size in which any candidate law has an exception. Let’s call a region chaotic iff either there are abrupt changes of laws within it or it is lawless. Causation is a matter of law. On a covering law view, the actual causal process is subsumed under laws: given the causes and the laws, there’s no way to avoid the effect. On my own view, the laws are applied counterfactually, roughly as follows: take away the cause, allow the counterfactual situation to develop lawfully, and you don’t get the effect. But either way, the laws matter. In a heteronomic super-world, the relevant laws will be those governing the region where the cause and the effect are. But how does this make sense if the region is chaotic? I think you said emphatically that the super-world was to be causally interconnected. Then my problem was that I thought that if the super-world were heteronomic (to provide for contingency of laws) and if it obeyed a principle of recombination (to provide for an adequately full range of possibilities) then it would have chaotic regions; and I couldn’t see how causal chains could pass through these chaotic regions; and so I didn’t see how parts of the super-world surrounded by chaotic regions could be connected to the rest of the super-world. I’d advise you to answer that the super-world doesn’t, after all, have to be causally connected throughout. Certainly large parts of it are, but why not leave it at that?

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64.  To David Sanford, 16 February 1987

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If the super-world isn’t causally interconnected, what makes it all one world? I’d advise you to say: the whole of it is spatiotemporally interconnected, even if not causally connected. That answer blocks you from running a causal analysis of the spatiotemporal connection; I think that project can be abandoned and not be missed. Likewise I say that every world is spatiotemporally interconnected, and no two worlds are causally connected, but I don’t say that every world is causally interconnected. The reason is that I want to provide for lawless chaotic worlds, in which no causation takes place. --‘Suppose the super-world we live in is heteronomic. Isn’t this contingent?’ So say I, of course; but I’m not a super-realist. Exactly as I deny that there is any contingency in the structure of the entire plurality of worlds, so the super-realist ought to deny that there is any contingency in the structure of the one super-world. (So say I if, contra my regularity theory of law, I granted the possibility of a heteronomic world in the first place.) --Expansions and engulfing. Let’s say that a C-expansion of several worlds w1, w2, . . . is a single world that contains distinct counterparts of w1, w2, . . .; whereas a  D-expansion of w1, w2, . . . is a single world that contains distinct duplicates of w1, w2,  . . . . Forrest and Armstrong argued that if for reductio there were a class of all worlds, there would have to be a D-expansion of this class, and then the D-expansion both would and couldn’t be one of the worlds originally in the class.2 I reply that this class doesn’t have a D-expansion; see PoW 2.2.3 Probably the same objection and reply could be imitated in terms of C-expansions, except that there wouldn’t be such a clearcut way of reaching contradiction from the supposition that a world is a C-expansion of a class including itself. Also, I might have an additional reply in that case: that similarity in respect of being the whole of a world is a weighty respect of similarity, so that (under at least some reasonable counterpart relations) nothing less than the whole of a world can be a counterpart of a whole world. No such reply is possible to the argument about D-expansions since the similarity of duplicates, unlike the similarity of counterparts, is entirely intrinsic. See PoW 88–89. --Thank you for the correction to the Hazen citation. I do have an erratum list in case of a future printing – very short, thanks to Blackwell’s excellent production of the book. Yours, David Lewis   ‘An Argument Against David Lewis’ Theory of Possible Worlds’ (Forrest and Armstrong 1984).   On the Plurality of Worlds (Lewis 1986c, 101–4).

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65.  To Frank Jackson and Robert Pargetter, 8 May 1987 [Princeton, NJ] Dear Frank and Robert, Thank you very much for ‘Causal Statements’.1 You, Frank, were of course right to say I wouldn’t agree; but I like it anyway, and find I have a lot to say about it. Trade-off. If the profligate theory is workable at all, the economical theory still might be preferable, depending on which of two alternative problems proves more tractable. It seems to me that one problem trades off with another. The profligate theory puts singular causal statements into the standard form, almost without exception; whereas you require exceptional treatment of the statements that get treated as comparative, so you have a problem about just which statements get just what sort of exceptional form. But the profligate theory has a problem that you dodge entirely: if there are many versions of an event (versions of your serving in which the tension is essential and versions in which it’s accidental, for instance) I have a problem about just which version an event-term denotes. This semantic problem isn’t addressed in my papers, because I’ve been talking about the causal relation of given events rather than the analysis of given causal statements, but it’s still there before the whole story is done. I don’t know which of the two problems is easier; or even whether they’re really very different or whether a solution for one can be translated into a solution for the other. Tollens. The main reason the profligate theory is supposed to not work is that it has so many events that, in distinguishing them, it has to treat them as some sort of abstract entities – sets of possible regions, thing-property-time triples, tropes, . . . – and abstract entities can’t cause anything. I tollens this: As for . . . the denial that abstract entities enter into causal interaction, this too seems to disagree with the [thesis that to be abstract is to be a set or a universal]. . . . Many authors have proposed to identify an event – the very thing that most surely can cause and be caused – with one or another sort of set. . . . Must any such identification be rejected . . . just because sets are supposed to be abstract? (On the Plurality of Worlds, pages 83–84). Let me put it this way. We have a conflict between (1) events cause – so we all agree; (2) abstract entities never cause – so it is often said; (3) events are a certain sort of set – so some reductive theories propose; and (4) sets are abstract – so it is also often said. I think (3) is by no means the most suspect of the four; we ought also, or we ought 1

  ‘Causal Statements in Metaphysics’ (Jackson and Pargetter 1988).

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65.  To Frank Jackson and Robert Pargetter, 8 May 1987

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first, to doubt (2) and (4). What I really doubt is that we mean anything uniform when we say ‘abstract’, so I wouldn’t mind granting that we could sometimes mean something that makes (2) true and sometimes mean something that makes (4) true – which is not to say we ever mean anything that makes them true together. Events as trans-world sums of regions. But if you still think sets can’t cause, consider that my theory of events could just as well have been done in mereology: an event is a certain sort of mereological sum of suitably related regions, at most one per world. Since this sum has a unique decomposition into the appropriate kind of parts (worldslices, these being intersections of the sum with a world that are not part of any other such intersection (I pass over the complications that arise if there are universals)) it matters not that sums in general lack unique decompositions. But I suppose you’d say – thinking as I do that judgements of concreteness are a mess, I don’t much go in for them myself – that a mereological sum of regions is concrete, so on that score at least it is eligible to cause. Irrelevance of the otherworldly parts of events. Even so, profligacy says that often many events, the ones we think of as alternative versions of the same event, will differ only in their otherworldly parts. So how can what’s out of this world make a difference to the causing that happens in this world? – I protest that the counterfactual analysis of causation tells you just how the otherworldly part does make a difference. It makes a difference by determining what you have to change, what other world you have to go to, to suppose away the given event. This does not conflict with the intuitive idea that causation from one possible world to another makes no sense. The causal isolation of worlds can still be stated and defended as in Plurality of Worlds, pages 78–81, even if we take an event to be something that extends through many worlds, and in such a way that its otherworldly part matters to what it causes in this world. Not just profligacy. The problem just answered arises not just for profligacy, but for any theory that allows that sometimes two events occur in the very same region. They needn’t be two versions of something; they can be as different as you please. They can be the cooling of the sphere and the spinning of the sphere; the passing of light through the glass window and the passing of sound through the same glass; or what have you. Then again the thisworldly regions of the two events won’t differ. The difference is in the otherworldly extensions, the other worlds where the sphere spins but doesn’t cool, or the window passes light but not sound. Unspecific tropes. Why is it an ‘essential feature’ of trope theory that tropes are fully specific? I prefer that sort of trope theory – it lends itself better to the job of defining natural properties, and it dodges the question of how the less and more specific tropes of the same kind, and at the same location, are related. But it’s not clear to me

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that the advantage is so great as to be ‘essential’, especially if it spoils the idea that unspecific tropes should be the unspecific versions of events. My impression had been that Williams and Campbell did allow unspecific tropes, however I haven’t found passages that confirm this. But neither have I found passages that clearly go the other way. Williams often speaks of ‘the’ colour trope of something, but this is far from a commitment to uniqueness. Harlac, a main example in ‘On the Elements of Being’2 and ‘Universals and Existents’,3 does seem to be a specific colour trope, though this is said more definitely in U&E than in EoB. But Harlac is just one example. Kim. I think your reason against identifying Kim’s events with their constitutive ’tuples is inconclusive. If the thing didn’t have the property at the time, the ’tuple would still exist but the event wouldn’t – well, a defender of the identification could say that the ’tuple is the event, however what we want for de re modality of events, qua events, is the event-counterpart relation. [x, P, t] is an event, at world w where x has P at t; at a world wʹ where x has counterpart xʹ, t has counterpart tʹ, and xʹ doesn’t have P at tʹ, the ’tuple [xʹ, P, tʹ] is not an event; maybe [xʹ, P, tʹ] is a tuple-counterpart of [x, P, t], however [xʹ, P, tʹ] is not an event-counterpart of [x, P, t]; in fact, [x, P, t] has no event-counterpart at wʹ, which is the same as to say that [x, P, t], taken qua event rather than qua ’tuple, doesn’t exist there. It’s the usual story – multiplication of counterpart relations trades off with multiplication of entities. The same reply goes against another reason, one you didn’t give. Kim says somewhere that the constitutive ’tuple needn’t be essential: an event which in fact is given by [x, P, t] might have existed and not been given by [x, P, t] – for instance, it might have been postponed. A defender of the identity of events and their ’tuples could say that this is a case where the event-counterpart of [x, P, t] exists, but is not the ’tuple-counterpart of [x, P, t]. There’s a better reason not to identify Kim’s events with their ’tuples: he says that in relational cases, the same event may have more than one constitutive ’tuple. For instance the event given by [x, y, R, t] might be given also by [y, x, Rʹ, t] where Rʹ is the converse of R, and likewise for more complicated permutations. But this doesn’t take you far from the identification – the fallback would be that events are equivalence-classes under permutation of their ’tuples. Whether ’tuple or whether equivalence class, the issue whether sethood disqualifies them from being causes remains the same.

  (Williams 1953a, 1953b). Reprinted: (Williams 2018, Ch. 2).   (Williams 1986). Reprinted: (Williams 2018, Ch. 3).

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65.  To Frank Jackson and Robert Pargetter, 8 May 1987

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I know that Kim discusses permuted ’tuples. I faintly remember a discussion (not necessarily in print) about a parallel problem with aggregation. Consider the quadruple [E, C, P, t] and the 42-tuple [el, . . ., e20, c1, . . ., c20, Q, t] where E is the team Essendon, e1, . . ., e20 are the 20 players that comprise the team on afternoon t, likewise C is the team Carlton and c1, . . ., c20, are its 20 players, P is a binary version of the relation ‘plays’ and Q is a 40-ary version. It’s plausible that the quadruple and the 42-tuple are constitutive of the same event; I see no reason Kim shouldn’t grant this, and faintly remember that he did; but if so, the fallback is again that events are equivalence classes of ’tuples. No reference? The no-reference theory puts existential quantifiers in place of definite descriptions: Some (fully specific) event that was a brake or steering failure caused some (fully specific) event that was the (contextually definite) accident. The point of doing this isn’t that you want specificity: there’s no reason why an unspecific definite description can’t denote a highly specific event. Rather, the problem arises because there may be more events than one that satisfy the unspecific description – one event that was a brake or steering failure caused an accident, another didn’t. You think that if you’d left the definite descriptions, and a (fully specific) brake failure caused the accident, and a (fully specific) steering failure didn’t cause the accident, you would have to make an arbitrary decision to settle the truth value of ‘Brake or steering failure caused the accident’. I don’t agree. When there are two F’s, ‘the F’ is not denotationless; rather, it’s ambiguous or indeterminate in its denotation. When denotation is ambiguous or indeterminate, contextual factors make a difference. One important effect is accommodation: ceteris paribus, the right denotation is the one that makes true what’s been said. So if there are two F’s, f1 which is G and f2 which isn’t G, and you say ‘the F is G’ then, ceteris paribus, that favours making ‘the F’ denote f1 so that what you say comes out true. Or if there are three, f0 and f1 which are both G and f2 which isn’t G, then ceteris paribus saying ‘the F is G’ favours making ‘the F’ ambiguous between denoting f0 and f1 but excluding f2; we can apply supervaluationism to the residual ambiguity; and again ‘the F is G’, when said, comes out true. If it weren’t for the ‘ceteris paribus’, which covers other effects that might overrule accommodation, the definite description would come out just like an existential quantifier! So you can have something equivalent to the no-reference theory which still uses definite descriptions, provided that these definite descriptions are subject to the appropriate – and, I think, ordinary – contextual resolution of (some or all) indeterminacy of reference. Causation by e alone. Formula (18) bothers me, because I don’t see how the propositional attitudes alone – or any e alone, if e is a fully specific event and part of what

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actually caused your bad serving – could possibly have caused your serving. Don’t the propositional attitudes have to combine with working muscles, non-interfering circumstances, . . . to cause your serving? But if the circumstances are included, we look to be back to your overdetermination problem. Include the actual fully specific non-interfering circumstances in e, and e wouldn’t have existed in the counterfactual case (because of the balloon popper). Exclude them, and e wouldn’t have been enough by itself to cause your serving. Because some possible circumstances, not the balloon popper but something worse, say a dynamite exploder, would have been enough to present the serving. --Winter plans are taking shape, but still tentative. Since I’m on leave for 1987–8, I don’t need to be back for the beginning of classes. I thought I might arrive early August (perhaps the 7th), leave late September (perhaps the 25th), divide my time before the conference between Sydney and Canberra, spend my time after the conference mostly in Melbourne. Steffi might arrive just before the conference and leave in the second week of September, but as always the big uncertainty is when and how long she can take off from work. Last year, I was short of papers to read around, because virtually all my writing for three years had gone into Plurality of Worlds and Papers II. (Had I known how much more delay there was to be with the latter, I wouldn’t have hesitated to read the things forthcoming there.) But this year I’ll have more to offer. Not all entirely written yet, but done enough to speak from. ‘Mill and Milquetoast’ – non-technical, a polemic about the feebleness of, and a replacement for, Mill’s utilitarian defence of toleration. (I’d like to try it on an audience including Chin-liew4 and H.J.,5 if possible.) ‘Statements Partly About Observation’ – low tech, an effort to salvage something from Ayer’s 2nd edition definition of verifiability, though not enough to serve Ayer’s purposes. ‘Desires as Beliefs’ – low tech, a refutation of one form of the idea that we can be motivated just by a belief about what would be good, without benefit of any additional desires. A relative of one of the triviality results against the prob­abil­ ity conditional. and, I hope, (but this will be for the conference if it gets far enough) ‘Parts of Sets’ – expansion of what I’ve said elsewhere to the effect that the oneout-of-many aspect of set theory is just mereology, and the distinctive (and mysterious) thing in set theory is the operation of making unit sets.   Chin Liew Ten.   

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5

 H.J. McCloskey.

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66.  To D.H. Mellor, 3 November 1987

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We may have seen the last of that miserable lounge in Honolulu in the middle of the night. Qantas is about to start running three non-stops per week to and from San Francisco. See you soon, Yours, David PS Ian Pratt has raised a nice question 1) Is there an indicative may-condition with assertability given by ‘If A, may be that C’ assertable iff P(C/A) not too . 2) If so, how does the implicature-of-robustness theory explain it?

66.  To D.H. Mellor, 3 November 1987 Princeton University Princeton, NJ Dear Hugh, Peter Menzies (T&M, Sydney) has spotted a problem about the counterfactual analysis of probabilistic causation. I think it’s a problem equally for both of us – it doesn’t depend on anything we disagree about. Take my neuron diagram for early preemption, as in Papers II, page 200. Suppose that all the neurons along the bottom path from C2 through I and M to E are surefire neurons: their probability of firing if stimulated (and not also inhibited) is 100%, or near enough. But suppose the neurons along the top path and the branch – C1, J, D, the next two, and the one between J and I – are cheapo unreliable neurons: their probability of firing if stimulated is only 60%. (Peter tells it a little differently: a cheapo neuron fires reliably, but its firing may fail to stimulate the next neuron along. The difference doesn’t matter. I’ll stick to what I’m used to.) C1 and C2 fire sim­ul­tan­ eous­ly. The cheapo neurons all happen to work. I is inhibited, so the two shown dotted don’t fire. Compelling intuition: C1’s firing caused E’s firing. C2’s firing didn’t. I’m sure we’ve talked about this set-up before (when you spoke at Princeton, and probably not only then), as one in which I claim that we have causation without causal dependence, and a cause that lowers probability. C1’s firing raised the prob­ abil­ity of D’s firing, which raised the probability of E’s firing, and thereby C1’s firing caused E’s firing. Yet C1’s firing lowered the probability of E’s firing from 100% to

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72%. (When both C1 and C2 fire, there are three ways for E to fire. J fails: probability 40%. J fires, but the neuron between J and I fails: probability 24%. J fires, the neuron between J and I fires, so the surefire chain gets stopped, but then all the cheapo neuro­ns fire: probability only 8%, but ex hypothesi it’s what happens. Total: 72%.) So far, a familiar issue; it’s essentially the same thing I discuss (unfortunately, without the neurons) on pages 179–80 of Papers II. But what Peter spotted, and I kick myself for overlooking it, is that beside the problem about how to make C1’s firing count as a cause when it doesn’t raise prob­ abil­ity, there’s also an opposite problem about C2’s firing. It clearly isn’t a cause of E’s firing. Yet it does raise the probability of E’s firing from 13% to 72%! (When only C1 fires, the only way for E to fire is for the four cheapo neurons on the top path all to fire.) By contributing a chance that the reliable bottom path would escape inhibition and go through – even when it turns out that this doesn’t happen – the preempted cause raises the probability of the effect. According to my analysis, that’s causal dependence, and a fortiori it’s causation. I’m persuaded that it’s a fair counterexample and my analysis needs fixing. Unless I’ve overlooked something, so does yours. Intuitively, we seem to have a choice of two different reasons why C2’s firing isn’t a cause of E’s firing. (1) There’s no completed continuous causal chain running from the putative cause to the putative effect. Or (2) although it’s true that without the putative cause, the probability of the putative effect would have been less, that’s not because the probability of the putative effect caused as it actually was caused would have been less; rather, it’s because the probability of the putative effect caused as it was not actually caused would have been less. Correspondingly, we have two approaches to fixing the analysis. Peter’s choice is (1): requiring a continuous chain. There’s a bit of bother about formulating the requirement, but I have little doubt it can be done. The trouble is that we’d rule out action at a distance: this exactly is causation without a continuous chain of inter­ medi­ates running from cause to effect. If it really is good old-fashioned conceptual analysis we want – and for me it is – then I think it’s quite bad to rule out action at a distance a priori. If there isn’t any of it in this world, OK, but we shouldn’t build that into the analysis. I know what to say to defend the chain requirement: action at a distance is a far-fetched case, contrary to the ways of this world and also to what we habitually take to be the ways of this world. Are we really so sure what we think about it? Maybe we fool ourselves by thinking we’re imagining action at a distance when really we’re imagining inconsistently, or imagining some very subtle sort of intermediates which make a continuous chain after all. Spoils to the victor! – But to me this doesn’t ring true. I feel a bit too sure about the possibility to leave it as a spoils-to-the-victor question.

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67.  To Gene Cline, 21 December 1987

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So I’m inclined to prefer (2): shifting from counterfactuals about the prob­abil­ ity of the effect’s occurring to counterfactuals about the probability of its occurring in the way it actually did. But how to make this work? Of course ‘caused as it actually was caused’ is prima facie circular. Maybe fall back to ‘preceded as it actually was preceded’? That might well get in trouble by admitting spurious causes, causes not of the event itself but of preceding events without which the main event would have been differently preceded. Or maybe ‘immediately caused as it actually was immediately caused’, avoiding the circularity by first defining immediate causation and then going on to remote causation? But one division into immediate versus remote causes seems crude, when we’re at least normally dealing with continuous chains. Suggestions? Yours, David c: Peter Menzies

67.  To Gene Cline, 21 December 1987 [Princeton, NJ] Dear Gene Cline, Thank you for your letter. You’re quite right about what I claim.1 So what do I say about the examples? CF1 and CF2.2 Goldbach’s states of mind don’t depend on the facts of arith­ met­ic; they depend on what he believes about the facts of arithmetic. If he came to believe, whether rightly or wrongly, that there was an even number not the sum of two primes then he would be surprised; and if he came to believe, whether rightly or wrongly, that there was no such number (or better, that it had been proven that there was no such number) then he would be happy. I have no objection to taking your CF1 and CF2 as short for such psychological-to-psychological counterfactuals, and therefore non-vacuously true; but if they’re read literally, as arithmetical-to-psychological, they’re vacuous. CF3 and CF4.3 I don’t agree, of course, that the one with the impossible ante­ cedent is false. What is false is not the counterfactual itself but what is conversationally   On page 111 of On the Plurality of Worlds.   CF1: if there were an even number which is not the sum of two primes Goldbach would be surprised. CF2: if there were no even numbers which fail to be the sum of two primes Goldbach would be happy. 3   CF3: if Goldbach’s conjecture were true, it would have been proved by now. CF4: if Goldbach’s conjecture were false, it would have been disproved by now. Examples are from Gene Cline’s letter to Lewis, 10 December 1987. 1 2

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implicated by it: namely, that Goldbach’s conjecture is not an unproved truth (for CF3) or not an undisproved falsehood (for CF4). We think ‘that’s false!’ because the message conveyed is false; and then the accusation sticks to the wrong target, namely the literal content of what was said instead of the message implicated thereby. John Mackie once thought that counterfactuals were condensed arguments, with some premises left out. Accordingly they were not true or false, and so the conditions for asserting them could not have to do with whether the speaker believed they were true or false. To assert the conditional ‘If it were that A, it would be that C’ is like saying ‘Suppose A; therefore C’; you’re manifestly taking for granted some premise that would complete the argument from A to C, without bothering to say just what that premise is. (It may be more or less definite from context what the missing premise is supposed to be.) I think something rather like this is right for coun­ter­ fac­tuals with impossible antecedents. Only rather like this, of course; because I say they are true or false, because one and all vacuously true. But since they’re not one and all assertible, their vacuous truth condition can’t have much to do with why we assert one rather than another. We assert the ones that correspond to arguments that we want to convey in a rough way, without taking responsibility for getting all the extra premises quite right. That’s silent about when we deny conditionals with impossible antecedents. And rightly silent, I say, because we don’t deny them. What we often do is respond negatively to them by way of denying some premise of the argument we think the speaker must have had in mind; but if it turns out he had some different argument in mind, the denial doesn’t stick. That shows it wasn’t a denial of the conditional itself. And there’s always some good argument from impossible A to any C. (As in Russell’s famous argument that if 5 + 7 were 11, he’d be the Pope: if 5 + 7 were 11, then subtracting 10 from both sides 2 would be 1; Russell and the Pope are two; so if 2 were 1, he and the pope would be one; which is to say that he’d be the Pope.) So you wouldn’t want to deny any vacuous counterfactual outright, seeing that in some unlikely context or other it could be used to express some good argument. Partly, of course, I’m mounting a defensive operation: any possible worlds theory of counterfactuals will have trouble making discriminations between one impossible antecedent and another, hence will prefer to treat all impossible antecedents alike. Since for any C there will be some impossible A for which ‘If it were that A it would be that C’ will seem true, that means treating all vacuous conditionals as true. I say that by invoking considerations of implicature, I can live with that conclusion. (Just as Grice, or better Jackson, says that by invoking considerations of implicature we can live with the conclusion that all indicative conditionals with false antecedents are true.) Yet even if some otherwise nice theory were available that did call some vacuous counterfactuals false, I think I wouldn’t want it. Whenever it told me that ‘If

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68.  To Peter van Inwagen, 30 November 1989

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A then C’ was a false counterfactual with impossible A, I would worry that we could make the counterfactual look true after all by putting it in the context of some sneaky Russell-and-the-Pope-style argument from A to C. Sincerely, David Lewis

68.  To Peter van Inwagen, 30 November 1989 [Princeton, NJ] Dear Peter, I’ve just read, not far apart, your ‘When is the Will Free?’1 and the exchange between Adams and Plantinga in the Profile book.2 This set me thinking about something that may or may not be a serious problem for a position that may or may not be Plantinga’s. What do you think? The position – never mind whose it may be – is Molinist incompatibilism. It goes as follows. There are determinate true counterfactuals about what would be freely done by a given possible free creature in given circumstances. ‘Free’ means what an incompatibilist thinks it means, whatever exactly that is. It’s contradictory to say that someone freely does what he has no choice (at the time) about whether to do. Your Beta-prime is valid. Now let’s suppose that one true counterfactual of freedom is (*) If Curley (in circumstances C) were offered a bribe of $35,000, he would freely take it. And suppose Curley (in C) is offered it, and does freely take it. I suppose Curley has no choice about whether Curley (in C) is offered the bribe. (He may have had a choice earlier, but not anymore at the time of decision.) And I suppose he has no choice about whether If Curley (in C) is offered the bribe, then if (*), then he freely takes it. That’s just logic. If Curley has no choice about whether (*), then by Beta-prime he has no choice about whether to freely take the bribe, contra our supposition that he does freely take it. So it’s crucial to the position that Curley does have a choice about whether (*). Then (*) cannot be a necessary truth; and it cannot hold in virtue of   (van Inwagen 1989).   

1

  (Tomberlin and van Inwagen 1985).

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God’s decree, or in virtue of laws of nature plus ancient history, or in virtue of Curley’s past intentions, or in virtue of anything else that Curley doesn’t now have a choice about. So what does (*) hold in virtue of? It would be nice to say that (*) holds in virtue of Curley’s actual choice. His free choice about whether (*) is to be true is exactly his free choice about whether to take the bribe. So, ex hypothesi, he has a choice about whether (*). So far, so good. But now let’s suppose another true counterfactual of freedom is (**) If Curley (in circumstances C) were offered a bribe of $34,995, he would freely decline it. This time the antecedent is false: Curley (in C) is not offered the $34,995. In virtue of  what is (**) true? It cannot be in virtue of Curley’s actual choice to decline the $34,995 – he made no such choice. I suppose it’s desirable to treat (*) and (**) alike. How desirable, I’m not sure. Suppose we do. Then the answer to ‘in virtue of what is a counterfactual of freedom true?’ has to be the same for both. We eliminated some answers in connection with (*) because they led to the conclusion that Curley had no choice about whether (*). We eliminated another answer in connection with (**) because there was no actual choice. We’ve eliminated all the answers I can think of except this one: a counterfactual of freedom holds in virtue of nothing except itself; it’s a sui generis, irreducible, brute fact, not supervenient on the rest of what’s true. (There had better be some brute facts somewhere. It couldn’t very well turn out that everything true had to hold in virtue of something else! Myself, I can’t believe coun­ter­ fac­tuals are among the irreducible brute facts, but some might say that’s just a Humean prejudice, or even that it reflects my stake in a particular reductionist proposal.) Now I think nobody ever had any choice about whether (**). And I think the hypothesis that it’s brute and irreducible explains this. If someone once did have a choice about whether (**), wouldn’t that make (**) supervene on how that someone made that choice, contra its hypothetical irreducibility? But now if (*) and (**) are being treated alike, it seems that the same should go for (*)! But if Curley has no choice about whether (*), then as we already saw, by Beta-prime he has no choice about whether to take the bribe he’s actually offered. In a nutshell: what Curley chooses and whether (*) is true must agree. Is that because (*) controls Curley or is that because Curley controls (*)? If (*) controls Curley, Curley isn’t free. If Curley controls (*), then (*) and (**) must work in very different ways, because Curley certainly doesn’t control (**). How bad is it for Molinist incompatibilism to conclude that (*) and (**) work in very different ways? Yours, c: Bob Adams

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69.  To Peter van Inwagen, 15 January 1990

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PS on the matter of your tu quoque.3 I’ve changed my mind in a big way about set theory, thanks to some recent inventions by John Burgess, Allen Hazen, and Quine. Pairing can be introduced in the framework of plural quantification and mereology. The Fitzgerald plan4 of Ramsification, PoC 2.6, does work.5 I don’t need to claim any primitive understanding of singleton. I can deny it without thereby rebelling against mathematics. My first choice, if I could have it, would probably still be a way to claim primitive understanding of singleton with an easy conscience. I still think that’s unlikely. But now that Ramsification is feasible and runs at least a close second, accepting primitive singleton with uneasy conscience is decisively beaten.

69.  To Peter van Inwagen, 15 January 1990 [Princeton, NJ] Dear Peter, I’m not sure I agree that free-will theodicy is easier if there are no coun­ter­fac­ tuals of freedom, and no middle knowledge thereof. There’s one way in which it’s easier, just as you say. But in another way, maybe it’s harder. Anyway there’s a new problem, whether harder or whether easier, about what you should do if you don’t have middle knowledge but you do have foreknowledge of what free creatures or chance set-ups will actually do. I usually think of it as a problem about time travelers, prophets, etc.; but I suppose it could also apply to God. (Not if we deny His foreknowledge. But I’d expect to be told that a theodicy that denies God’s foreknowledge is unacceptable.) You have this choice. You may gamble: 90% objective chance of getting Best, 10% objective chance of getting Worst. Or you may choose the sure thing: Bad, for certain. Bad is nearer to Worst than to Best, but the distance from Bad to Worst isn’t negligible. What to do? – Gamble. But now suppose you have foreknowledge that you will in fact gamble, and you will get Worst. Now, what should you do? You could think: it’s a choice of Bad for sure versus Worst for sure, so you should choose Bad. Or you could think: it’s just as true as ever that the objective expected value is better if you gamble, so you should gamble – too bad you’ll lose, but doing what you should never guarantees success. Somebody is sure to say: this isn’t a real decision problem, because in decision you don’t know what you’ll do until you decide. To this I say three things. (1) Would   See Letter 198. To Peter van Inwagen, 20 December 1990, and Letter 193. To Michael Jubien, 14 June 1989, Volume 1: Part 2: Modality. 4   ‘Meaning in Science and Mathematics’ (Fitzgerald 1974).    5  Parts of Classes (Lewis 1991, 45–54). 3

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a believer be willing to conclude that, thanks to His foreknowledge, God has never made any decisions? (2) Maybe it’s true by definition that a decision must be a transition from ignorance to knowledge, and if so then this isn’t exactly a decision, but it may be just like one in all other ways. (3) I never said it was a decision problem. Be it a decision problem or no, I still want an answer to my question: what should you do? ‘Should’ needn’t presuppose there’s a decision. Imagine that you are protected by a robot bodyguard. It doesn’t have a humanoid belief-desire psychology, it’s deterministic, not even a compatibilist would say it has free will. It definitely doesn’t make decisions. We can still ask whether it does what it should if you are simultaneously attacked by a playful puppy and a gang of punks with knives. --Plantinga’s Molinism is at least concessive. But at times it’s more, though short of outright endorsement. See the reply to Adams: ‘Indeed I think there are coun­ter­ fac­tuals of freedom I believe’ (373). Then follow several pages of defense of them against Adams. ‘I don’t believe there are any good arguments against counterfactuals of freedom, or middle knowledge, or the claim that some of God’s actions are to be explained in terms of middle knowledge’ (378–9).1 --2 Yes: we can have a version of set theory whose primitive vocabulary is that of a plural-quantificational extension of first-order logic, plus ‘is a part of’. At present, the co-authored appendix about how it’s done has been approved by only three of its four co-authors, so I shouldn’t show it around. Soon, I hope. Yes, you could try a tu quoque either on the apparatus of plural quantification or on the apparatus of mereology. If you did, I couldn’t answer as before: too right it’s mysterious, but it’s the only game in town. Because, as you know, I think plurals and mereology are unproblematic and perfectly understood. I also think that in both cases we have something very close to identity. The plural copula ‘it is one of them’ is like an infinite disjunction of identities. (In the finite case, someone is one of the Cobbers iff he is John or he is Chris or he is Ron or he is Maitland.) Composition, interdefinable with part-whole, I take to be a many-one extension of identity: I am my atoms, they are me. (Better: I am my temporal-parts-of-atoms.) So if you could run a tu quoque against either the plural copula or composition, I expect you could run one against identity itself. Identity is, on my account, external for the same sort of reason part-whole is. (I get flak over this.) Earth = Earth; Twin-Earth and Earth are duplicates, likewise Earth and Earth, but Twin-Earth ≠ Earth. ‘But if identity is external, then why can’t anything be identical to anything? Why can’t Earth be identical to Twin-Earth?’ Now in a sense I do say that Earth can be identical to Twin-Earth; I mean there’s a world where they have a common counterpart. But that’s not true of anything and   (Plantinga 1985).   See Letter 198. To Peter van Inwagen, 20 December 1990, Volume 1: Part 2: Modality.

1 2

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69.  To Peter van Inwagen, 15 January 1990

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anything. Still less is it true that for anything and anything, there’s a world where they have a common duplicate. Whatever a principle of recombination applying to external relations ought to say, it had better not say that. If it does, that’s a loophole left by careless drafting. In PoW, I followed Hume’s example – no necessary connexions between distinct existences – and wrote distinctness into my principle of recombination. (As always, by distinctness I meant non-overlap, not just non-identity.) ‘We are dealing with something akin to our Humean principle of recombination . . . which prohibits a necessary connection between the intrinsic character of a thing and the intrinsic character of distinct things with which it coexists. We equally need a companion principle which prohibits a necessary connection between the intrinsic character of a thing and its external relations to other things’ (181).3 I might better have said: ‘between the intrinsic characters of one or both of two distinct things and their external relations’. That would allow the appropriate necessary connections involving the external relations of identity and part-whole themselves: it can’t happen that (a duplicate of) something red all over is identical to, or is part of, (a duplicate of) something green all over. --What prevents the Ersatzer from appropriating my methods and Ramsifying the selection relation out of his modal ontology?4 Well, what does his Ramsey sentence look like? Choice 1 he quantifies over classes of ordered pairs, or Choice 2 he quantifies plurally over ordered pairs themselves. (They might be Kuratowski pairs. If he already accepts set theory, he needn’t appropriate new methods of making pairs without it.) ‘There are some pairs, and one of these pairs is the pair of the concrete world and a certain abstract simple . . .’ – so what are the other pairs? – ‘. . . and, if there had been a talking donkey, that pair would not have been one of them . . .’ – yes it would! – ‘. . . but instead the pair of the concrete world and a different abstract simple would have been one of them’. This way, taking the relation in extension, I either don’t understand or don’t believe the Ramsey sentence. So try Choice 3: he quantifies over relations-in-intension, which I suppose are things of the same kind as properties and propositions. ‘There is a relation-in-intension that relates the concrete world to a certain abstract simple, and, if there had been a talking donkey, it would have related the concrete world to a different abstract simple’. I say that ‘relates to’ is just the dyadic version of ‘selects’, the primitive we were supposedly Ramsifying out. --The connection with Protector escaped me,5 though maybe if I’d read the two close together6 . . . Nice! [. . .] Yours,   (Lewis 1986c, 181).    4  Cf. ‘Ersatz Possible Worlds’ (Melia 2008, 149).   (Niven 1973).  6   That is, Protector (Niven 1973) and van Inwagen’s ‘When Is the Will Free?’ (1989). 3 5

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70.  To Galen Strawson, 16 July 1990 Melbourne, Australia Dear Galen, Regularity analyses of causation (in the sense of my ‘causation’) and regularity analyses of lawhood are independent. I reject the former. I accept the latter. The latter, not the former, is your target. Whatever laws of nature may be – whether necessary or contingent, whether explicable or not, whether defeasible or exceptionless – I think we can still say that laws are regularities, distinguished somehow from other regularities that aren’t laws.* I hope that’s neutral terminology, common ground between all concerned. The issue between us has to do with how lawful regularities differ from other, accidental regularities. I think lawhood supervenes on local matters of particular fact;** I do not think ultimate laws have any explanation whatever. (In a way, they are worse than coincidences: a coincidence can at least be explained piecemeal. When I met Frank Jackson unexpectedly in the Adelaide airport, the explanation of that coincidence consisted in the explanation of why he was there then, plus the separate ex­plan­ation of why I was there then.) Nowadays, my side of these issues would often be called the ‘regularity theory’ of lawhood; not so when ‘Causation’ was written.1 So the terminology of that paper has retroactively been made confusing. Anyhow, the ‘regularity analysis’ of causation was roughly this: whatever it may be that distinguishes some regularities as lawful, cases of singular causation are instances of lawful regularities. That’s what I rejected, in favour of a counterfactual analysis. (One that has itself developed a distressing number of complications in later years, and faces at least one problem to which I don’t now have an answer: that raised by Peter Menzies in Phil. Sci. Dec 89.)2 That analysis still makes singular causation depend on the laws, but in a different way: instead of applying the laws to the actual situation with the cause present, it applies them to a counterfactual situation with cause absent, but history held fixed so far as possible. The counterfactual analysis of causation, like the regularity analysis, is meant to be neutral between different the­or­ ies about what distinguishes some regularities as lawful. *   A lawmaker theory like Armstrong’s has a terminological choice: there is the lawmaking relation of universals N(F, G), there is the (defeasible) regularity that all F’s are G’s, and the first somehow necessitates the second – then which is the law, the lawmaker or the regularity? Armstrong says the lawmaker is the law, I’d say (if I held this view) that the regularity is the law. But I think this is an arbitrary choice, a n ­ on-issue. **   Considerations about chance might force me to back down from this. But since none of the alternative ways of dealing with chance seem to me satisfactory, let me leave these issues in abeyance. See my Papers II, xiv–xvii and 121–131. 1   (Lewis 1973a). 2   ‘Probabilistic Causation and Causal Processes: A Critique of Lewis’ (Menzies 1989).

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71.  To John Earman, 12 February 1991

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In virtue of what are counterfactuals true? In virtue of what do singular causal relations hold, if I’m right to analyse those in terms of counterfactual dependence? Answer: in virtue of the qualitative and nomic character of the actual world, its history and its laws. (This is meant to be neutral as to whether the laws supervene on the history.) The other worlds enter the story only as points of comparison. I can say concisely that the qualitative and nomic character of this world, where I didn’t strike the match and it didn’t light, make this world resemble some worlds where I struck the match and it lit more than it resembles any worlds where I struck the match and it didn’t light. In principle, I could say the same thing about the character of this world directly, without benefit of the comparisons. But it would take an enormous disjunction of very specific descriptions. The comparative method is not only the concise way, but the only feasible way. Still, neither the resemblance of worlds nor the counterfactuals are ‘basic’ – they afford ways of describing (describing rather unspecifically) the character of this world. Please don’t think the lack of a reply when you sent me ‘Realism and Causation’3 signals any kind of adverse judgement. I read it with interest and respect. But you’re right to guess that my volume of ‘incoming’ has become overpowering. I still try to read it all (except when it’s gratuitously technical). I answer letters, not always promptly. But I’ve nearly given up on writing letters in response to papers. Perhaps I reply to 5% or so, and there’s no rhyme or reason about which 5%. (As it happens, I think I get letters back about 5% of the time when I send papers to other people, so I dare say I’m not alone in being hard-pressed.) It’s sad that this has happened; but I reluctantly concluded that I had no other choice, if answering the mail was not to be a full-time job. Yours, David Lewis

71.  To John Earman, 12 February 1991 [Princeton, NJ] Dear John, I like your ‘Defense of Laws’1 and agree with it entirely. Two comments. Page 25: ‘coherence and unity are certainly desiderata . . . not the same as simplicity’. I might think that unity, while not the same as the whole of simplicity, was   (Strawson 1987).

3

  (Earman 1993).

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one aspect of simplicity, so not a distinct desideratum alongside simplicity. Maybe the same goes for coherence? – but I’m not so sure what coherence is, if it’s distinguished both from unity and from consistency. (It can’t just mean consistency here, since in MRL2 we’re running a contest between theories that are all at least true, and a fortiori consistent.) Page 28: ‘very different optimal compromises’. I take it this worry can be sep­ar­ ated from the radical baloney about myriad ways of carving up the world. Note that there are two versions of the problem. (1) There might be two theories exactly tied for best, with very little in common. Or (2) there might be two theories, with very little in common, such that which one is the winner is very sensitive to the exact details of our standards of simplicity, strength (and whatever other desiderata you might throw in), and balance between these. Then if these exact standards are a psychological matter, or if they vary from person to person or culture to culture, lawhood too will be psychological or variable (‘subjective’). You can see how (1) and (2) might, but needn’t, combine. My answer to the problem in either version is: yes, that might happen, I have no a priori guarantee that it doesn’t happen, and if it did then, indeed, there would be fewer laws than we like to think, or the laws would be more subjective than we like to think. But it doesn’t have to happen. If nature is kind to us, there may be one theory very far out in front of the rest; and so far out in front of the pack that its victory is robust, insensitive to the exact standards of simplicity, strength, and balance. It wins no matter how, within reason, you measure and balance the desiderata. I have no a priori guarantee that nature is kind to us in that way; but in the present state of science (and ignoring present fashions in the humanities) it seems a pretty reasonable hope. I think Bas would find it an unreasonable hope. He seems to think there are probably lots and lots of completely un-dreamt-of good theories which are very unlike our accepted theories and yet would give them a strong run for the money. What’s an example? Well, we have none; but maybe that’s only because once we have one good theory we’re not motivated (anyway, not enough really smart people are motivated) to work hard enough to come up with another. I find this quite unbelievable, but I don’t know what to say next in debating the matter. Yours,

  The Mill-Ramsey-Lewis theory of laws.

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72.  To Donald Bedford and Henry Stapp, 11 April 1991

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72.  To Donald Bedford and Henry Stapp, 11 April 1991 Princeton University Princeton, NJ Dear Donald Bedford and Henry Stapp, Some time ago, you sent me a paper titled ‘Bell’s Theorem in an Indeterministic Universe’.1 I regret to say that when I first looked at it, I thought it was badly confused, so I put it aside. But when I showed it to Michael Redhead, who has been briefly visiting Princeton, he said I was wrong: what I took for confusion was nothing worse than your consistent use of a nonstandard terminology and notation. On a second look, it seems to me that he was right about that. Also it seems to me that I’m in agreement with the point of your paper, at least insofar as it concerns the in­ter­ pret­ation of my views. Let me put the key question in my own way, starting fresh, leaving out the previous debates and indeed leaving out the application to the specific case of a Bell experiment. Suppose we have a future light cone (henceforth ‘the cone’); and suppose we have a contrary-to-fact supposition A about what goes on at the apex of the cone. Suppose we have true counterfactuals If it were that A, it would be that C1 If it were that A, it would be that C2 ... where each one of the Ci’s is entirely about what would go on, or about what the physical probabilities of various goings-on would be, inside the cone. (Let’s count the boundary as ‘inside’.) Let C be the conjunction of all such Ci’s (including A itself, since if it were that A it would be that A); so we have a true counterfactual If it were that A, it would be that C which, intuitively, tells all that’s definitely true about how the inside of the cone would be if it were that A. Now let B be the whole truth about what goes on outside the cone in the actual world. Suppose B & C violates no law – there is no non-local law of faster-than-light influence, or whatnot. (Suppose also that B&C does not constitute what I’ve called a ‘quasi-miracle’. See my Philosophical Papers, Vol. II, 58–65. I don’t see how this complication could matter for what you’re doing.) Then what do we think of the counterfactual

  (Bedford and Stapp 1995).

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(1) If it were that A, it would (still) be that B which says, intuitively, that if it were that A, that would make no difference to anything whatever outside the cone? If I understand you, you say that my theory, with the similarity relation appropriate to causal counterfactuals, is committed to accepting this counterfactual from A to B. For that’s the way to get an A-world that maximizes the spatiotemporal extent of perfect match, and ex hypothesi there’s no fear that you’ll have to pay for this extended match with any miracles, whether large or whether small (or with any quasi-miracles). If that’s what you’re saying, then I agree with you. Now if we assume that the goings-on outside the cone are indeterministic, then B wasn’t inevitable; there was some chance (that is, there is non-zero physical probability) of getting some alternative history, instead of B, outside the cone. And just as this is true in actuality, so it would still have been true if it were that A. So we have another true counterfactual (2) If it were that A, there would be some chance that not-B. One may well think that (1) conflicts with (2); so that if, as you and I think, my theory supports (1), then my theory is in trouble. Redhead is inclined to think that (1) conflicts with (2); and I admit to having felt that way myself sometimes. But my con­ sidered opinion is that (1) does not conflict with (2); and in the hypothetical case we’re considering, without non-local laws, both of them are true together. You’ll find discussion of just this issue in my Papers II, 63–65. I had a problem about extending the treatment in ‘Counterfactual Dependence and Time’s Arrow’ to the indeterministic case; about 1984, I saw how that problem would go away if things like (1) and (2) did not have to conflict; and once I focussed on that issue, I found other arguments for non-conflict. That leaves a residual problem: how to explain away the impression that there is a conflict? It seemed to me that the seeming conflict arose in two stages, and involved a might-counterfactual (3) If it were that A, then it might be that not-B. It seemed as if (2) implied (3), (3) conflicted with (1), and that was how (2) conflicted with (1). But maybe there are two kinds of might-counterfactuals. (Bob Stalnaker has been saying this for a long time, though my two kinds aren’t quite the same as his two kinds.) Maybe (3) is ambiguous between a would-be-possible interpretation and a not-would-not interpretation: (3-wbp) If it were that A, then there would be a chance that not-B; (3-nwn) Not: if it were that A, then it would be that not-not-B.

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72.  To Donald Bedford and Henry Stapp, 11 April 1991

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Then (2) does imply (3-wbp), and (3-nwn) does conflict with (1); and if we overlooked the ambiguity of (3), it’s understandable how we might come away with the mistaken impression that (2) conflicts with (1). Not so: in the case at hand, (2) and (3-wpb) are true, (1) is true, and (3-nwn) is false. The not-would-not sense of ‘might’, of course, is the one I’ve favoured all along. The would-be-possible sense is an unwelcome complication in the story, but maybe it has to be there to explain the inclination some of us sometimes feel to think that (2) implies (3). If anyone says that (2) implies (3-nwn), though, I just deny it outright. (Now at this point somebody may ask if there’s a corresponding ambiguity in the ‘would’ counterfactual as well. In my original simple story, ‘might’ is not-wouldnot, and equally ‘would’ is not-might-not. Now that we have this new would-be-possible sense of ‘might’, do we also have a new sense of ‘would’ which is to the new ‘might’ as the old ‘would’ is to the old ‘might’? Is there a new interpretation of (1), call it a ‘might-be-necessary’ interpretation, that works as follows? (1-mbn) Not: if it were that A, then it might-wbp be that not-B i.e.   Not: if it were that A, there would be some chance that not-B i.e.   If it were that A, there might-nwn be no chance that not-B i.e.   If it were that A, it might-nwn be necessary that B I take it that (1-mbn) is false in the case at hand; so if (1) can be read as (1-mbn), that should satisfy anybody who wants to accept (2), infer a might-counterfactual, respect the would-might duality, and so reject (1). But is it credible that there is any such thing as a would-mbn? Of course, nothing stops us from introducing it by stipulation, but is there any such sense of ‘would’ in the language already? I think not. For if anything seems unequivocally certain, it is that if it were that P, then it would be that P. Yet would-mbn violates this principle!) The present problem was raised, in effect, in footnote 33 to Michael Slote, ‘Time in Counterfactuals’, Philosophical Review 87 (1978), 27. Morgenbesser’s example, reported by Slote, does not involve an event outside the light cone associated with the counterfactual supposition; but we could make it so without changing the conflict of intuitions that the example raises. Morgenbesser tells you that a coin is being tossed, right now, on Mars. (Assume coin tossing is a genuine indeterministic process; but see Papers II, 117–120.) He offers you good odds that it will not come up heads; you decline the bet; a few minutes later the news arrives from Mars that the coin did fall heads; and he says ‘You see, if you had bet on heads, you would have won’. My theory endorses that statement. But Slote was (hesitantly) inclined to say: ‘No, if I had bet heads the coin might have come up differently and so I might have lost’. Maybe Slote was rightly asserting a might-counterfactual taken in the would-­be-possible sense, and wrongly taking it to conflict with Morgenbesser’s

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would-counterfactual in the same way that it would have conflicted if taken in the not-would-not sense. Now for the problem of terminology and notation that originally threw me off. A truth-functional conditional ‘if A then C’ is true at world w iff A is false at w or C is true at w, regardless of what might happen at any other worlds. A strict conditional ‘if A then C’ is true at w iff, for every world v that is possible relative to w, either A is false at v or C is true at v. The term ‘material’ and the hook symbol ⊃ are conventionally reserved for truth-functional conditionals; whereas in your paper you use them, uniformly so far as Redhead and I can tell, for strict conditionals. This is very confusing: it’s as if you used the symbol ‘+’ and the word ‘plus’ for multiplication. I would urge you as emphatically as I can to fix this in the published version of your paper. There’s a different symbol, a double hook ⥽, that’s conventionally reserved for the strict conditional. The villains of the piece are the early logicians who used ‘implies’ as their English reading for the truth-functional conditional. Of course that’s preposterous, and what’s defensible – up to a point – is to use ‘implies’ as a reading for the strict conditional. At least those early logicians had the excuse that much of the time they were talking about propositions of pure mathematics, for which presumably there’s no variation of truth value from one world to another, so the difference between strict and truth-functional conditionals doesn’t matter. But those who came after and continued to read the truth-functional conditional as ‘implies’ had no such excuse. I dare say you learned that the (single) hook is read as ‘implies’ and you assumed, wrongly but understandably, that what it meant would fit that reading. There’s another thing, no fault of yours, that helped throw me off. I was mistaken about how much ‘counterfactual definiteness’ Stapp demanded. I hadn’t actually read Stapp’s earlier papers, but I’d read the 1977 paper by Eberhard2 and the 1978 paper by Herbert and Karush.3 These papers both assume that for any unperformed pair of measurements in the Bell set-up (without non-locality), there’s a definite true answer to the counterfactual question what the outcomes would have been. Eberhard says his assumption ‘is related to Stapp’s concept of “counterfactual definiteness” ’; Herbert and Karush just say that it is ‘christened “counterfactual definiteness” by Stapp’.4 So when I saw your paper, I thought you’d be claiming that my theory vindicated the sweeping assumptions of Eberhard and of Herbert and Karush. I was certain, and I remain certain, that this couldn’t possibly be so. But it turns out, and here again I have Redhead to thank for setting me straight, that you claim much less. We have three kinds of counterfactual question about the Bell set-up.   ‘Bell’s Theorem Without Hidden Variables’ (Eberhard 1977).   ‘Generalization of Bell’s Theorem’ (Herbert and Karush 1978). 4   See also ‘Postscripts to “Causation” ’ (Lewis 1986d, 182, n. 7). 2 3

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73.  To Rob Clifton, 11 June 1991

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If the settings had been changed on just one side, what would the outcome have been on the side where the settings were unchanged? If the settings had been changed on just one side, what would the outcome have been on the side where the settings were changed? If the settings had been changed on both sides, what would the outcomes have been on both sides? The counterfactual definiteness that Eberhard and Herbert and Karush assume is that all three questions have definite answers. But if I understand you properly, what you use and defend is counterfactual definiteness for the first question only. Sincerely, David Lewis c: Clifton, Butterfield, Redhead

73.  To Rob Clifton, 11 June 1991 [Princeton, NJ] Dear Rob, Thank you for your several letters and printouts. I have only a few comments. Bedford and Stapp. Do we really have any dispute over my 11 April letter to B & S? I said ‘I’m in agreement with the point . . . at least insofar as it concerns the interpretation of my views’. That’s not a blanket endorsement, and in particular it’s not an endorsement of their proof. I didn’t try, and still haven’t tried, to check their proof, because I don’t have the physics enough at my fingertips. I leave that job to you. I am interested, and not greatly surprised, by your news that B & S have tacitly used an unannounced form of CFD.1 CFD1 says that there’s a definite answer to this counterfactual question about the Bell set-up: if the settings had been changed on just one side, what would the outcome have been on the side where the settings were unchanged? (Answer: unchanged.) CFD2 says that there are definite answers to the other counterfactual questions about the Bell set-up as well. We agree that CFD2 is no good. Given locality, both my intuitions and my theory say that CFD1 is OK. That, and only that, is what I endorse. Do you dispute it? You say you would dispute it if the

  CFD = Counterfactual Definiteness.

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B&S proof could get by with nothing but CFD1; but if you’re right that the proof doesn’t really get by just with CFD1, that’s not an issue. My Compatibility Claim. I say that ‘If it were that A, there would be some chance that C’ is compatible with ‘If it were that A, it would be that not-C’. I don’t see why you set aside the simple argument in which A is probabilistic: A = ‘there is some chance that C and yet not-C’. Be that as it may, you concentrate mainly on the three-world argument. (Pages 9–10 of your printout headed ‘Counterfactual/Causal Dependence’.) From my point of view, the trouble with your reply is that you assume that the ante­ cedent Φ must describe an event; and then you wonder, quite rightly, what sort of an event could manage to happen in only two worlds. You think that maybe a very big event could do so; and that if it did, the two worlds might be so much alike that they would indeed be tied in similarity to any third world whatever. But I don’t see how even a very big event could manage to happen in only two worlds! So don’t think of Φ as describing an event in any ordinary sense. (But there’s a far-from-ordinary sense you sometimes meet in probability theory in which ‘event’ just means ‘proposition’.) Think of Φ rather as a disjunction: ‘either the world is u or the world is v’. If so, there’s no reason at all why u and v should be similar, or tied in similarity from the standpoint of a third world w. Now maybe all is not lost; maybe all you really want to say is that when A is the right sort of antecedent – namely an event-describing one, hence neither explicitly about probabilities nor disjunctive – (and maybe also when C is the right sort of consequent?) then we’ll never get ‘If it were that A, there would be some chance that C’ and ‘If it were that A, it would be that not-C’ true together. Something like that might be true, I guess. Minor comment. There is one short stretch in your ‘C/C Dependence’ printout that I couldn’t really follow: bottom of page 7 and top of page 8, apparently connecting your discussion of the Limit Assumption to your discussion of the future similarity problem. May I suggest some rewriting and expansion? Dependence of Families. I don’t remember why I stated the distinctness condition as I did, and I see no harm in your amendment. However I don’t quite buy your ‘posi­ tive reason’ for the amendment. The example you give involves three non-distinct ‘events’ O & S, -O & S, O & -S (O for oxygen; S for striking of the dry match) and whether the match lights depends causally on which of these ‘events’ takes place. I don’t agree that you get a genuine event by negating another event – events can’t be too miscellaneously disjunctive – so I don’t believe that -O & S or O & -S (or -L, for that matter) are really events. (Except in that peculiar sense from probability theory.) But all that means is that, given my views on events, we have to change the ex­ample. How about this: whether the red light or the yellow light or the green light goes on depends on how the three-way switch is set when the power is turned on. With the obvious abbreviations: if P & S1, then R; if P & S2 then Y; if P & S3 then G. And now

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74.  To Daniel M. Hausman, 16 June 1991

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I think we have causal dependence of one family of genuine events on another; and the causing family has the event of turning on the power as a common part. I think this will probably make them overlap in the sense of the mereology of events section of ‘Events’ in my Papers II. The reason I’m not sure (without a copy of the book to hand) is that the discussion there was intended to apply to events that actually occurred, not to alternative possibilities. I don’t recall whether the definition carries over to the second case. Anyway, making your amendment is a good way to play it safe. Yours, David Lewis PS I’ve now checked the definitions in Papers II, 258–260, and confirmed that alternative events can indeed have a common part. [. . .]

74.  To Daniel M. Hausman, 16 June 1991 [Princeton, NJ] Dear Prof. Hausman, Thank you for your paper on causal and counterfactual dependence.1 As you know, I agree with the point that the antecedent might have come about in any of many ways; there isn’t likely to be any one way that the antecedent would have come about. (Besides the passage you cite, there’s a place in ‘Are We Free to Break the Laws?’, also in Papers II, where I use the same point.) And I agree that inasmuch as we don’t attend to the question how the antecedent would or might have come about, we equally don’t attend to the answer: by a miracle, if the world is deterministic. Still, however much we ignore it, that is the answer. Why not instead take various worlds with no miracle and difference all the way back (‘Bennett worlds’). Three reasons. (1) Bennett worlds are queer worlds. They’re full of traces as of a past such as to determine that the pipe won’t burst, and yet they have a past that determines that the pipe does burst. They’re deceptive. Yet no one, on having this pointed out, would agree that if the pipe had burst, the world would have been queerly deceptive. (2) We don’t know much about what might have gone on in

  ‘Causation and Counterfactual Dependence Reconsidered’ (Hausman 1996).

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the pasts of the closest Bennett worlds, especially given the deceptiveness of present traces in those worlds. But sometimes we have counterfactuals – perfectly ordinary counterfactuals – which say how some event, if it had happened, would have been related to the events of the past. ‘If that pipe had burst, OSHA’s most far-fetched worry would have come true!’ You just don’t have to ask whether OSHA would still have had that worry if the pipe had burst. (3) You can have counterfactuals – perfectly ordinary ones – that say in so many words that a divergence would have taken a miracle. ‘OSHA was fussing about that pipe all last year. The more fools they. We know now, from the X-rays after it was taken out of service, that the metal was completely sound. We know, from the pressure records, that it never got anywhere near its pressure limit. And of course there wasn’t any earthquake, sabotage, or whatnot any time last year. If that pipe had burst, it would have been a miracle!’. What’s the problem about the Stevenson counterfactual? As you say, it doesn’t give a dependence among actual events, so doesn’t give spurious backward caus­ ation. Further, it looks like a back-tracker. Rest assured, I don’t say that back-trackers are anomalous; no, we can and do use them comfortably in conversation. In fact, I think your engineers making counterfactuals about the pipe bursting are likely to be using back-trackers in conversation. Likely – not necessarily, as witness the dialogue in the previous paragraph. Small correction to the first line: if c and e are distinct events that actually ­occur. . . . Otherwise every event causes itself. And in fact ‘distinct’ should mean not just non-identity, but non-overlap. Sincerely, David Lewis

75.  To Huw Price, 23 September 1991 [Princeton, NJ] Dear Huw, Thank you for your paper on causal asymmetry,1 which I’ve now read with interest. My main comment is that the world of your example differs from the world we take to be ours in more ways than meet the eye: it’s not just a world of classical

  ‘Agency and Causal Asymmetry’ (Price 1992).

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76.  To James Woodward, 4 February 1992

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physics! Do marbles act as gravitational sources? Do they interact with the electromagnetic field? If so, then after a marble miraculously disappears, you won’t get reconvergence just by putting the marble back (with appropriate position and vel­ ocity). To reconverge, you’ll have to fix up the gravitational and electromagnetic fields as well. But it’s still true that this is quite an easy reconvergence, compared with reconvergence to cover up the fact that Nixon pushed the button. The sooner you get started on the cover-up job, the less work you have to do. I wasn’t too worried by your first objection on page 11. So long as there’s an asymmetry of miracles for macroscopic departures from actuality – Nixon pushing the button – we’ve got causal asymmetry for macroscopic causation; and further, macroscopic causation reduces to a pattern in the microworld, even if it isn’t a pattern of microscopic causation. So far, so good. But that doesn’t do me much good; because I do agree with your second objection on the same page. Yes, we ought to be able to talk about microscopic causation, and it ought to come out asymmetrical. At least, it ought to in a world enough like ours. But maybe not in a simple one-particle world; and maybe not in a world like the one in your example where marbles leave no footprints in the gravitational and electromagnetic fields, and hence won’t be missed if they briefly go missing. The caption ‘Lewis’s proposal’ on your Diagram 5 bothered me. I don’t see how my asymmetry of overdetermination is at all the same thing as the fork asymmetry; especially if the fork asymmetry is defined in terms of probabilities, and the asymmetry of overdetermination holds in a deterministic world where all the relevant physical probabilities are zero for what doesn’t happen or one for what does. Yours, David Lewis

76.  To James Woodward, 4 February 1992 Princeton University Princeton, NJ Dear Professor Woodward, At long last, I’ve read the offprint you sent me on supervenience and singular causal statements. (Where does it come from?)1 I found it very interesting, and I dis­ agree with you less than you might expect, and maybe not at all. I no longer believe   ‘Supervenience and Singular Causal Statements’ (Woodward 1990).

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the analysis of causation that appears in ‘Causation’ and its several postscripts in Papers II, thanks to a decisive counterexample from Peter Menzies. Let’s start with Menzies’ counterexample, because it turns out to have a lot to do with the question in your paper. It’s in his ‘Probabilistic Causation and Causal Processes: A Critique of Lewis’, Philosophy of Science 56 (1989) 642–63. Take my usual example with a network of neurons: forward arrowheads are stimulatory synapses, the

backward arrowhead is an inhibitory synapse; a neuron not stimulated or stimulated and simultaneously inhibited doesn’t fire, a neuron stimulated and not also inhibited fires for sure if it’s a surefire neuron, fires with probability 70% if it’s a cheapo neuron; the four neurons in the top row, to the right of neuron C1, are cheapos; all the other neurons in the picture are surefires. C1 and C2 fire simultaneously. As chance would have it, all the cheapos in the chain do fire; hence the fourth surefire in the bottom row gets inhibited and fails to fire. A correct analysis ought to say that the firing of C1 caused the firing of E, whereas the firing of C2 did not cause the firing of E because the chain of firings from C2 to E didn’t go to completion. Right? Now, I was interested in the question: how come the firing of C1 causes the firing of E even though it doesn’t raise, and in fact it lowers, the chance of the effect? My answer is that the firing of C1 raises the chance of an intermediate event – the firing of the third cheapo – and that this intermediate event in turn raises the chance of the effect; so we have a two-step chain of chance-raisings. So far, so good. But what I completely overlooked, until Menzies told me, was that the firing of C2 also raises the chance of the firing of E! Because without the firing of C2, the chance of E firing (as of the time when C1 had just fired) would have been the chance that all four cheapos would fire: 70% to the 4th power, roughly 25%. Whereas with the firing of C2, the chance of E’s firing is roughly 55%: the 25% as before, plus an extra 30% chance that the first cheapo will fail and hence the chain of firings of the surefire neurons won’t get stopped by inhibition. So chance-raising is not, contra my theory, sufficient for causation. That is, we have a counterexample – a decisive one, I think – to what you called (L1), and a fortiori to what you called (L2). I don’t have a new analysis to replace the one Menzies shot down. One solution would be to say that in a genuine case of causation there has to be a spatiotemporally

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continuous chain of chance-raisings; but I’m not prepared to go for an analysis that rules out action at a distance a priori. I’d like to think that quite a lot of my old analysis will survive somehow. But without a solution, that’s talking through my hat. However, it does seem clear to me that Menzies’ example is not a counterex­ ample to thesis (T), which says that singular causal relations supervene on the Humean mosaic of particular (non-causal) facts plus the (perhaps probabilistic) laws. It seems to me that the reason why the firing of C1 does cause the firing of E and the firing of C2 doesn’t must be something we can read off from the wiring diagram of the network, the history of which neurons fired when, and the probabilistic laws governing neuron-firings. For it seems to me that when I told you all these things, I told you all that you needed to know to decide which firings caused which. Now, let’s contrast two cases, both of the kind you call Ex.1. First case. Tommy is a soldier, running across no-man’s-land. Fritz and Heinz are two machine gunners, both firing in a random pattern through the area where Tommy is. Let it be a genuinely random pattern (quantum events in the nervous system make the hand jitter which makes the gun jitter . . .). Fritz’s firing raises the chance that Tommy will die; Heinz’s firing raises the chance that Tommy will die. In due course Tommy is hit and dies. Fritz’s firing was the cause, Heinz’s wasn’t. Why? Simple – Tommy was hit by only one bullet, and that bullet came from Fritz’s gun. Second case. Tommy is an unstable, photosensitive molecule, running through a glass reaction chamber. Fritz and Heinz are two light bulbs, both illuminating the chamber. The illumination from both together is, of course, more than the il­lu­min­ ation from either one alone. The chance per unit time that Tommy will absorb some light and decay is an increasing function of the total level of illumination at the point where Tommy is. In due course Tommy does decay. Given suitable assumptions about the physics of the situation (see below), I very much want to deny that there’s any secret fact about whether it was Fritz or Heinz that caused the decay. Their effects are pooled in the level of illumination that they jointly produce, which in turn causes Tommy to have a certain decay probability, and thereby, as it turns out, causes Tommy to decay. In positing some secret fact that makes Fritz the cause and not Heinz, we’d be positing something repugnant to parsimonious metaphysics. But worse – much worse – we’d also be going against what we know (or rather, what I’ll later suppose) about the physics of the situation. It may seem, intuitively, that there was some chance that Fritz would cause a decay and some chance that Heinz would cause a decay, and then one thing or the other happened. But we mustn’t let such intuitions dictate to physics! (If Fritz is a much brighter bulb than Heinz, and so contributes much more light, and so contributes much more to raising the chance of decay, and if Heinz’s contribution is negligible, then it’s appropriate to name Fritz as the cause of Tommy’s

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decay, and ignore Heinz; but I’m not very happy to deny outright that Heinz is a cause. I guess I’d rather deny it than affirm it; but what I really want to do is dodge the question ‘Did Heinz cause the decay? – Yes or No!’ and just say that Heinz made a small contribution to the causing, and leave it at that. Anyway, this seems to me to be a side issue. So let’s assume henceforth that Fritz and Heinz each contributed a lot of light, and each raised the chance substantially. Maybe they’re equal in brightness and in chance-raising; or maybe Fritz is a little brighter. But I think neither of us would want to say that the mere fact that Fritz was a little brighter meant that Fritz was the cause and Heinz wasn’t!) In case 1, Fritz is the cause and Heinz isn’t; and in the Humean mosaic of particular facts, together with the relevant laws, we find the reason why. The case is not a counterexample to the supervenience of singular causation upon the particular facts together with the laws. In case 2, I say that Fritz is no more and no less the cause than Heinz is; so if nothing in the mosaic and the laws gives a reason why one is the cause rather than the other, that’s just as it should he. Again, the case is not a counterexample to the supervenience of causation upon the particular facts together with the laws. (L1) and (L2) fall; but supervenience stands. When I wrote the ‘Chancy Causation’ postscript in Papers II, and in particular the passage on pages 180–2 rejecting ‘hidden features’, I only had in mind cases like the present case 2; I was totally overlooking cases like the present case 1. Which is to say, as I said before, that I totally overlooked Menzies’ problem; because case 1, I take it, just is another instance of Menzies’ problem. Indeed, what I now see, mainly thanks to your paper, is that in a chancy world, Menzies’ problem will be everywhere. It is not an odd quirk of some very special set-ups like my little system of neurons. If we have a disagreement at all, it’s about case 2, not case 1. Do we? I’m not sure; I take it your footnote 28 was meant to cover cases like case 2 (under the right assumptions about the physics – see below). But the end of the footnote suggests that instead of saying as I would that Fritz caused Tommy’s decay (even if Heinz does so equally), maybe you’ll say that it’s indeterminate whether Fritz or Heinz caused the decay. If you say that, we do have a remaining disagreement. But I don’t think it’s a disagreement relevant to the supervenience question. Supervenience of superstructure S on basis B means that the whole truth about S – but not more than the whole truth about S! – is determined by the whole truth about B.  So if S is infected with indeterminacy, S can still supervene on B; it’s just that sometimes, instead of making S be some determinate way, B makes it true that S is in­de­ter­min­ ate in a certain way. (See On the Plurality of Worlds pp. 223–4, for more about supervenience and indeterminacy.) Case 2 comes in several versions. Some work better than others to make my point. Case 2A. De Broglie was right: there are particles and pilot waves. Light bulbs

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are photon guns, and in addition they emit waves that exert forces on the photons. Then it may indeed be that Fritz rather than Heinz causes Tommy’s decay, thanks to a feature of the world that’s hidden in practice but not in principle, a feature supervenient on the Humean mosaic: the photon that hit Tommy came from Fritz and not Heinz. This heterodox – maybe not so heterodox nowadays? – version of case 2 is, of course, just a microscopic equivalent of case 1. It’s useless to make my point. Set it aside. Case 2B. The case as a working chemist might think of it: quantum chemistry, classical optics. The light is a vibration of a classical electromagnetic field, even though the decay which it probabilistically causes is a quantum phenomenon. This way, there’s nothing known to the (supposed) physics that can connect the decay with Fritz rather than Heinz, as I said. But this is bogus physics, mixing quantum and classical treatments in an unprincipled, Bohrish way. Case 2C. De Broglie was wrong, orthodoxy is right. Light bulbs are photon guns, and indeed it’s true that Tommy was hit by a photon that came from one gun or the other; but many different histories of photon emission and absorption are in a superposition, and in some the photon that hit Tommy came from Fritz and in some it came from Heinz, and (this aspect of) the superposition never gets resolved even when Tommy is hit. So again, this time thanks not to a classical field but rather to superposition, there’s still nothing known to physics that can connect the decay with Fritz rather than Heinz. Case 2D. Back to case 2B: electromagnetism is classical. But now interpret classical electromagnetism not as a theory of physically real fields, but rather as a theory of action at a distance between charged particles – the fields are a fiction, a mere bookkeeping device. This theory may once have been tenable, and I gather it once had supporters; it seems pretty hopeless now, once you start to think that radiation can itself be the source of a field! This version, apart from being fictitious, serves my purpose best. It forces us to face the question: is it so that each of Fritz and Heinz, just in virtue of raising the chance of the decay, thereby causes it? It doesn’t allow us to dodge that question by saying: be that as it may, each of Fritz and Heinz causes the decay via a two-step causal chain, since they jointly cause the illumination which in turn causes the decay. Again, thanks for your paper. It’s certainly changed my mind; though not perhaps in the direction you meant it to, since I still don’t doubt the supervenience of causation on particular fact plus laws. Sincerely, David Lewis c: Peter Menzies, Michael Tooley

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77.  To Alvin Plantinga, 18 May 1992 Princeton University Princeton, NJ Dear Al, Since I phoned you and since I finished my long previous letter,1 I’ve changed my mind several times about the NoN definition of (transworld) depravity.2 What I think now is that it does the job it’s meant to, but that there’s a simpler and weaker definition that also does the job. Here I’m not talking about individual versus col­lect­ ive depravity, as in my previous letter; I mean a simpler and weaker definition of individual depravity. Thank you for your 7 May letter. Starting from that will simplify life quite a lot. Preliminaries Let’s assume that whatever option O God chooses, there is a world W such that if O, then W would be actual; in other words, for any option, there is a definite world that would be weakly actualized thereby. This will require (non-vacuously true) coun­ter­ fac­tuals not only of freedom, but also of chance. Then we can introduce a Stalnaker selection function defined on options: f(O) is the world that would be actual if God were to strongly actualize O. (Equivalently: if O were true.) Let selection always be from the standpoint of the actual world, despite the heavy weather I made over this in my 1976 letter.3 T(W), as usual, is the option God strongly actualizes at world W; so f(T(W)) is the world God weakly actualizes at W; so God can weakly actualize W iff f(T(W)) = W. This is equivalent to your original definition of ‘can weakly actualize’ by the argument of my 1976 letter. Some equivalent definitions The following definitions for ‘P is depraved’ are equivalent. (‘Essence E is depraved’ can be defined in parallel ways.) The equivalences are pretty obvious, given my 1976 letter and our present assumptions and definitions. (1)  (2)  (3)  (4) 

If W is any world where P is blameless, f(T(W)) ≠ W; God cannot weakly actualize any world where P is blameless; For any option O, f(O) is not a world where P is blameless; For any option O, if God actualized O, P would not be blameless.

  Letter from David Lewis to Alvin Plantinga, 10 April 1992 (not published here).   The Nature of Necessity (Plantinga 1974b).    3  Letter 32. To Alvin Plantinga, 22 October 1976.

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(5)  For any option O, if God actualized O, then either P would not exist, or P would not be significantly free, or P would sometimes freely do evil. A misguided definition In my last letter, I considered a hypothesis (ID) of individual depravity, which was that every possible free creature P was depraved in the sense of the following ­def­i n­ition: (6)  For any option O that implies the existence and freedom of P, if God actualized O, then P would sometimes freely do evil. I now think that (6) was a misguided stab in the direction of (5). (5) implies (6), but not conversely. Further, (6) allows God to weakly actualize a world where P is blameless. Let (6) be true. But suppose God has an option O that is true in two worlds: W, where P is blameless (exists, is free, and never does evil) and V where P either isn’t free or doesn’t exist at all. Thus by choosing O, God doesn’t settle whether or not P is to exist and be free. He leaves that to chance, or maybe to the free decision of some other creature. So (6) is silent about O. Now suppose the counterfactuals of freedom (and chance?) are such that f(O) = W; if God were to choose O, he would thereby weakly actualize the world W where P is blameless. Then P is not depraved in the sense of definitions (1)–(5). In fact, P might be in especially good shape! Even if (6) holds, it might also be true that: for any option O that doesn’t settle whether P exists and is free, if God actualized O, then P would be blameless. So my (6) is no good at all as a definition of depravity. Your NoN definition The NoN definition as restated in your 7 May letter is equivalent to (7)  If W is any world where P is blameless, f(T(W)) is a world where P goes wrong with respect to some action A. By definition, a world where P goes wrong is not a world where P is blameless. Therefore (7) implies (1), hence also (7) implies (2)–(5) (and (6), for what it’s worth). Since (1)–(5) do the job of defence, so does (7). Nevertheless, (7) is not equivalent to (1)–(5). We can suppose that (1)–(5) hold and yet (7) doesn’t. For suppose we have a certain world W where P is blameless; but suppose f(T(W)) is not a world where P goes wrong, rather it’s a world where P either doesn’t exist or isn’t free. (Then again T(W) must be an option whereby God doesn’t settle whether or not P exists and is free.) That will still mean that God can’t weakly actualize this world W where P is blameless, but not for the reason stated in (7).

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The NoN definition in its original form is not quite equivalent to the restatement in your 7 May letter. There’s an extra clause, which I think makes it equivalent to (8)  If W is any world where P is blameless, f(T(W)) is a world where P goes wrong with respect to some action A that is morally significant for P in W. Obviously (8) implies (7) and hence all of (1)–(6); but obviously (7) doesn’t imply (8). Which of P’s choices are morally significant might depend on chance or on the free choices of other creatures; and so might be not at all the same in W and in f(T(W)). Two moral issues that turn out irrelevant As I said at the beginning, I changed my mind several times. The reason why is that I got the mistaken impression that if (7) or (8) was to do the job of defence, it had to imply (9)  If W is any world where P is blameless, f(T(W)) is a world where P goes wrong with respect to some action A such that P is significantly free in f(T(W)) with respect to A. (7) by itself doesn’t imply (9); but (7) plus the moral premises (Pl) and (P2), and plus your official definition of significant freedom, do imply (9): (P1) One can go right or wrong with respect to A only if one is free with respect to A. (P2) One can go wrong with respect to A only if one can go right with respect to A. Roughly, (P1) is a sort of ought-implies-can; (P2) is a sort of denial of dilemmas. I don’t think I accept either (P1) or (P2), but many would accept them both. Anyway, all that’s a red herring. The crucial thing about (7) is just that f(T(W)) differs somehow from W. It doesn’t matter how, and in particular it’s not necessary that the wrongdoing mentioned in (7) has to be significantly free wrong-doing. (Here’s another way to think of the role of (P1) and (P2). Let’s say that P is blameless- iff P exists and is significantly free and always, when making significantly free choices, does only what’s right. This leaves open that P might go wrong when unfree, or when free only to choose between different wrongs; but these are exactly the cases ruled out by (P1) and (P2). So given (P1) and (P2), ‘blameless’ and ‘blameless-’ are equivalent. Now if we obtain (1-) by putting ‘blameless-’ in place of ‘blameless’ in (1), (9) seems to be related to (1-) as (7) is to (1).) Your GFE definition4 Point taken: NoN is the official statement. All the same, I think the GFE definition is interesting. It simplifies in an unexpected way. The simplification has a clear intuitive meaning. It looks as though it would do the job of defence, but it doesn’t.   God, Freedom, and Evil (Plantinga 1974a).

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77.  To Alvin Plantinga, 18 May 1992

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Let’s define depravity for actual people; extension to creaturely essences will be routine. Lemma: Sʹ is a maximal segment included in world W iff Sʹ obtains at W and at most one other world. Proof. It must obtain in W, else it doesn’t include W. And if Sʹ obtained in three worlds W, V, U then we can add to Sʹ a state of affairs – namely, U’s not being actual – that is compatible with Sʹ but not included in it, and yet the result will not be an entire world. QED. Lemma: if Sʹ includes neither of a pair of contraries X and Y, then Sʹ obtains at two worlds, at least: an X-world and a Y-world. Lemma: if Sʹ obtains at worlds W and V, and Sʹ includes Z, then Z holds both at W and at V. Using the formal skeleton of my theory of counterfactuals – but not my opinions about the relevant respects of similarity – we have a fourth lemma: if Sʹ holds exactly at worlds W and V, and if, if Sʹ were actual then something would be true that is false at W, then V is closer to actuality than W is. Using these lemmas, the GFE definition is equivalent to: (10)  If W is any world where P is blameless, there is another world that is closer to actuality than W is, where P freely goes wrong with respect to some morally significant action (such that P is also significantly free with respect to this same action at world W). The parenthetical part seems useless. But the rest is equivalent to something which, at first sight, looks both simple and promising: (11)  For any world where P is blameless, there is a closer world where P is not blameless. But in fact the hypothesis that every possible person is depraved in the sense of (11), or (10), doesn’t do the job of defence. The reason is that we don’t know that the two worlds mentioned in (11) are worlds where God strongly actualizes the same option. Any twoworld state of affairs is a maximal segment – the worlds can be as different as you like, and in particular they can differ in what God does. Take a 4-world model: U, W, V, @ in increasing order of closeness to actuality. W and V are worlds where P is blameless; U and @ are worlds where P is not blameless. (And we can add, if we like, that there’s some one action on which P goes wrong at U and @, right at W and V; and on which P is significantly free at all four worlds.) (11) holds, and so does (10): @ is closer to actuality than either of the worlds W and V where P is blameless. But now suppose T(U) = T(W) and T(V) = T(@). Then God could have weakly actualized the world W where P is blameless. Correcting the GFE definition The GFE definition seems like a near miss: and in fact it can be corrected to make it equivalent to (1)–(5). Indeed this correction may be what you had in mind all along.

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On page 46, I take it that your official definition of ‘maximal world segment’ is given by the sentence: That is, add to Sʹ any state of affairs compatible with but not included in it, and the result will be an entire possible world. But in the surrounding text we get a strong suggestion that there’s more to the notion than that. A maximal segment that leaves X unsettled is supposed to be as nearly complete as leaving X unsettled will allow. Let’s concentrate on completeness with respect to what God does and doesn’t strongly actualize; and let’s write this explicitly into the definition of depravity by adding a clause to the definition on page 48: . . . world segment Sʹ such that: (0) For any state of affairs G of God’s strongly actualizing something, either Sʹ includes G or Sʹ precludes G . . . This revised definition will be equivalent to something resembling (10): (12) If W is any world where P is blameless, there is another world V such that V is closer to actuality than W is; such that T(V) = T(W); and such that at V, P freely goes wrong with respect to some morally significant action (such that P is also significantly free with respect to this same action at world W). Again we can drop the parenthetical part, which seems not to be doing any work, to get a weaker definition resembling (11): (13)  For any world W where P is blameless, there is another world V such that V is closer to actuality than W is; such that T(V) = T(W); and such that P is not blameless at V. And (13) is a satisfactory definition: it is equivalent to (1). Proof. Assume (1), and take any world W where P is blameless; let V be f(T(W)); we have T(V) = T(W) and f(T(V)) = V; we apply (1) to W to conclude that V ≠ W, so V is closer than W; we apply (1) to V to conclude that P is not blameless at V, else f(T(V)) ≠ V; so now we have the righthand side of (13). Next, assume (13), and again take any world W where P is blameless; again let V be f(T(W)); there is no world U closer than V such that T(U) = T(V); so we can apply (13) to V to conclude that P is not blameless at V; so V ≠ W; so now we have the right-hand side of (1). QED Correction to your 7 May letter? You say something surprising at the end of the first paragraph. I doubt you really meant it. W is the base world – the actual world, if we’re talking about the coun­ter­ fac­tuals of freedom that are true simpliciter. W* is a world where P is blameless. We have a counterfactual true at W:

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78.  To Adam Morton, 20 January 1993

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If God had strongly actualized T(W*) then P would have gone wrong with respect to A. Then you say that this same counterfactual ‘is presumably also true in W*’. Its ante­ cedent is true in W*; so it’s true only if its consequent is. But its consequent isn’t: W* is a world where P is blameless! So it seems that in W* the counterfactual is (trivially or degenerately) false. My whereabouts I’m away from 20 June to 14 September. My itinerary is complicated. My only mailing or fax address is c/o Department of Philosophy University of Melbourne Parkville Vic 3052 Australia Fax: 61-3-344-5142 The last day I can pick up mail in Melbourne is 21 August. If you allow 2½ weeks for air mail – likely to be safe but not certain – the last day you can post me a letter is 4 August. Yours, David Lewis

78.  To Adam Morton, 20 January 1993 Princeton University Princeton, NJ Dear Adam, Best wishes for 94, 93, and 95! [. . .] Suppose, suppose.1 I certainly agree that it’s hopeless to take ‘If P, then if Q, then R’ as a conditional with a conditional consequent. I’ll send you a draft about free-will theodicy2 (incomplete pending some help from Calvin on a historical question) and toward the end I actually want to talk about conditionals with conditional consequents: 1

  ‘Suppose, Suppose’ (Morton 1993).   

  ‘Evil for Freedom’s Sake?’ (Lewis 1993a).

2

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Philosophical Letters of David K. Lewis If infallible God foresaw that I’d do it, then: if I hadn’t done it, then: God would have been fallible.

Very hard to say that in plain English! However, I’d concluded that the right logical form for double suppositions in ordinary English was to take them as conjunctive antecedents: ‘if P and Q, then R’. That would be a multigrade construction, of course, if conjunction is a multigrade construction – as obviously it is, except in some logic texts. You don’t buy that either, as witness your example about Jack and Jill and their trip abroad and their car. But I find that unconvincing. (1) Suppose they went abroad; suppose they replaced their car; then it would be that -----. (2) If both they went abroad and also they replaced their car, then it would be that -----. (3) The closest worlds (to the world of the story) in which they both go abroad and also replace their car are worlds where -----. In all three cases I’m undecided about how to fill in the blank: whether to go for the case where the car suddenly goes kaput after they’re committed to going to Japan (or indeed after they’ve gone), or whether to go for the case where the car gives out gradually and gives them enough warning that they save money by going only to France. But it seems to me that I’m undecided to the same extent and in the same way in all of (1)–(3). So I get no wedge between the double conditional (1) and the conjunctive antecedent (2); or between those and analysis (3). What favours the car giving out gradually, I suppose, is that gradual failure is more the way things are thought to mostly happen in the base world. What favours the car giving out suddenly when it’s too late to settle on France might be that it postpones the divergence from the base world, in which case the line I take in ‘. . . Time’s Arrow’ applies.3 Or it might be a Gricean effect, familiar in connection with conjunctive stories: we suppose ceteris paribus, by the ‘maxim of order’, that the order in which the events took place is the same as the order in which the story-teller mentioned them. Why shouldn’t the same thing happen in the conjunctive antecedent of a conditional? (We have to lump the events together properly. It’s not that the date of the departure for abroad must precede the date of when Jack and Jill become legal o ­ wners of their new car; rather, the whole train of events leading up to the departure must be over, or at least well underway, before the whole train of events leading up to the carreplacement gets going.)   ‘Counterfactual Dependence and Time’s Arrow’ (Lewis 1979b).

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79.  To Ken Gemes, 25 January 1993

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Mind you, I have no general objection to the idea that how the antecedent is worded may play a role in picking the appropriate similarity relation. I think that may well be the story of why ‘If it were that P or Q, it would be that R’ seems to entail ‘If it were that P it would be that R’ and ‘If it were that Q it would be that R’, even when one of P and Q seems offhand to be much closer to actuality than the other. Somehow the explicitly disjunctive antecedent seems to call for a similarity relation in which both disjuncts matter, i.e. one that puts the closest P-worlds and the closest Q-worlds equally close. I suppose this is a defeasible tendency, but still a pretty strong tendency. So I wouldn’t be averse in principle to a solution in which (1) and (2) were both conditionals with the same conjunctive antecedent, but (1) tended to evoke a different similarity relation than (2) did. It’s just that I doubt that the Jack-and-Jill story is evidence for this. Yours,

79.  To Ken Gemes, 25 January 1993 [Princeton, NJ] Dear Ken Gemes, Your objection 1 1) If I had free time in Sydney, I’d ride a ferry. (true) 2) If I had free time in Sydney, I’d ride a ferry or pigs would fly. (true) I think the inference from 1 to 2 is OK intuitively; though (as you suggest) 2 may be pragmatically fishy because the hearer falsely thinks that the speaker had some good reason to tack on the superfluous disjunct. 3) If I had free time in Sydney and didn’t ride a ferry, pigs would fly. (false) Yet 3 is a consequence of 2 by what you claim is an intuitively valid inference! I’ll lose no sleep over the fact that my account does validate the inference from 1 to 2, and doesn’t validate the inference from 2 to 3. Your objections 2 and 3 These two are really the same problem, I think. The problem is that ‘If A or B, it would be that C’ seems to imply both ‘If A, C’ and ‘If B, C’; though this may stop happening if you replace ‘A or B’ by a logical equivalent not of overtly disjunctive form. This has

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been noticed by a number of people, independently, in the late ’70s. I enclose a note1 which mentions four solutions (counting the one in the ‘postscript’ as the fourth) and I wonder whether yours will turn out to be one of the four. When I wrote the note, I preferred the first solution: take it that what seem to be counterfactuals with disjunctive antecedents have a logical form at variance with their superficial grammar. The trouble with that idea is that occasionally we really do have a counterfactual with a disjunctive antecedent, and then we really do get something resembling the truth of your sentence (3): see the Spain example in McKay and van Inwagen, Phil. Studies 1977.2 Nowadays, I think I prefer a version of the third solution. I think I learned it first from Stalnaker; but he didn’t publish it and eventually Nute did, JΦL 1980.3 The idea is that we have a pragmatic influence on the choice of the governing similarity relation (or selection function, or system of spheres, or . . .). If the antecedent has an explicitly disjunctive form, that tends – defeasibly! – to favour a similarity relation on which the disjuncts are tied for closeness. Yours,

80.  To Michael McDermott, 1 July 1993 [Melbourne, Australia] Dear Michael, 1) Right you are. I’d have preferred to be more parsimonious about events. 2) I believe that ‘Events’ slightly predates postscript E to ‘Causation’, but without papers that are home in Princeton I can’t be confident. I’m unaware of conflicts. Even if there’s an accidentally vigorous firing of B, and even if it causes the firing of E, can’t it still be true that there’s an event, namely the essentially vigorous firing, that’s jointly caused without redundancy by the firings of C1 and C2, and that causes the firing of E? (This requires us to say that we suppose away the essentially vigorous firing by supposing that B doesn’t fire at all. But I think I say this anyway somewhere – to suppose away an event is to suppose it away entirely – but I can’t find where.)

  ‘Possible-World Semantics for Counterfactual Logics: A Rejoinder’ (Lewis 1977).   ‘Counterfactuals with Disjunctive Antecedents’ (McKay and van Inwagen 1977). 3   ‘Conversational Scorekeeping and Conditionals’ (Nute 1980a). 1 2

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80.  To Michael McDermott, 1 July 1993

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3) This is what you object to in the next question. Unintuitive? Well, I guess intuition can be led either way here. In the closest world without the Sydney Opera House, would there be a building just barely different enough not to be (a counterpart of) the actual Opera House? I could imagine being in a mood to say that, but it’s not unintuitive to say the opposite. Likewise I could go either way on whether there might have been a just-barelydifferent building. 4) This worries me partly because in the case of chancy causation of e by c there’s a sense in which even with c, e might not have occurred. (Papers II, p 64) And what if the closest c-worlds and closest not-c-worlds alike are worlds where the chance of e is 50-50. Then ‘without c, it might have been that not e’ looks true both in the notwould-not sense and in the would-be-possible sense, yet it doesn’t seem we have causal dependence. 5) I was never as eager as Bennett once was to say that hasteners are causes and de­ layers not, but yes, I sympathised with that to some extent. I’m certainly happy to say that a delayer causes death when it makes enough difference to time and manner. Intuition pump: say to yourself that it ‘replaces the death that the victim would have died by a different one’. In the revival case, there may well be considerations of manner that interfere with the identifications you suggest. And maybe the extrinsic feature of being the victim’s first death is relevant. I think it’s a bit up for grabs whether the second w3 death is the same event as the w2 death. I don’t object to rewriting to distinguish ‘caused his actual death’ from ‘caused him to die’. 6) I imagine the case as one in which each spell works, or would work, through some sort of mechanism. That is, I do imagine an intermediate event jointly caused by witch A’s act and the prince saying ‘Rumpelstiltskin’. If you stipulate that there isn’t, OK; but then my intuitive judgement is disturbed. In that case, I feel you’ve misdescribed one of the spells. One witch put a conditional spell on the prince; the other witch replaced it with an unconditional spell, which then did its work. Yours, David

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81.  To Peter Menzies, 6 July 1993 [Adelaide, Australia] Peter Menzies Comments on ‘Probabilistic Pre-Emption’.1 I thought it might be useful to write down what I said, plus a couple of things I didn’t. Handout. If you’re going to use it again, correct §1.3. Should be: ‘Lewis says that it is possible to have causation without probabilistic dependence’. Probability Trajectories. I take it the proposal is that the reason we don’t have caus­ation from a to e in figure 1 is that we don’t have the right sort of trajectory: instead of a steady rise, or at worst a rise with plateaus there’s a fall. Evidently you reject this. But the handout doesn’t say why. Is it this? – The test rules out good cases along with the bad. In fact, in the neuron example, the genuine b-f-g-e causal chain has the same probability as the spurious a-e, so you can disqualify the bad one by its trajectory without knocking out the good one as well. Theoretical Identification of Mental States Gone Wrong. Suppose you said: S occupies the pain role iff S typically occurs when the skin is cut and you moan and groan (or whatever – never mind that this is simple-minded). This would look like Jack’s ori­gin­al topic-neutral translations; but since he neither offered them as equivalent to attribution of pain nor used them as premises of arguments for identification, he’s not in trouble. But suppose he’d been less cautious. Suppose that after specifying the painrole in that thin, non-causal way, he’d gone on to say that a state is pain iff it occupies the pain-role. Then there’d be trouble. Because one state that occupies the pain role thus specified, not just typically but invariably, is the state of having cut skin and moaning and groaning; But if you conclude that this state is pain, you lose the desired conclusion that pain can atypically occur without the cut skin and without the moaning and groaning. Theoretical Definition of the Causal Relation. But the wording in §5.1 is trouble in the same way. Consider the relation: being distinct and increasing the chance of. This relation typically, in fact invariably, exists between two events just when they are distinct and one increases the chance of the other. But if we conclude that this is the causal relation, we lose our atypical cases of causation without chance-raising and chance-raising without causation. 1   ‘Probabilistic Pre-Emption’ (Handout, 1993 AAP conference). See ‘Probabilistic Causation and the Pre-Emption Problem’ (Menzies 1996).

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81.  To Peter Menzies, 6 July 1993

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In the case of pain, the solution – maybe the main difference between Armstrong and I and Jack – is to add more to the role, namely being causally between the cut skin and the moaning and groaning. In the case of the causal relation likewise, something needs to be added to the role to keep out trivial and unwanted occupants. Adding to the Role. We might add that a candidate to occupy the role must be a relation intrinsic to its relata – as I take it chance-raising is not if chances are constituted by patterns throughout space and time. But now we might get correlations between very specific and very uncommon relations and chance-raising that just happens to coincide with these relations on the very few occasions when they occur. So maybe we should also add to the role that our candidates also are to be relations that occur frequently and in a great variety of surroundings. Now maybe we’ve characterised some causal relations – not all the special and idiosyncratic causal relations there are, but the basic ones (e.g. the relation of acceleration to charge immersed in a field) out of which all others are composed. But if so, we have a condition to impose on any other candidate to be a causal relation that it be composed of the basic causal relations we’ve characterised already. The spurious a-e causal relation in the neuron example wouldn’t qualify either as basic – too rare and idiosyncratic – or as composed. Objection. In a nice world, all causal relations are composed of a few basic ones, these basic ones being widespread and insensitive to surroundings. We do expect the world to be nice in this way. But should we build this hope into our analysis of caus­ ation? Shouldn’t conceptual analysis work in any world, be it nice or be it nasty? Isn’t this like building in a prohibition against action at a distance? Well, maybe the prohibition against action at a distance is more risky. For instance, maybe it’s violated in this world in collapse of an EPR superposition – the distant part of the superposition collapses in consequence of a measurement of the near part, without any known messenger. (I don’t suppose we have no alternative to granting this, but is it not ever one of the possible hypotheses?) Maybe we might say that a perfect deserver of the name of causal relation has to live in a nice world. We assumed this was what we had in the world of our neuron examples. But we don’t have to conclude there’s no causation at all in not-so-nice worlds. Maybe in other worlds there are imperfect-but-good-enough deservers of the name. Maybe we have no good solution to the problem of allowing probabilistic dependence without causation in these not-so-nice worlds. Counterintuitive? So what? Just shows our intuitions are made for the nice worlds.

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82.  To T.L.S. Sprigge, 15 November 1993 [Princeton, NJ] Dear Professor Sprigge, Thank you very much for the note and photocopy you gave me when I was in Edinburgh last month. Since returning to Princeton, I’ve read Facts . . . XII.51 and Vindication . . . 2.5.2 Sure enough – your 1970 analysis of counterfactuals is very like Stalnaker’s and essentially identical to mine. (The only difference I spot concerns the case of an impossible antecedent: your counterfactual goes false, mine and Stalnaker’s go true. Very much a side-issue.) I wish I’d known about your analysis and given you due credit years ago, but better late than never! As for chronology, it’s all very close. It was in May 1968 that I wrote to Stalnaker saying ‘You and I have proposed very similar theories of counterfactuals’.3 (I’d just heard of his work from Richmond Thomason.) At that point he had a final version of his soon-to-be-published ‘A Theory of Conditionals’;4 I had seminar notes; and if my experience with production of books is any guide, you must already have had a manu­script of Facts . . ., in pretty much final form. Stalnaker’s paper appeared later in 1968; my theory as told by Howard Sobel (with my permission and with full ac­know­ ledge­ment) appeared in 1970 in Inquiry, as an appendix to Sobel’s paper on utili­tar­ ian­ism;5 your book and Stalnaker and Thomason’s joint paper6 appeared that same year; and my own first paper on counterfactuals appeared in Theoria in 1971.7 Paul Benacerraf beat us all by many years. But alas, he let Carnap persuade him that because of the vagueness of similarity, the idea wasn’t worth pursuing! If I believed in complex structural universals, one of which is the total nature of the actual world, and the rest of which could have been, then I might be willing to join you and others in identifying these structural universals with (at least some of) the possible worlds. I resist not the identification, but rather the structural universals themselves. I have trouble making sense of the relation between a structural universal and the simpler universals which are its constituents. I’m sending you an offprint about this from the Australasian JP, 1986.8 Sincerely, David Lewis c: Stalnaker     5   6   7   8   1 3

Facts, Words and Beliefs (Sprigge 1970).    2  The Vindication of Absolute Idealism (Sprigge 1983). Letter 7. To Robert C. Stalnaker, 31 May 1968.    4  (Stalnaker 1968). ‘Utilitarianisms: Simple and General’ (Sobel 1970). ‘A Semantic Analysis of Conditional Logic’ (Stalnaker and Thomason 1970). ‘Completeness and Decidability of Three Logics of Counterfactual Conditionals’ (Lewis 1971b). ‘Against Structural Universals’ (Lewis 1986a).

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83.  To Michael McDermott, 10 August 1994

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83.  To Michael McDermott, 10 August 1994 [Melbourne, Australia] Dear Michael, Some time ago, you sent me two very interesting papers about counterfactuals and causation. Here, belatedly, are some comments. First, the paper on indeterministic causation.1 If chance-raising in indeterministic cases were exceptional, I might have a good deal of sympathy for the view that the Plain analysis gives the right answer even without benefit of Molinist*+ alleged truths about how unactualized chance processes would have gone – this supposedly right answer being that chance-raising never suffices for causation, except when the chance is raised from exactly zero. But I don’t think it’s exceptional, if the world is chancy in the way we have reason to think it is. The result of following where the Plain analysis leads, while rejecting Molinism, is that there may well turn out to be no causation ever – or hardly ever – in the actual world. That’s a reductio! The combination of the Plain analysis and Molinism is at any rate more at­tract­ ive than that. And as you say, it has the advantage in agreeing with what many are inclined to say. But Molinism is unacceptable, and not just because it conflicts with my Humeanism. As DMA2 would say: what are the truthmakers – Humean or other! – for Molinist counterfactuals? As Bigelow would say: how does their truth supervene on being? If you invent truthmakers for them, as Molina did, and if these truthmakers would carry over into the counterfactual situation in which the chance process takes place, it seems as if they’d determine its outcome and so make it not a chance process after all. --Second, the paper on amending the counterfactual analysis.3 I find this tan­tal­ iz­ing. I don’t like the amendment, I know pretty well what my misgivings are, yet I can’t turn them from misgivings into a counter-example. There’s a certain dread disease. It gives the victim years of agony, and there’s no safe cure. But there’s a kill-or-cure pill: 50% chance of cure, 50% chance of kill. Not

  ‘Metaphysics and Conceptual Analysis: Lewis on Indeterministic Causation’ (McDermott 1997). speaking, Molina had in mind counterfactual truths about unactualised free choices, in an incompatibilist sense of ‘free’. But I think unactualised chance processes are the same issue. +  R.M. Adams ‘Middle knowledge and the problem of evil’, APQ 14 (1977) 109ff. 2  D.M. Armstrong. 3   ‘Redundant Causation’ (McDermott 1995). 1

*  Strictly

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really chance, however: what happens depends deterministically on all sorts of mi­nute details of the patient, the pill, the weather, the phases of the moon . . . . The desperate patient resolves to take a k-or-c pill. He buys a bottle of five pills. He puts them on the table. He reaches out, chooses one of the pills (event c) and swallows it. . . . As luck (but not chance) would have it, he’s cured (event e). But there’s nothing special about the pill he chose – it’s no more effective or less dangerous than the other four. If he hadn’t taken that one, he’d have taken another, and who’s to say what might have happened then? They’re not indeterministic kill-or-cure-pills, and they’re not precise duplicates. Yet for all practical purposes they might as well be duplicates, and they might as well be indeterministic. It just doesn’t matter which one he takes. Yet we have Oc & Oe,    ∴ Oc  ⁄ Oe ¬Oc ¡ ¬Oe,  ¬(¬Oc ⁄ Oe) So on the amended analysis, c causes e. Yet I don’t consider this a counterexample. Even though it doesn’t matter which kill-or-cure pill he takes, still I do want to say that c caused e! (And so do two others I consulted.) I expected the analysis to go wrong by counting differences that don’t matter as causes. But it doesn’t go wrong. What it may do, though, is give the right answer for the wrong reason. On my own view, the reason c caused e though it made no difference is that c is a preempting cause, with potential alternatives waiting in reserve. And the way I handle (this kind of) preemption makes essential reference to transitive chains. Although e doesn’t depend on c, since ¬(¬Oc⁄ Oe), there is an intermediate event i – for instance, the swallowing of the chosen pill – such that e depends on i which in turn depends on c. You bypass all that and get the right answer anyway! And yet all that about the transitive chain wasn’t just an ad hoc dodge to get the right answer. It feels right. That is, it feels like the real reason why c is a cause of e. Or is it just that I’ve had 20-odd years to get accustomed to it? Yours, David PS I’m at Melbourne Uni through 23 August, home in Princeton after 9 September.

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84.  To Michael McDermott, 2 March 1995 [Princeton, NJ] Dear Michael, Here’s a first version of your argument. Let T be the actual complete set of laws of chance; let F be an undermining future. F has nonzero chance of occurring, according to T; but if F did occur, F would complete a pattern in history which would make a system of chance laws that conflict with T, so if F did occur, T would be false. So T says that F will not occur. But a system of laws has no business saying both that a future has nonzero chance of occurring and that it will not occur. If it says both things it’s incoherent. Alternatively (second version): . . . so, according to T, T has nonzero chance of being false; T has chance less than one of being true. Yet T implies T. So according to T, T has a chance equal to one. But a system of laws has no business assigning two different chances to a single proposition; if it does it’s incoherent. Both times, I reject the underlined step1 and I accept the rest. In the first version, I deny that T says that F will not occur. To conclude that F will not occur, we need not only T but other premises as well. For one thing, we need the rest of past and present history which, if F occurred, would join with F to complete a pattern that undermined T. For another thing, we need the theory of chancemaking that takes us from a pattern in history (past, present, and future) to a system of chances which would disagree with those given by T. To get around the need for the rest of history, we could reinterpret F to be not just the undermining future, but rather the undermining pattern throughout all of history. Call this U.  Then the alleged incoherence would be that U has a nonzero chance of coming true, according to T; yet T says that U will not come true. I don’t object to this amendment. Suppose it to be made. To get around the need for the theory of chancemaking, we could say that this theory is analytic; or we could say that it is presupposed, and therefore analytically implied, by T itself. For T ascribes chances; chances are implicitly defined in terms of the theory in question; T couldn’t be true unless that theory were true. (Just as a statement that these dry leaves are full of phlogiston presupposes phlogiston theory, hence couldn’t be true unless phlogiston theory were true, hence implies phlogiston theory. Or at least it presupposes and implies some central core of phlogiston ­theory.) I don’t object to either of these moves; however, I note that they have the

  The underlined steps are the italicized sentences of the two previous paragraphs.

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consequence that when T says that F will not occur, that ‘saying’ is not a matter of narrowly logical implication, but rather of implication with the aid of an arguably analytic, but unobvious and controversial, auxiliary premise. The coherence requirement says that whenever A has nonzero chance according to T, then T does not also imply that A will not occur. A strong coherence requirement employs a looser notion of implication, namely implication with the aid of analytic auxiliary premises. A weak coherence requirement employs instead a tighter notion of implication, namely narrowly logical implication. Unless I’m missing something, the possibility of undermining does indeed contradict strong coherence; whereas weak coherence is unthreatened. Well, which coherence requirement did I mean to impose? I’m not sure I asked myself that question very clearly, but I think you’ll find that what I wrote is consistent with demanding only weak coherence. Be that as it may, what I think now is as follows. It would certainly be nice to have strong coherence; that’s why the possibility of undermining is intuitively peculiar, as I willingly grant. But only weak coherence is non-negotiable. In the second version, I deny that according to T, T has a chance equal to 1. It’s like the daring prediction D: ‘this sample has a chance less than one of undergoing 50% decay in the next 12.6 years, but will nevertheless do so’. According to D, the second conjunct of D has a chance less than one of coming true, so the whole of D has a chance less than one of coming true. This shows that ‘According to D . . .’ should not be read as a statement of conditional credence or confirmation, since of course C(D/D) = 1. Rather, it should be read as a statement about what D says, in other words about what D implies. From the fact that P implies P, it does not follow that P implies that P has a chance equal to one, and indeed P implies no such thing. Likewise, from the fact that T implies T, it does not follow that T implies that T has a chance equal to one. (So far, I think it doesn’t matter whether you take the implication to be narrowly logical or whether you allow it to be aided by appropriate auxiliary premises.) So T may instead, without contradiction, imply that T has a chance unequal to one. Without contradiction – but without incoherence? Now it does matter what’s meant by implication. The coherence requirement as you quoted it from Philosophical Papers II, page 128, says that ‘each candidate system must imply that the chances are such as to give that very system no chance at any time of being false’. Then, as before, a strong coherence requirement employs a looser notion of implication, allowing use of auxiliary premises; whereas a weak coherence requirement employs a tighter, narrowly logical, notion of implication. Which did I intend? – I’m not sure there’s any fact of the matter. Which do I now want to require? – It would be nice to have both, but only weak coherence is non-negotiable. Which is threatened by undermining? – Only strong coherence. How decisively threatened is it? – I’m not very clear

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about that, since the total ‘candidate system’ which includes T may include more than just T. I hope this helps. Thank you for your letter. Yours,

85.  To Michael McDermott, 8 May 1995 [Princeton, NJ] Dear Michael, Let’s review the history. In 1986 I discussed a best-system theory of chance laws that I had favoured (not in print) in 1975.1 I said that part of my plan had been to include a coherence requirement, as follows: each candidate system must imply that the chances are such as to give that very system no chance at any time of being false. (Papers II, 128.) But just a little lower down the page, I said ‘Never mind the details if, as I think, the plan won’t work anyway’. And on the next page, still referring to the same plan: ‘All this seems very nice. But it doesn’t work . . .’. And then I explain the problem of undermining as the reason why it doesn’t work. That explanation makes it plain that non-zero chance of undermining futures means violation of the coherence requirement. ‘A peculiar situation, to say the least’. And then I explained that it was ‘worse than peculiar’, in view of an argument using the Principal Principle and ending in contradiction. Forward now to 1994, ‘Humean Supervenience Debugged’.2 ‘The resulting rescue of Humean chance won’t give us all we might wish, but I think it gives us enough’ (473). My rescue turns out to be an amendment of the Principal Principle (in­de­pend­ ent­ly motivated) to stop the contradiction. That doesn’t get rid of the non-zero chance of undermining futures. Of course not: the use of the Principal Principle came only after we already had that non-zero chance. My 1994 presentation of the problem follows the same lines as in 1986, including mention of the coherence requirement (fn., 480). Again it’s shown how the problem of undermining arises. But what I say about it in 1994 is ‘This undermining is certainly very peculiar. But I think that, so far, it is no worse than peculiar. I would not join Bigelow, Collins, and Pargetter . . . when they intuit a “basic chance principle” to exclude it outright’ (483).   ‘Postscripts to “A Subjectivist’s Guide to Objective Chance” ’ (Lewis 1986d, 114–32).   (Lewis 1994a).

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Then I present the argument using the unamended Principal Principle that takes us from undermining to contradiction. ‘I could tolerate undermining as merely peculiar. But not contradiction!’ Then I amend the Principle to get rid of the contradiction. ‘We’re left with nothing worse than peculiar undermining’ (485). I conclude ‘Because of undermining, nothing perfectly occupies the role [of chance], so nothing perfectly deserves the name. But near enough is good enough’. OK. So the 1975 (unpublished) position is that there should be a coherence requirement; the 1986 position is that a best-system analysis of laws and chance, including a coherence requirement, doesn’t work; the 1994 position is that undermining – in other words, violation of the coherence requirement – is peculiar but nevertheless to be tolerated, but at the cost of giving us not all we might wish, and giving us an imperfect deserver of the name ‘chance’. I understand that you join Bigelow, Collins, and Pargetter3 in thinking the coherence requirement (= zero chance of undermining futures) is non-negotiable. Whereas I think it’s negotiable and turns out to be unaffordable. But you seem to think that I have throughout joined you (and Bigelow etc.) in insisting on the coherence requirement at all costs – even when expressing toleration for undermining! – and thereby fallen into contradiction. I don’t understand. Yours, David Lewis PS The relevance of what ‘says’ or ‘implies’ means is that there is a sense – narrowly logical implication, unaided by other premises even if they’re analytic – in which it’s false, when F is an undermining future, that T implies that F will not occur. T by itself narrowly logically implies nothing about whether F will occur; that takes auxiliary premises.

86.  To C.B. Martin, 18 January 1996 [Princeton, NJ] Dear Charlie, You’ve sent me a paper, joint with John Heil, titled ‘Rules and Powers’:1 it takes the line that a straight dispositional solution to Kripkenstein’s problem works, if only we start from an adequate theory of dispositions. I have two requests and a comment.   ‘The Big Bad Bug: What Are the Humean’s Chances?’ (Bigelow, Collins, and Pargetter 1993).

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  (Heil and Martin 1998).

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86.  To C.B. Martin, 18 January 1996

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Request. I may want to cite this paper when I write about finkish dispositions. The copy you sent is marked ‘submitted for publication’. Once it is accepted, could you please tell me where it will appear and – if possible – when? Thanks. Request. Could I please have a more legible copy? Most of the one you sent is at least barely legible, but some parts, especially footnotes, are not. Thanks. Comment. When I wrote about the problem, the objection I made to a straight dispositional solution was that the subject might be disposed, when asked some arithmetical questions, not to add and not to quadd but rather to refuse to answer and instead to complain that the question is too hard. This would be a fair counterexample under (the simplest version of) the conditional analysis, but we agree in rejecting that analysis. So far, so good. How do you deal with the case? You might say: the subject has two conflicting dispositions. He does have the disposition I mentioned to refuse and to complain, but also he has the disposition to add. The former disposition prevents the manifestation of the latter. He anyway does not have any disposition to quadd. (This is a little different, I think, from saying that he has a finkish disposition to add: I’m supposing not that his disposition to add would go away if put to the test, but rather it would still be there but its manifestation would be prevented.) So far as I can tell, it’s open to you to say this. It resembles what you and Heil say toward the end of your paper, provided we may construe ‘behavioural limits’ as dispositions – dispositions to refuse to answer. OK? Here’s another comment, not on the ‘Rules and Powers’ paper. Kripke, arguing against dispositional analyses of colour, once imagined that there might be a shade of yellow – ‘killer yellow’ – which is instantly fatal to anyone who sees it. So killeryellow things, he said, are yellow yet aren’t disposed to cause experience-of-yellow; they’re disposed to cause death instead. I say: this is a case of finkishness. How so? – It’s not that the killer-yellow thing loses its own former disposition when someone looks at it! But consider that dispositions come in reciprocal pairs: A has a dis­pos­ ition to produce M when it meets B, B has a disposition to produce M when it meets A. (A favorite point of yours, I think.) The killer-yellow thing’s disposition to produce experience of yellow when it meets a person is not itself finkish, but the person’s reciprocal disposition to undergo experience of yellow when he meets a killer-yellow thing is finkish: that’s a disposition that he has until he meets the killer-yellow thing, then straightway loses. And the pair’s disposition to produce experience of yellow when its two halves meet is finkish. Yours, David Lewis

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87.  To Wolfgang Spohn, 13 February 1996 Princeton University Princeton, NJ Dear Prof. Spohn, [. . .] Let me answer not your question but a generalization of it. The problem is that a certain analysis says that X (in this case, lawhood) depends on Y (in this case, our standards of simplicity etc.) and yet we would ordinarily think this wasn’t so. If Y were different, X would be just the same – or so we offhand think. A proposed answer is that ‘X’ is a rigidified designator of the actual value of something that depends on Y, and of course it’s not true that the actual value would be different if Y were different. That’s supposed to explain our opinion that there’s no dependence. Well, if that’s so – I’d think that it well might be so under at least some le­git­im­ ate disambiguation – let ‘⨥X’ be a derigidification of the rigidified term ‘X’. Maybe there’s some nice ordinary-language reading of the derigidifying modifier; or maybe not, but in any case we can introduce it into our language by a suitable semantic explanation (as is done, for instance, in Stalnaker’s paper ‘Assertion’, Syntax and Semantics 9).1 Then it might turn out that our original opinion that X doesn’t depend on Y survives in modified form: as the opinion that even ⨥X doesn’t depend on Y. If so, the alleged rigidification of X ends up making no difference. I think that’s what does happen in the case of lawhood and our standards of simplicity etc. And that’s why the hypothesis of rigidification, even if true, doesn’t make the problem of counter-intuitive dependence go away. It makes it harder to state, because to state it you must first introduce the notion of derigidification. Sincerely, David Lewis

  (Stalnaker 1978).

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88.  To Wolfgang Spohn, 14 February 1996

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88.  To Wolfgang Spohn, 14 February 1996 Princeton University Princeton, NJ Dear Prof. Spohn, This continues yesterday’s letter to you. You asked: what if nature isn’t kind? What if there are two competitors for best system that are so evenly matched that slight differences in our standards really will matter? There are two ways to go. First alternative: in that case, one of the two systems definitely will be the system of laws for the world in question, the other one definitely won’t be. But in that case, it seems that in the unkind worlds, at least, lawhood will not supervene on the arrangement of local qualities. There will have to be some other lawmaker, I know not what, to settle these cases. Humean supervenience of lawhood will need to be compromised somehow. I reject this alternative. Second alternative: in the case of unkind worlds, what supervenes on the arrangement of qualities will not be the definite superiority of one system or the other, and not the definite lawhood of one set of regularities or the other, but rather a state of indeterminacy about what exactly is the system of laws. Humean supervenience of lawhood – including supervenience of whether there are determinate laws, as well as supervenience of what the laws are – will be uncompromised. What is compromised instead is our expectation that just any world, however unkind, will have a determinate system of laws. Likewise, of course, for the determinacy of chances – exactly as you say, except that you find this conclusion more peculiar than I do. Sincerely, David Lewis

89.  To Murali Ramachandran, 17 October 1996 Princeton University Princeton, NJ Dear Murali Ramachandran, Some while ago, you gave me two papers about causation: ‘Introducing the “Sufficiency” Analysis of Causation’ and ‘Causation, Pre-emption and Indeterminism:

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Menzies’ Challenge Taken Up’.1 I thought it best to wait until I was teaching a graduate seminar on causation and so had these matters more at the front of my mind, and consider your papers then. That time has now come, and in fact yesterday I spent about 2/3 of my seminar discussing your papers. So now I have some comments. Briefly: I think the moves you make succeed in solving the problems you set. But I also think that if you take those problems seriously, then you ought to take some further problems seriously as well, and I doubt that your solutions extend to those further problems. Let me concentrate mostly on the ‘Menzies’ Challenge’ paper. It is, if I’m not mistaken, the later of the two papers; and I find it easier to keep track of the v-dependence strategy when it is not entangled with the near-sufficiency strategy. (Indeed, I’m not perfectly sure whether the v-dependence part is the same in both papers or not.) Late preemption and gappiness. In the first place, I agree with you that the v-dependence analysis solves the late preemption problem in a simple case under determinism and without gappiness. And I think that, for that case, it’s a nice solution – all the nicer, for me, because it departs so little from taking causation as the ancestral of counterfactual dependence. I agree with you, further, that the v-dependence analysis allows causation by action at a distance; including delayed action at a distance, that is, causation over a gap both in space and in time. And I agree further that the analysis allows a case of late preemption in which both the preempting chain and the preempted chain have gaps in them. So far so good. But if we have decided that we ought to allow gaps, then I think we ought to allow even quite big gaps; and some of these quite big gaps mess up your solution to late preemption. Here’s how. Singh and Patel return to the fairground. Singh has his old-fashioned gun, as before. But Patel brings his new magical delayed-action-at-a-distance gun (for short: his gap-gun). If only Patel fired, the balloon would burst a split second after he fired; and there would be absolutely no relevant events in between the firing of the gapgun and the bursting of the balloon. If only Singh fired, of course a bullet would travel from his gun to the balloon and pierce the rubber skin and cause the balloon to burst. But as it is, they fire more or less simultaneously; the balloon bursts when Singh’s bullet is only halfway there; and when Singh’s bullet finally arrives where the balloon used to be, there is no longer a balloon there, only some shreds of rubber and puffs of gas departing in various directions. Patel’s gap-gun preempts Singh’s bullet. If Patel’s gap-gun had caused some event g which was an immediate precursor of the bursting but not actually a part of the bursting, your analysis would give the right answer. For that g would belong to a minimal dependence set for the bursting;   Cf. ‘A Counterfactual Analysis of Causation’ (Ramachandran 1997). See also ‘Counterfactuals and Preemptive Causation’ (Ganeri, Noordhof, and Ramachandran 1996). 1

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89.  To Murali Ramachandran, 17 October 1996

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and there would be no event in any g-containing minimal dependence set that is spatiotemporally closer to the bursting than g is. And further, that event g would counterfactually depend, and hence would virtually depend, upon Patel’s pulling the trigger of his gap-gun. So far, so good: this is the kind of gappy late preemption that you can handle. But a gap-gun isn’t like that: as I stipulated the case, there is no such event g. All there is, along the chain that begins with the firing of Patel’s gap-gun, is the bursting itself. Nothing on Patel’s chain – nothing that is distinct from the bursting itself, and is a virtual ancestor of the bursting – is closer to the bursting than is an event midway along the non-gappy chain from Singh’s old-fashioned gun. Worse still: according to your analysis, an event midway along the chain from the firing of Singh’s gun does turn out to cause the bursting; it gets closer to the bursting than does any event – any event that is a virtual ancestor of, and distinct from, the bursting – along the chain from Patel’s firing. What good is it to solve some cases, in fact many cases, of action at a distance if I can’t solve this one? Indeterminism. As you say, my ancestral-of-counterfactual-dependence ana­ lysis, unamended, already permits causation under indeterminism as well as caus­ ation under determinism. Namely, it permits the kind of causal dependence where the chance of the effect is raised from exactly zero up to some positive value; and further, it permits chains of that kind of causal dependence. What’s more, this kind of causal dependence under indeterminism can’t land us in Menzies’ problem: because Menzies’ case of probabilistic dependence without causation was a case where the chance of the effect was not raised from zero; it was only raised from a low value to a higher one. (If the unraised probability had been zero exactly, the preempting chain of low-grade neurons would have had zero chance of working. Yet the actual case was a case where that chain did work. Yet what has zero, as opposed to low, chance, can’t happen. Here it’s crucial that I distinguish zero chance from infinitesimal chance, which is standardly miscalled ‘probability zero’.) However, there is a second kind of causation under indeterminism; and my unamended analysis can’t handle it. (See my Papers II, 175–6.) And when you make the amendment required to handle it, the amendment of allowing probabilistic dependence, then you do open the way to Menzies’ problem. I don’t think we should be content to make room for just the first sort of causation under indeterminism. If we live in an indeterministic world of the very sort we think we probably do live in, we have causation of the second kind as well as (or perhaps instead of?) the first. Think of a nuclear bomb. Even when the plutonium isn’t compressed into a critical mass, there’s still some minute chance that all of it will undergo spontaneous fission simultaneously; or some minute chance that the spontaneous fission of a few atoms will lead to a chain reaction just because all the released neutrons happen to travel

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toward other nuclei instead of escaping. Yet of course we want to say that compressing the plutonium caused the explosion, despite the negligible yet non-zero background chance of a spontaneous explosion. Causing deaths by saving lives. I agree with you that there is something the matter with some of the causal judgements we reach by transitivity, including judgements that by causing lives we cause deaths, and that by saving lives we cause deaths. As you anticipate, I wonder what’s the matter: whether it’s the outright falsehood of the questionable judgements, or whether instead these judgements are truths that are, for some reason, inappropriate to mention in normal contexts. If the second hypothesis were right, we might find some special contexts where the questionable judgements would seem less peculiar. And I think that can indeed be done. Imagine that there’s something remarkable about the death that someone dies. The death he dies is momentous, in a way that a more ordinary death that he might have died instead, or the ordinary deaths died by other people, wouldn’t have been. For instance, we might think that the death he actually died, unlike the death he might have died instead, was a martyrdom – or even, for that matter, that it was the Atonement. In such a case we may be more eager to attend to the remote causes of that unique and momentous death. Now I think we have contexts where we become happy to judge that the unique and momentous event was indeed caused by events of causing lives, or by events of saving lives. Yet if we go for an analysis that makes such judgements false, why shouldn’t they still be false no matter how unique and momentous the death caused may be? I also think that, whether the peculiarity of the judgements is the peculiarity of falsehood or whether it’s just some sort of pragmatic inappropriateness, you may be misdiagnosing it. And therefore your remedy, which I think would be right if your diagnosis was right, may be misplaced. Maybe this is so in some but not all of your cases: I have especially in mind the cases of causing death by saving lives. I note that these are cases of causation by what Ned Hall calls double prevention. In such cases, c causes e by preventing d, where d is something which, if unprevented, would itself have prevented e. To save a life is to prevent an early death which, if unprevented, would have prevented the later death. Causation by double prevention, while unproblematic under a simple counterfactual analysis, turns out to be exceptional and troublesome in lots of ways. (Ned’s excellent paper on the subject, so far unpublished, is titled ‘New Problems for an Analysis of Causation’.)2 For one thing, they make for much more gappiness than we would otherwise have suspected – no need for magical delayed-action-at-a-distance-guns! For another thing, when you have causation by 2   This paper was presented at the 1994 AAP conference. It remained unpublished, but Hall’s (2004) ‘Two Concepts of Causation’ is its most direct descendant.

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89.  To Murali Ramachandran, 17 October 1996

175

double prevention, a lot depends on things not intrinsic to the causal chain that actually takes place, and that’s bad news for Menzies’ ‘theoretical’ solution and for my halfhearted appeal to much the same idea in the form of ‘quasi-dependence’. But the relevant point at present is that causal chains that include steps of ­double prevention have a way, in general, of making transitivity come out sounding very questionable – and this is so whether or not we have failures of near-sufficiency. Here’s Ned’s example about an air battle. A goody pilot, Suzy, is flying her bomber to attack a target in the land of the baddies. A baddy pilot, Lucifer, takes off in an interceptor to try to shoot down Suzy’s bomber. But a goody, Billy, in a longrange escort fighter accompanying Suzy’s bomber, shoots down Lucifer’s inter­ cept­or, thus preventing the interception of Suzy’s bomber – an event which, had it not been prevented, would have prevented Suzy’s destruction of the target. In this way, Billy’s shooting down of Lucifer causes the destruction of the target. So far, so good. Now add this. It takes time for Lucifer to prepare himself to go on duty. So he sets his alarm clock to wake him up in time to get ready. The ringing of Lucifer’s alarm clock is therefore a cause of Lucifer’s getting shot down – without it, he wouldn’t have been up in the air at the time when Suzy’s bomber and Billy’s fighter went by, and so Billy wouldn’t have shot him down. And as we already saw, the event of Billy’s shooting down Lucifer was a cause, by double prevention, of the destruction of the target. So either transitivity fails – for reasons having nothing to do with a lack of near-sufficiency – or the ringing of Lucifer’s alarm clock is one cause of the destruction of the target. Myself, I think I’ll stick with transitivity and accept that this strange causal judgement is true. But it’s certainly strange! Well, there are a lot of known examples which seem to work the same way: when double prevention meets transitivity, we get strange results. And your causing-death-by-saving-lives examples look to me like more of the same. Here’s a speculation (due partly to one of my students, Laurie Paul). I haven’t much idea whether it really works. (1) Causation by omission – causation by what doesn’t happen rather than by what does – is indeed a genuine kind of causation, but (2) it’s a different kind from ordinary ‘positive’ causation by genuine events. (3) Positive causation is transitive. But (4) a mixed chain, with some steps of positive causation and some steps of causation by omission, is not transitive; it may be that its first event doesn’t cause its last either by positive causation or by causation by omission, and there’s no third kind of causation, so its first event doesn’t cause its last one at all. And (5) double prevention cases always involve mixed chains, and that’s how they lead to failures of transitivity. Yours, David Lewis c: Peter Menzies, students in my seminar on causation

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90.  To Phillip Bricker, 13 March 1997 [Princeton, NJ] Dear Phillip, Thank you for the island universes paper.1 I taught a seminar last semester on causation. I don’t nowadays have an ana­ lysis of causation: I’m convinced that the counterfactual analysis is mostly right, but I don’t know how to fix it up so it’ll be entirely right. The problems center on preemption: cases where one of two redundant potential causes really is a cause and the other isn’t, though the effect doesn’t counterfactually depend on either one of them. Four problems. (I’ll start from what I said in the postscripts to ‘Causation’ in Papers II.) (1) I proposed to deal with late preemption by ‘quasi-dependence’: even if there’s no chain of counterfactual dependence running from c to e, at least there’s a chain of events which, in its intrinsic character, is like chains of dependence; it’s only because of its peculiar surroundings that it’s not itself a chain of dependence. However, there are genuine, and perfectly ordinary, cases of causation where there isn’t any (relevant) chain of events running from cause to effect. These are cases of what Ned Hall calls ‘double prevention’: c is a cause of e because it prevents d, where d, if unprevented, would have prevented e. (How does an escort fighter contribute to the success of a bombing mission? By shooting down the enemy interceptor which would otherwise have shot down the bomber.) Double prevention is not in itself a problem (had the escort fighter not been there, the target would not have been destroyed). But when you have a preempting causal process that works by double prevention, there isn’t much of anything going on; so my quasi-dependence solution doesn’t work. (2) I proposed to deal with early preemption by taking the ancestral of counterfactual dependence, and finding an intermediate event to complete a chain from c to e. But this requires the assumption that causation – unlike counterfactual dependence itself – is transitive. There’s a class of prima facie counterexamples to transitivity. These too involve double prevention. (The alarm clock awakened the pilot of the ­enemy interceptor. Without it, he wouldn’t have been up in the air, so he wouldn’t have been shot down. His getting shot down, as we saw already, was a cause of the target being destroyed. By transitivity, the ringing of the alarm clock is a cause of the target being destroyed! False? Or just pragmatically bad to say? Rain in April saved the forest from burning in April, so it was still there to burn in June; thus rain in April was a cause of the fire in June. This one sounds not so bad, but still not marvellous. Etc.)   ‘Island Universes and the Analysis of Modality’ (Bricker 2001).

1

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91.  To Ned Hall, 22 April 1997

177

(3) I said that probabilistic counterfactual dependence is a matter of the singlecase objective probability of e being substantially higher than it would have been without c. For short: c raises the chance of e. But Peter Menzies pointed out that a preempted alternative can raise the chance of e without thereby causing it. (4) Preemption cases involving action at a distance are especially troublesome. Jonathan Schaffer, a Rutgers grad student, has such a case which is a simultaneous counterexample against many different ideas about how to treat preemption.2 I’ve tried to get him to write it up, but he seemed disinclined. Maybe at some point I’ll write about it – at least a letter, though I’m not sure I’d be entitled to discuss it in print. [. . .] Yours, David Lewis

91.  To Ned Hall, 22 April 1997 as from: Princeton University Princeton, NJ University of Melbourne Melbourne, Australia Dear Ned, Thank you very much for the draft of ‘Two Concepts of Causation’.1 I wish I had a theory of causation again! I’m convinced that late preemption is the trouble spot. You’ve convinced me that piggybacking doesn’t work. Fragility doesn’t always work – not, e.g., in the Billy-Hillary case, or in Schaffer’s case. (But it often works. And, as Laurie Paul has pointed out, it needn’t rely on implausible identity conditions for events. And maybe we can tolerate all the minor hasteners and delayers counting as causes by claiming they’re causes normally not worth mentioning?) What’s left? – The PCA analysis2 and its countless relatives, and here I’m not clear what’s deep ­trouble and what can be fixed. Three main comments. §4.1 seems to me to call for an interpretation – or amendment – of the counterfactual antecedent, as follows: when we suppose that c

  ‘Trumping Preemption’ (Schaffer 2000).

2

  (Hall 2004).   See ‘Counterfactuals and Preemptive Causation’ (Ganeri, Noordhof, and Ramachandran 1996).

1 2

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had not been, we’re supposing more than just ~oc. We’re supposing c to be completely excised from history, not just replaced by some substitutive event that is almostbut-not-quite c. See Papers II, pp. 210–211; but that’s not a very good job, in part because it dodges the interpretation-or-amendment issue. (I have a notion I made the same point somewhere else, but I can’t now find it. Maybe it’s just that I’ve said it in seminars?) --§4.3, figure 7. Though you don’t say so, you consider three instances of this structure and you have opposite intuitions about them. ü ìHillary wouldhaveshot himdown ï ï If Billy hadn ’t shotLucifer down íHillary wouldhavedisabledhim by jamming ý ïHishome base wouldhaveorderredhim home ï î þ so he wouldn’t have shot down Suzy, so the target would have been destroyed, ìButactually Billy ’saction wasacauseof thedestruction;Hillary or home base ‘playednoactiverole ’ ü í ý îLucifer posesnothreat toSuzy,so itisfalsetosay thatBilly ’saction wasacauseof the bombing. þ

Which way to go? I’m not perfectly sure, but I think you’re trying to have it both ways. The case resembles one from Michael McDermott, except that McDermott’s is a case of single, not double, prevention. A cricket ball is heading straight for a glass window, but you catch it. Thereby preventing the window from breaking? – Maybe, maybe not. Because between you and the window there stands ìa high, wide,strongconcrete wall ü d havestopped the ball if it had got past you. í ý that would îa skilful fielder þ

ì wall ü Argument that you did save the window: surely you and the ífielder ý between you î þ ìit ü saved the window; and íhe ý didn’t play any active role, didn’t even touch the ball. So î þ

the way it actually happened, stopping the ball and saving the window was entirely your doing. Argument that you didn’t: the window was never under any threat. McDermott and John Collins have found that many naïve subjects go one way and many go the other; and further, many want to say that you did save the window if you were backed up by the fielder, but not if you were backed up by the wall. Collins suggests very plausibly that what we want to say depends on whether we regard a failure of the back-up as a possibility too far-fetched, too remote from actuality, to take seriously. Now your reactions are as if you regarded the possibility of home base failing to stop Lucifer as far-fetched; the possibility of Hillary failing to stop Lucifer as not far-fetched. (Hillary is like the fielder; home base’s decision to call off Lucifer is like the wall.) Is that it? Or is there some other difference? Or is it that you’re ambivalently

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91.  To Ned Hall, 22 April 1997

179

disposed about both cases and, considering them one at a time, happened to go one way about one and the other about the other? Or what? (By the way, when I think about how precarious communications, not to mention the survival of airfields, would be under WWIII conditions, it seems to me that a failure of home base to stop Lucifer would be not at all far-fetched. Hillary might be more like the wall!) --What you say in favour of transitivity in the April-rains-and-July-fire examples seems right; and yet the case continues to seem a bit counterintuitive. (It’s too bad that Lombard clouds the issue by giving a misguided objection to transitivity.) Note that this is a double-prevention case: the rains prevent an April fire which, had it occurred, would have prevented the July fire by removing the fuel. Now, there are a lot of cases in which transitivity applied to chains of double prevention comes out counter-intuitive. (False? – Maybe, maybe not.) Lucifer’s alarm clock is another of these cases. Yet another is Hartry Field’s: your enemy sets a bomb outside your door, you find it and extinguish the fuse in the nick of time, which causes you to be alive the next day. Counter-intuitive transitivity: setting the bomb causes extinguishing the fuse causes being alive the next day. Double prevention: extinguishing the fuse prevents the explosion which would have prevented you from being alive. (Here I’m again indebted to Laurie Paul.) Now if these cases – April rain, Lucifer’s alarm clock, the bomb – exhibit a common pattern in which double prevention somehow makes transitivity counterintuitive, it would be nice to treat them alike – which is not what you’re doing. --Assorted trivia [. . .] Yours, David c: Laurie Paul

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92.  To Ned Hall and L.A. Paul, 29 April 1997 University of Melbourne Melbourne, Australia Dear Ned and Laurie, I really like Ned’s idea of treating Schaffer’s Two Wizards example,1 along with other cases of trumping overdetermination, in terms of the sensitivity of the details of the effect to the details of the cause, but not to the details of the preempted alternative. (Laurie: I enclose a copy of Ned’s letter about this.) I just gave a ‘nothing works’ talk about the two wizards at Monash, in which I said that sensitivity was one of the things that didn’t work. Dumb! My mistake was to look at too narrow a range of variation. I said (considering the version where Morgana trumps because her spell is earlier) that I was free to stipulate vari­ations in time and manner of Morgana’s prince-to-frog-at-midnight /spell/ would make absolutely no difference to the time and manner of the prince’s transformation. Right, but irrelevant. If it had varied a little more it would have been, say, a princess-to-snakeat-11:45 spell; and that would have made a difference to what happened; and nothing parallel is true in Merlin’s case so long as he goes second and so is trumped. (Likewise, mutatis mutandis, in the version where it’s the later spell that trumps the earlier one.) (DH Rice drew my attention to sensitivity years ago, I have his paper on file at home, but I think it never appeared. Others?) So now I wonder just how much more we can do with sensitivity. Maybe the pieces could go together as follows – (But before we go too far, I suggest we get into the habit of saying ‘influence’ instead of ‘sensitivity’. It’s a non-technical word with the right meaning; it’s short; it can be used as a verb.) Here’s the theory: c causes e iff c and e are distinct events (or they are distinct absences of events, or one is an event and one is an absence) and c influences e to a substantial extent. The end. Comments. (1) ‘causes’ means ‘is among the causes of’. (2) ‘substantial extent’ is vague and is meant to remain so. Influence, as we shall soon see, admits of degree in a messy and multi-dimensional way. This is meant to answer the objection that if every influencing event counts as a cause, we get more causes than we believe in, as in my example of Boddy eating a big dinner, which to some extent affects the time and manner of his death from the poisoned chocolates.

  ‘Trumping Preemption’ (Schaffer 2000).

1

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92.  To Ned Hall and L.A. Paul, 29 April 1997

181

I say: not enough influence. But not decisively not enough. Saying the big dinner was among the causes of his death would be wrongish, but not decisively wrong. (3) I’m not taking an ancestral, so I’m giving up on unrestricted transitivity. Of course it’s usually true that if c influences d and d influences e, then c influences e; and that a cause of a cause is a cause. But maybe not always. In particular, maybe not in cases that combine preemption with double prevention: Lucifer’s alarm clock, Lucifer and the impending message from home base, Lucifer and Hillary(?), Hartry’s bomb. Much more about this soon. (4) That means I’m giving up my solution to early preemption with an inter­ medi­ate. Sadly: where it worked, it was nifty! But it was too much a special solution for the special case. Better would be a uniform solution to all the cases: early preemption with or without an intermediate, late preemption, trumping. The hope is that in all these cases the effect is influenced much more by the preempting cause than by the preempted backup. And in the intuitively clear cases, influenced substantially by the preempting cause, not at all by the backup. (5) And in symmetrical overdetermination, influenced much more by the redundant ‘causes’ taken together – by their fusion? – than by any one of them taken separately. (6) I’m also giving up on quasi-dependence. Not because the idea is under­devel­ oped – as of course it is. (I think it would have been premature to develop it further without being clearer whether it was a good idea at all.) More generally, I’m giving up Peter Menzies’ thesis that causation is a matter of intrinsic relations (intrinsic to their parts, not to their relata) maybe Humean-supervenient or maybe not, that qualify as causal because they occupy a theoretical role that links them normally to laws and to counterfactual dependence. The trouble is that I can’t figure out what an intrinsic relation between absences (or between events and absences) might be. Think of the little circle: an intrinsic relation never differs between duplicate pairs, duplicate pairs instantiate the same intrinsic relations. Now, when would two pairs of absences (or two mixed pairs) be duplicates? – I haven’t a clue! But I’m not willing to let the absences go. Because the more I keep my eyes open, the more I see cases of double prevention everywhere. (Including cases where no one could tell, without knowing the secret inner structure of the chip, or whatnot, whether the causation was by double prevention or not.) Enough preliminaries. What is influence? Start with some special cases. 1. Whether e occurs or not depends (counterfactually) on whether c occurs or not O( c ) ØO( c )

O(e) ( or , O( c ) & O(e)) ØO( e )

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or, what is not quite the same, 2. Whether e is present or absent depends on whether c is present or absent O( c )

O( e ) ( or , O( c ) & O( e ))

Absent ( c )

Absent ( e )

When I say that an event is present, I just mean that it occurs. But when I say that it is absent, I mean not just that the event itself doesn’t occur; further, no close approximation to it and no substantial part of it occurs either. It is cleanly and completely excised from history. ì whether coccurs ü 3. When and how e occurs depends on í ý whether cispresent or absent î þ O(c) & O(e) ¬O(c) ü ý ⁄e occurs at a different time or manner from its actual time or manner Absent(c)þ This is fragility; but fragility as Laurie understands it, not fragility in the full original sense. We need not say – and we need not deny either – that e occurring at a different time or manner would be not e itself but a different event taking e’s place. In other words, we need not say – or deny – that e has a fragile essence. 4. When and how e occurs depends on when and how c occurs. 5. When, how, and whether e occurs depends on when, how, and whether c occurs. 6. Whether e is present or absent and, if present, when and how e occurs depends on whether c is present or absent and, if present, when and how c occurs. Somewhat more generally we might think of the influence of c upon e as given by a pattern of counterfactuals like this. Oc0 ⁄ Oe 0 Oc1 ⁄ Oe1 Oc2 ⁄ Oe2 . . . where c0 and e0 are the versions of c and e that actually occur; and the other ci’s are other versions of, or alternatives to, c; and likewise for the other ei’s. A version of c is

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92.  To Ned Hall and L.A. Paul, 29 April 1997

183

an event whose occurrence in a given spatiotemporal region strictly implies that c occurs there; whereas an alternative to c is an event whose occurrence in a given region implies that c does not occur there. Policy: let nothing be said that turns on which ones are the versions and which ones are the alternatives – on how far through logical space the event itself extends – because that is presumably a highly unsettled and arbitrary matter. I said before: ‘influence admits of degree in a messy and multi-dimensional way’. Here are some of the dimensions: 1) How wide is the range of variation spanned by the ci’s as measured by their number? By their similarity-distances from c0? By their similarity-distances from one another? How specific are the various ci’s? 2) Likewise for the ei’s? 3) Is the mapping from the ci’s to the corresponding ei’s one-to-one? Or does it sometimes happen – how often? Where? – that different ci’s would result in the same – or compatible – ei’s? But I’m still oversimplifying! Who says that a pattern of influence can consist entirely of ‘would’-counterfactuals? Maybe sometimes we’ll have to settle for ‘might’ coun­ter­ fac­tuals. Or for ‘would’-counterfactuals whose consequents pertain not to the ei’s themselves but to the objective chances of various ei’s. Let’s forget about these complications at least. It might happen that we have a nice one-one pattern of influence covering a rich range of versions or alternatives fairly close to the actual version c0. Call this inner. Or we might have a one-one pattern covering distant alternatives: specifically, the absence of c. Call this outer. A pattern might be both inner and outer. That’s the nice, central case. Or a pattern might be inner but not outer. If various different close-in versions of c had occurred, various correspondingly different close-in versions of e would have occurred. But if c had been absent – if some far-out alternative to c had occurred – it’s not that e would have been absent; rather, some close-in version of e would have occurred. This is characteristic of the influence of a preempting cause with a backup in reserve. Or a pattern might be outer but not inner. Close-in versions of (or alternatives to) c0 would just result in e0; but the absence of c would result in the absence of e. This is characteristic of the influence of a cause by double prevention. (Or just plain prevention.) That’s because an absence doesn’t have (much of?) any way to come in slightly different versions.

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184 Diagrammatically: INNER & OUTER

INNER BUT NOT OUTER

OUTER BUT NOT INNER

These classifications are crude, of course, but they’ll do to make my next point. Suppose c influences d to a substantial extent; suppose d influences e to a substantial extent; and suppose certain further conditions for transitivity of counterfactual conditionals are met. Then if we feed the pattern of influence of c on d into the pattern of influence of d on e, we get out the pattern of influence of c on e. If the influence of c on d is (at least) inner, and so is the influence of d on e, then so also is the influence of c on e. And if the influence of c on d is (at least) outer, and so is the influence of d on e, then so also is the influence of c on e. In the nice central case, if the influence of c on d is both inner and outer, and so is the influence of d on e, then so also is the influence of c on e. In all these unmixed cases, causation is transitive. But it turns out, in accordance with an idea I learned from Laurie (though I’m not sure how far she’s now committed to it), that in mixed cases – specifically the mixed cases that arise from combining double prevention with pre-emption – the transitivity of influence and hence of causation may fail. Let the influence of c on d be inner but not outer; let the influence of d on e be outer but not inner. Feed the first into the second. The influence of c on e comes out to be nil! Diagrammatically: (No significance to where or whether I draw the arrowheads)

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93.  To Galen Strawson, 23 June 1997

185

(The dotted arrows are idle – there’s nothing feeding into them.) Likewise (more or less) in the other order: if the influence of c on d is outer but not inner and the influence of d on e is inner but not outer. Diagrammatically (I picture the most extreme case possible):

--That’s that. Please handle with care – these views are new and tentative, who knows if I’ll continue to like them as well as I do now! There’s no good address for me until I return to Princeton at the beginning of June. Best you can do is David Lewis c/o Jeremy Butterfield Fax 44-1223-33-5091 Expect delay. Ann should be willing to send me even quite a long fax at Princeton’s expense. Yours, David c: Allen Hazen

93.  To Galen Strawson, 23 June 1997 Princeton University Princeton, NJ Dear Galen, One little thing and then another. My ‘then’ was not especially or exclusively temporal; the little things are spread out both in space and in time. (Better: in spacetime.) My passage wasn’t an echo of Ayer, at least not knowingly. What is the Ayer passage you thought I might have been echoing? It’s not so much that possible worlds are in the mosaic as that each possible world – or rather, each one of a limited range of possible worlds – is one such mosaic.

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Do I believe you?1 No; and I don’t disbelieve you either. You make an impressive case, but I take it you and your allies have not yet convinced the entire learned world. I don’t know what can be said by way of rejoinder. So long as the experts are divided, I am not entitled to an opinion. I am not enough of an historian to judge the question for myself. As a neutral bystander, I now have an urgent practical problem. Whether or not he is a fictional character, the Hume of popular (mis?)understanding remains a figure of much interest to me. I take him to be right about some important things. I consider him vastly more interesting than your Hume. I want to carry on using him as a point of reference in discussing various questions. So I need an adjective applying to things as they are according to this perhapsfictitious Hume. Unless your view of the historical Hume gets knocked down de­cisive­ly, ‘Humean’ is an unsuitable word – to say the least. What’s the replacement? ‘ “Humean” ’ with inverted commas and a footnote? Reviewing Armstrong.2 Yes, I will. I hope I can write the review in July or August. But I might have to take all the time you’ve allowed me – that is, until the end of 1997. If I do write it in July or August, I will (I hope) be in Melbourne and parted from my word processor. Can you cope with a handwritten manuscript – my writing is fairly legible – or would you rather have it a little later and properly typed? The main question, now resolved, was whether I could read the book at all. David warned me that it had been set in rather small print. If it had been as small as the print in my Philosophical Papers, Vol. I, so that I could only read it a little at a time through a magnifying lens, I would have refused to review it. But I’ve had a look at the book now, and it turns out that the print isn’t quite that small.3 Yours, David

1   That is, does Lewis believe the main thesis of ‘David Hume: Objects and Power’ (Strawson 2008), wherein it is argued that Hume is a realist about causal influence and not a regularity theorist, as is commonly supposed. See also ‘Humeanism’ (Strawson 2015). 2   A World of States of Affairs (Armstrong 1997). 3   See ‘A World of Truthmakers?’ (Lewis 1999, 215–20); originally published as ‘The Truthmakers’ (Lewis 1998b).

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94.  To Ned Hall, 23 June 1997

187

94.  To Ned Hall, 23 June 1997 Princeton University Princeton, NJ Dear Ned, Preliminary question: how do you want to be known professionally? ‘Ned’, ‘Edward’, initials, . . .? I’ve seen plenty of typescripts headed ‘Ned Hall’ – is that how I should cite them? Provided, of course, that I have permission to cite them at all? Main business. I’ve been talking to Laurie about, among other things, probabilistic causal dependence and Menzies’ problem. The question is how the solution mentioned in fn. 4 of the ‘New Problems . . .’ draft1 is meant to work, and whether it does work. I have some doubts.2 Terminology: considering the question whether e depends probabilistically on c, let the immediate chance of e be the chance of e as of a time immediately after c; and let the last-minute chance of e be the chance of e as of a time immediately before e occurs. I agree with you that my specification that it’s the immediate chance of e that gets raised by c ‘steers the analysis straight into Menzies’ problem’. But it doesn’t ­follow that taking the last-minute chance instead would steer the analysis into safer waters, and I’m not sure it would. The pictures I’m going to draw are branching possible histories, with time running from left to right. The solid line is the actual history, in which c near the beginning is followed by e at the end. The dotted lines are unactualized alternative histories. There are two kinds of branches. In each picture, we first have a deterministic branching: c sends us to the upper branch, not-c would have sent us to the lower branch. The immediate chances are the chances on the upper branch right after this first branching. In each picture, we then have indeterministic branching on one or both branches (labeled with a question mark). These second branchings are the only point in the picture where anything objectively chancy happens. First case.

1   ‘New Problems for an Analysis of Causation’ (read at the 1994 AAP conference), which was an ancestor of ‘Two Concepts of Causation’ (Hall 2004). 2   Hall abandoned this solution – which involves taking the ‘last-minute’ chance of the effect – so it does not appear in print. However, Noordhof independently proposes using the ‘last-minute’ chance in a counterfactual analysis of causation in (Noordhof 1999).

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As things actually are, the last-minute chance of e is 1. If not-c, the last-minute chance of e would still have been 1. So if we go by last-minute chances, it seems that c has made no difference to the chance of e. Yet if we go by immediate chances, c has ­lowered the chance of e – maybe by a little, maybe by a lot. How much should this worry us? – It isn’t actually giving us a wrong answer about whether or not e depends on c – the answer we get is ‘no’, and that seems right. Second case

As things actually are, the last-minute chance of e is 1. Is this more than the lastminute chance of e would have been if not-c? Well, what would the last-minute chance of e have been if not-c? It doesn’t seem as if there’s any ‘would’ about it: it might have been 0 and it might have been 1. Yet if we go by immediate chances, it seems that c raises the chance of e: raises it to 1 from something less, maybe even something much less, depending what the chance distribution for the indeterministic branch-point is. Maybe the thing to say is that e depends on c iff the actual last-minute chance of e is much higher than the last-minute chance of e might have been if not-c. So the second case qualifies, because the actual last-minute chance of 1 is much higher than the might-have-been last-minute chance of 0. Third case

The actual last-minute chance of e is 1; the last-minute chance of e if not-c might have been 0. So this case meets the condition just proposed. And yet I haven’t assumed anything about the chance distributions at the two indeterministic branch-points. For all I’ve said, the top one could be overwhelmingly loaded in favor of not-e and the bottom one could be overwhelmingly loaded in favor of e, so that if we’d gone by immediate chances, we’d be saying that c enormously reduced the chance of e. Now, notice something I’m not doing: I’m refusing to assume that there are any true ‘would’-counterfactuals about how unactualized indeterministic branchings would have gone. (I’m refusing to assume what some physicists call ‘counterfactual definiteness’.) Assume that, and it’s a different ball game. But I reckon that counter-

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95.  To Ned Hall, 24 June 1997

189

factual definiteness is utter hocus-pocus, and if that’s what your solution needs, well that completes the reductio. So far, I’ve also assumed that both ‘would’- and ‘might’-counterfactuals obey the principle of centering: if you have c and e, that suffices to make it true that if it were that c, then it would be that e; and suffices also to make it false that if it were that c, then it might be that not-e. You could weaken centering, and think that if c was actually followed by an indeterministic branching between e and not-e, that makes it true that if it were that c, then it might have been that e; and also makes it true that if it were that c, then it might have been that not-e. If we say that, the third case comes out differently: the chances that e might have had if c are just the same as the chances that e might have had if not-c. So now it seems that c makes no difference to the range of chances that e might have had – and this regardless of what the chance distributions at the two indeterministic branchings might be! Yours, David c: Laurie

95.  To Ned Hall, 24 June 1997 Princeton University Princeton, NJ Dear Ned, Continuation of yesterday’s letter. If the switch to last-minute chances doesn’t work out, what might be an alternative cure? The problem was that a preempted potential cause of e may well raise the immediate chance of e by raising the chance that e will be caused via the preempted chain; yet that ought to be irrelevant, because that wasn’t the way e actually was caused. So might we say that e depends probabilistically on c iff c raises the immediate chance of some one course of events which actually happens and which culminates in e? The worry is that what comes of this may depend on how we delineate courses of events one from another. Suppose we were too lax about this: we could think that there was one single ‘course of events’ that could take place in different ways, one way if e was caused as it actually is via the preempting chain, another way if e had been caused as it might have been via the preempted chain. Then Menzies’ problem would not have been avoided. I want to say that what I’ve just described is not all one

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‘course of events’. But I don’t know whether there’s any way to make that stick without circularity. Change of subject. There’s a matter of terminology that we ought to settle now, lest we go different ways and cause confusion. Cases hitherto called ‘preemption’ have three things in common. (1) They are cases of redundant causation; we have two potential causes, c and d, and either one of them without the other would have caused e. (2) They are asymmetrical: we feel quite sure that c and d do not have an equal claim to be considered causes of e. Rather one of the two, the preempting cause, let it be c, is a cause of e; and the other one, the preempted alternative, d, isn’t. (3) The preempted chain is cut: there is some event which is prevented by c but which, if c hadn’t been there and if d instead had caused e, would have been a causal intermediate between d and e. Now, which of (1)–(3) should be built into the definition of ‘preemption’? If we have a case with (1) and (2) but not (3), is that ‘preemption’? I’ve been inclined to say that it is: the essential feature is the asymmetry. Thus I’ve wanted to speak of trumping as a new kind of preemption, and to say that it turns out that preemption doesn’t always involve the cutting of the preempted chain. And thus I can express the hope that the ‘influence’ approach will solve all kinds of preemption – early, late, and trumping – in a uniform way. You, on the other hand, speak of ‘trumping overdetermination’. Is this a decision you really want to stick to? If so, I should fall into line – though the original example was Schaffer’s, characterizing the class of trumping cases was your doing, and I guess the customary rule applies: the discoverer gets to choose the name. Yours, David c: Laurie

96.  To Hugh Rice, 27 June 1997 Princeton University Princeton, NJ Dear Hugh, In 1984, I gave a talk on redundant causation to the Phil. Soc. in Oxford: an ancestor of the ‘Redundant Causation’ postscript that appeared in my Philosophical Papers, Volume II, pages 193–213. You commented. Your comments included some

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interesting suggestions about how to handle causal preemption, suggestions which are well worth a further look and mostly have not reappeared in the published literature. At present, I’m especially interested in the idea that appears on pages 3–5. To quote two of your key passages: It won’t do . . . to say that if something is a cause of the very fragile death it is also a cause of the unfragile death. What I want to suggest is that the converse does hold . . . if C is a cause of E, it must also be a cause of . . . E together with any actual details of the case. If C1 and C2 are redundant causes of E, and E would have occurred (more or less) just as it did if C2 had not occurred, but would not have occurred more or less just as it did if C1 had not occurred, then C1 is a cause simpliciter of E and C2 is not. I had said that we have causal dependence of E on C iff whether E occurs depends counterfactually on whether C occurs. But that’s not the only kind of counterfactual dependence of E upon C that there might be. Even if there’s no whether-whether dependence, yet when and how E occurs might depend on whether or when or how C occurs. The dependence might be confined to minute details, which I think was what you had especially in mind; or it might instead, or as well, involve larger differences (as in the example that will follow). Let’s cover all these kinds of dependence by saying that C influences E. It turns out in many (most? all?) cases of causal preemption that, even though there’s no whether-whether dependence of the effect upon the preempting cause, still the preempting cause influences the effect in ways that the preempted alternative potential cause doesn’t. I was content for a long time with the two solutions for preemption that I proposed in my postscript: transitivity and quasi-dependence. But it slowly emerged that there were more cases than I thought where neither of these solutions is avail­ able – and further, that these cases include some that cannot be dismissed as farfetched, that could take place under this-worldly laws of nature. Some of these are cases that combine preemption with what Ned Hall calls double prevention: cases in which C causes E by preventing some event which, had it not been prevented, would have prevented E.  One of Ned’s examples: the escort fighter causes the bombing mission to succeed by shooting down the interceptor that would otherwise have shot down the bomber. At the same time, cases turned up in which transitivity of causation seemed doubtful; whereas my transitivity solution turned on taking the ancestral of counterfactual dependence, and thereby declaring that causation was invariably transitive. Often, the cases in which transitivity seems

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doubtful are again cases that combine preemption and double prevention. And so I gradually came to be in the market for a different solution to the problem of what distinguished a preempting cause from its preempted alternative. The problem became urgent last fall. Jonathan Schaffer, a graduate student at Rutgers, attended a seminar I gave on causation here at Princeton, and gave us a case that was a simultaneous counterexample to quite a wide range of solutions to the preemption problem. Schaffer’s example was a bit complicated and far-fetched, just so that it would hit as many different targets as possible; Ned Hall later pointed out to me that it fell in a class with many other examples, some of them not far-fetched. I’ll give a different example, not Schaffer’s. The Major and the Sergeant are – for some reason – simultaneously shouting orders at the troops. ‘Advance!’ they say in unison, and the troops advance. It’s redundant causation, sure enough: if the Major’s order had occurred and the Sergeant had been silent, or if the Sergeant’s order had occurred and the Major had been silent, the troops would have advanced just the same. Nevertheless, over a wide range of alternative orders, the Major’s orders influence what the troops do and the Sergeant’s do not. Holding fixed the Sergeant’s order, if the Major had ordered ‘Retreat!’, the troops would have retreated; if the Major had ordered ‘Take cover!’ the troops would have taken cover; and so on. Whereas, holding fixed the Major’s order, the Sergeant’s order does not influence what the troops do. If the Sergeant had ordered ‘Retreat!’ but the Major had still ordered ‘Advance!’, the troops would have advanced; and so on. They know enough to obey the higher-ranking officer. In case of conflict, the Major’s order trumps the Sergeant’s. And so it seems that in the case of non-conflict that we considered first, it was the Major’s order, not the Sergeant’s order, that caused the troops to advance. Even though there’s no whether-whether dependence in either case, what the troops do is sensitive to the Major’s order’s but not to the Sergeant’s order; and that sensitivity, I submit, suffices for causation. Besides placing Schaffer’s example in a broader class, Ned also pointed out that there are asymmetries of influence throughout this class. I’m now inclined to think that asymmetry of influence is the right solution to many kinds of cases: preemption both early and late, and the trumping cases as well. There is causation iff (or, better, to the extent that) C influences E; but the influence needn’t take the form of whetherwhether dependence. We need no longer take an ancestral; we can be content just to say that influence is often but not always transitive. It’s an interesting, and perhaps tractable, question why the cases that combine preemption with double prevention tend to be exceptions to transitivity.

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97.  To U.T. Place, 13 August 1997

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We need no longer admit causation by quasi-dependence as a special case; we can just be content to say that there are certain intrinsic relations that are often, but not invariably, associated with causation. It seems to me that if we go this way, you should have a goodly share of the credit. (I don’t know whether Ned knew of your comments. He well might have seen them, as a past student in my seminar on causation.) So I’m working up to the point of this letter: may I, and others who are working with me in this area, have permission to cite your unpublished comments on my 1984 talk? (If indeed they are still unpublished. But I once did a search that failed to turn them up.)1 Whatever your decision, thank you. Sincerely, David Lewis c: Ned Hall, Laurie Paul, Jonathan Schaffer, Cian Dorr PS Just as I was finishing this letter, your answer arrived by E-mail to Laurie Paul. Thank you! But I’ll send the letter anyway, to explain what’s going on.

97.  To U.T. Place, 13 August 1997 University of Melbourne Melbourne, Australia Dear Ullin, Princeton has forwarded to me your letter of 22 July, but not the accompanying five papers.1 (I regret to say that even if I had the papers I would have to decline comment on them.) But there are a few things I can say just in reply to your letter. One is that, so far as I can tell, questions about the nature of possible worlds and laws of nature are orthogonal to the counterfactual analysis of causation. Likewise for the view that predicate logic is the foundation of the language of science – a view that I have not held for quite a long time. The other thing is that, while I am indeed reconsidering how the counterfactual analysis ought to go, these reconsiderations mostly concerned remote causation by chains. So if yours is a theory of immediate causation, it would mostly be immune to the problems I have been considering.   See ‘David Lewis’s Awkward Cases of Redundant Causation’ (Rice 1999).

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  (Place 1987, 1996a, 1996b, 1997a, 1997b).

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With one exception. Suppose A and B are hooked up (in a suitably ‘immediate’ way) to C. Suppose A and B sometimes sound tones, and C echoes these tones, as follows. If A sounds a tone and B is silent, C sounds a tone at the same pitch as A. If B sounds a tone and A is silent, C sounds a tone at the same pitch as B. If A and B sound tones at different pitches, C sounds a tone at the same pitch as A (ignoring B). If A and B sound tones at the same pitch, C sounds a tone at the same pitch as A and B. Now in the fourth case, we seem to have redundant causation: C’s response is caused redundantly by A and B. Either one by itself would have sufficed. But, in view of A’s dominance over B in case of conflict (third case), I want to say that in the case of agreement (fourth case) it is A, not B, that is doing the causing. In other words, it is not a case of symmetric overdetermination, where the two redundant causes play an equal role. I conclude that we must look at patterns of counterfactual dependence involving several alternatives; not just the simple pattern cause → effect not-cause → not-effect. Yours, David

98.  To Jonathan Schaffer, 30 January 1998 [Princeton, NJ] Dear Jonathan, Now that we’re between semesters, I’ve had a chance to catch up with some jobs. For one thing, I’ve at last got around to reading ‘Trumping Overdetermination’.1 I like it. I agree with almost everything you say, and I think your strategy of presentation works well. It needs quite a lot of small-scale stylistic polishing, though – I won’t go into detail about that. One point where I disagreed came early on when you were arguing that the trumping cause (Merlin’s spell) had all five of the features at least typically characteristic of causation, whereas the trumped potential cause (Morgana’s spell) had none of 1

  ‘Trumping Preemption’ (Schaffer 2000).

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98.  To Jonathan Schaffer, 30 January 1998

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them. I think that knowledge of Morgana’s spell is some evidence – though of course not conclusive evidence – that the prince will turn into a frog. If you know that Morgana cast a prince-to-frog spell at 6 pm, and you don’t know whether hers was the first spell of the day, that evidence raises the probability that the prince will turn into a frog. For instance if you know the laws of magic, and if your prior probabilities were 25% Morgana cast a prince-to-frog at 6 pm 25% Morgana cast some other spell at 6 pm 50% Morgana cast no spell at 6 pm 60% No previous spell that day 20% First previous spell was a prince-to-frog 20% First previous spell was not a prince-to-frog (with the first three alternatives probabilistically independent of the second three) then the information that Morgana cast a prince-to-frog at 6 pm raises your prob­ abil­ity that the prince will turn into a frog from 35% to 80%. That looks like evidence to me. Your talk about ‘merely accidental’ truth might be part of an argument that it isn’t knowledge-conferring evidence. Agreed; but not all evidence confers knowledge. A matter of strategy. Replying to somebody – Martin Bunzl, if what he said to you resembles what he said to me – who refuses to take far-fetched examples ser­ ious­ly, you introduce the case of the soldiers. Your opponent replies that this is a case of old-fashioned preemption: the chain from the Sergeant’s order to the soldiers’ response is cut off. You mix two replies. (A) I’m free to stipulate that the mind doesn’t work the way the objector says, that both chains go to completion, and hence that it’s a case of trumping. (B) The man in the street doesn’t know which way the mind works, doesn’t know whether both chains go to completion or not, hence doesn’t know whether it’s oldfashioned preemption or whether it’s trumping. It might be trumping for all he knows. Nevertheless he remains confident that the Major’s order causes the troops to advance and the Sergeant’s order does not. I think (B) is your better response, since it’s open to the objector to complain that (A) makes the case far-fetched all over again. And I think the force of (B) gets diluted and obscured if you so much as mention (A). However, at present (A) is much more prominent. (B) shows up first in the parenthetical clause toward the bottom of page 13, and reappears, applied to a different example, in footnote 12. Another matter of strategy. I suggest you play down the MRL theory of law2 hood, since it’s not too widely believed, and since your point that the laws of magic

  The Mill-Ramsey-Lewis theory of lawhood.

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might be as you stipulate doesn’t depend on it. All you need assume is that the winner on simplicity-plus-strength might be a law; saying that it must be a law (because s-plus-s is constitutive of lawhood) is, for your present purpose, optional. (This will get more important when you present your positive theory of trumping, but that’s beyond the scope of this paper.) I like what you say when you return to this issue on page 16: ‘assuming that s-and-s are, if not constitutive, at least part of good methodology, scientists couldn’t ignore trumping and will never be able to rule out some possibility of there being trumping-inducing laws’. Terminology. I’ve adopted a different terminology from yours, as follows. Overdetermination =df symmetric redundant causation; preemption =df asymmetric redundant causation. See page 199 of my Philosophical Papers, Vol. II. In my ter­min­ ology, trumping is classified as a kind of redundant causation, a kind of preemption, and not a kind of overdetermination. The discovery of trumping is the discovery that not all preemption involves the cutting off of a potential causal chain. Your ter­min­ology, considered in itself, is fine; but it’s unfortunate that yours and mine differ. I think it’s important that we get this standardized, else much needless confusion will result. Finally, I thought there was something wrong right at the end of the paper, where you were talking about McDermott’s second suggestion. You say that on McDermott’s account, Morgana’s prince-to-frog spell all by itself would be sufficient for the prince turning into a frog. That was surprising, at least in the normal sense of sufficiency; because if Merlin had cast a queen-to-goat spell earlier in the day, then despite Morgana’s spell, the prince would not have turned into a frog. Peculiar! But of course McDermott means something special by sufficiency, so we should see what happens under his definition. Plugging in his definition (and simplifying by supposing that a set of events adds up to one single big event) it turns out you’re saying this: There is no actual event D (other than the event of the prince turning into a frog) such that if Morgana had cast her spell without D, then the prince wouldn’t have turned into a frog. In other words, you’re saying that Morgana’s success doesn’t depend upon any actual event (other than that success itself). And I think you’re thinking that Morgana’s success doesn’t depend on Merlin’s previous prince-to-frog spell; because with Merlin’s spell just taken away – and not replaced with some different spell – Morgana’s spell would have done the job. So far, so good. However, I think that for all we know from the story as you told it, there may indeed be some event D on which her success depends. For all we were told, maybe the laws of magic say that in order to gain magical powers, you have to sell your soul to the devil. Suppose Merlin and Morgana are the only wizards around. Then if they hadn’t sold their souls, the prince wouldn’t have turned into a frog no matter what

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99.  To Alexander Bird, 27 February 1998

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they did. Also, if Morgana had cast her spell without either her soul-selling or Merlin’s spell (even if Merlin had sold his soul), then again the prince wouldn’t have turned into a frog. I’m not saying this changes the outcome. I haven’t really thought it through, but I suppose that if the laws of magic say you have to sell your soul, that may just mean that Morgana’s spell is only part of a minimal sufficient condition (in McDermott’s special sense). And that would be just as bad for McDermott, since Morgana’s spell still isn’t a cause. On publication. Ned Hall and Laurie Paul have in mind to edit an anthology of recent work on causation, and that would be one nice place for your paper. But a journal would probably be quicker. Australasian? J. Phil.? Noûs? Yours, David Lewis

99.  To Alexander Bird, 27 February 1998 Princeton University Princeton, NJ Dear Alexander Bird, Thank you for your paper about dispositions and antidotes.1 I note that similar questions have been raised by Mark Johnston under the name ‘masking’,2 except that Mark’s masks are taken to be in place all along, whereas your antidotes are applied after the causal process from the stimulus and basis has begun, but before it has finished. Of the three defences you offer, I think (iii) is hopeless, but both (i) and (ii) succeed. And I think (i) and (ii) are not in competition, but apply to different versions of the problem. Take your case of the unstable nuclear reactor. Preliminary problem: my analysandum is a disposition to respond to a stimulus; you don’t specify a stimulus, saying only that the pile ‘has a disposition to chain-react catastrophically’. You call the catastrophe an explosion, but I think a melt-down is more realistic. But what’s the stimulus s that triggers the disposition? Say it’s a boiling-water reactor; then a cause

  ‘Dispositions and Antidotes’ (Bird 1998), which is a reply to ‘Finkish Dispositions’ (Lewis 1997).   ‘How to Speak of the Colors’ (Johnston 1992).

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of trouble could be that too much of the water boils off. So let’s say we’re talking about a disposition to melt down in response to a loss of water. As you say, we must be clear which object the disposition belongs to. If it’s the whole reactor, complete with rods and fail-safe mechanism, I agree with you that it is not disposed to melt down in response to a loss of water; rather, it’s disposed to fail safely. Defence (i) succeeds. If it’s just the uranium then I say that one disposition it has, not finkishly, is a disposition to melt down in response to a combined stimulus consisting of loss of water together with the absence of boron rods. Maybe it’s this disposition you’re invoking when you say ‘there is a clear sense in which the . . . disposition is retained. It’s not as if every fissile U-235 atom has been changed into a harmless U-237 atom’. (By the way, is that what you meant to say? U-237 doesn’t fission, but it’s not stable and not harmless: it beta-decays with a half life of about 7 days.) What if it’s the reactor core, including the uranium, including the boron rods when they’re inserted but not when they’re withdrawn, and not including the failsafe mechanism? Then I give defence (ii). The core has a finkish disposition to melt down in response to loss of water. Putting in the boron rods would not leave the basis unchanged. There is an intrinsic property B of the core, consisting partly of the arrangement and properties of the uranium and partly of the absence of boron from the core, such that B would not be retained if there were a loss of water; but such that, if B were retained for long enough, B and the loss of water would cause a melt-down. Absence of boron rods is not an intrinsic property of the uranium, but it is an intrinsic property of the core. (An intrinsic property is a property that never can differ between duplicates. If one core lacks boron rods and another has boron rods, the uranium in the first core duplicates the uranium in the second core, but the first core does not duplicate the second core; because the boron rods, when inserted, become part of the second core.) Bear in mind that my conditional is preceded by an existential quantifier: ‘for some B . . .’; and note that I explicitly allowed for the case that B might not be a ‘posi­ tive’ property. Your case where the sorcerer would save the glass by swiftly repairing the cracks before they spread is different. Indeed, there is a disposition of the whole glass-plus-sorcerer system to respond to a striking with a non-breaking; but let’s concentrate on the dispositions of the glass, considered by itself. And I think that the lack of sorcerous repairs, unlike the absence of boron rods from the core of the re­act­or, cannot be considered to be a negative part of a finkish basis, because it is not intrinsic to the glass. So I want to use defence (i), just as I did in my paper when I discussed antidotes to poisons.

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99.  To Alexander Bird, 27 February 1998

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When I spoke of inserting a condition ‘if no antidote is given’, I intended the second of the two readings you consider. The first never crossed my mind; and indeed I would not want to say that the poison loses its disposition to kill if an antidote is given. Rather, the disposition was all along more complex that it offhand seemed. The specification of the stimulus in ‘a poison is a substance disposed to cause death if ingested’ is oversimplified; really, it’s a substance disposed to cause death if ingested without an antidote. Likewise, the so-called ‘fragile’ glasses in a world (not ours!) where sorcerous repairs are possible are, strictly speaking, disposed to break if struck and not swiftly repaired; ‘soluble’ sugar cubes in worlds (not ours!) with Maxwell demons are disposed to dissolve when placed in water and not interfered with by demons; and so on, and so forth. Is something that’s poisonous in this qualified way strictly and literally a ‘poison’? – Yes; that is what we call it. Is something that’s fragile in this qualified way strictly and literally ‘fragile’? Is something that’s soluble in this qualified way strictly and literally ‘soluble’? – Who cares! I think these are idle questions, matters of semantic indecision. It would be misguided either to legislate answers or to try to discover the answers we’ve secretly legislated already. In any case, whether or not it’s strictly and literally true, it’s perfectly understandable why we might call the sorcerer’s glass ‘fragile’ even though the closest it comes to straightforward fragility is that it’s ­disposed to break if struck and not swiftly and sorcerously repaired. That’s close enough – to withhold the term ‘fragile’, even supposing that strictly and literally it doesn’t apply, would be pedantry. After all, sorcerous repairs are impossible in our actual world; and presumably they’re extraordinary even in the world under consideration. So it makes good sense to ignore them. I remind you, by the way, that my chosen analysandum was not the word ‘fragile’ (or ‘soluble’ or ‘poison’). Rather, it was a schema with such instances as ‘disposed to break if struck’ and ‘disposed to break if struck and unrepaired’. You say ‘there may be all sorts of other [possible] antidotes’. I agree. You say ‘we would need to mention them too’. I disagree. The sensible thing to do is to leave them unmentioned, unless something about the context or our conversational purposes requires attention to them. Rough specification of the dispositions we talk about is almost always good enough for all practical purposes. In this, as in other matters, a demand for limitless precision is not just pointless but pernicious. The question what are the limits of permissible imprecision is a general question in pragmatics, to be answered (insofar as it can be answered) by common-sense considerations having to do with the purposes of conversationalists in this or that context. It is not something that needs to be built into the analysis of one word after another.

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Your suggestion that ‘something like normal circumstances are implied’ is very much on the right track, I think. But it doesn’t belong in the analysans. And neither, I think, does it belong in a spelling-out of such analysanda (not my analysanda!) as ‘poison’, ‘fragile’, or ‘soluble’. Rather, it belongs to the general pragmatic topic of what qualifications we may permissibly leave unmentioned. Best regards, David Lewis c: Mark Johnston

100.  To Bruce Langtry, 14 August 1998 [Princeton, NJ] Dear Bruce, This letter continues the discussion that began with your good question when I read ‘Void and Object’ at Monash.1 Here are some things I said. (1) Only an intrinsic relation can be a (perfect) occupant of the biff-role. (Here I mean: a relation intrinsic to its pairs, not just to its relata.) (2) There is a relation that (perfectly) occupies the biff-role in the actual world. (3) If event c biffs event e – in other words, if c stands to e in the relation that actually occupies the biff-role – then c causes e. In other words, biff is sufficient, though not necessary, for causation. (4) Causation can be probabilistic – and, let me now add, some (or all?) causation in the actual world is probabilistic. Occupation of the biff-role therefore requires an association with probability-raising, not with outright lawful sufficiency or necessity. However, you said (5) It may happen, and indeed it plausibly does sometimes happen in the actual world, that c (probabilistically) causes e, cʹ does not cause eʹ, yet the pair of cʹ and eʹ is a duplicate of the pair of c and e. So if c bears any intrinsic relation to e, cʹ must bear that relation to eʹ. (1)–(5) add up to a problem, I agree. Initially, you took this problem as an argument against (1), or perhaps against the combination of (1) and (2). I replied that we might instead doubt (3).   (Lewis 2004e).

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As for (1): I take it to be merely definitional, and therefore beyond question. As for (2): that’s admittedly nothing more than a speculation about a contingent question, but I remain attached to it and want to give it more of a run for the money. As for (3): if we dropped it, I still can’t think of any watered-down substitute to put in its place. You and I agree on (4); and rejecting it seems to mean wholesale rejection of causal stories told by generally accepted microphysics. If what we think we know is true, for instance, the triggering of a nuclear warhead is only a probabilistic cause of the subsequent explosion – though of course the probability is only negligibly different from 100%. That leaves (5). After further thought, the solution I favour is to reject (5). However, (5) comes in two different versions, and the first step is to distinguish them. (5A) What happens is that, despite the intrinsic duplication of the pairs, c causes e and cʹ does not likewise cause eʹ, because of some relevant extrinsic difference between the two pairs. (5B) What happens is that, despite the intrinsic duplication of the pairs, c causes e and cʹ does not likewise cause eʹ, without any relevant extrinsic difference between the two pairs. I suspect it’s (5B) you had in mind – otherwise I don’t know why you mentioned that it was probabilistic causation – but anyway let’s consider both. First (5A). A simple example is this. Event c is accompanied by event d, but cʹ is not accompanied by any corresponding event dʹ, and that’s why c causes e but cʹ doesn’t cause eʹ. Not a problem, I say, because it’s not true that c biffs e. Rather, c + d biffs e. There’s no biff in the duplicate situation because the duplication is incomplete: there’s no duplicate of d, hence no duplicate of c + d, hence no duplicate of the pair of c + d with e. In this case, c was a merely partial cause; c + d was the whole cause of which c was a part. I’m of course perfectly willing to call a partial cause a cause, as we normally do; but I needn’t say on that account that the merely partial cause biffs its effect. Biff hooks up, in the first instance, with the relation of whole cause to effect. Here’s another way, previously overlooked, in which biff is sufficient but not necessary for causation. There are more complicated cases. For instance the relevant extraneous thing might accompany cʹ, and might interfere with the causation of eʹ. Without going through even one such case, I would expect that for all of them – or for all that could plausibly arise in the actual world – there’s a story of where the biff is that solves the problem. (5B) is much more interesting. I reject (5B); but to do so, I have to dispute a presupposition which is commonsensical and which is defended by some good

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­ hilosophers. I’ve discussed the issue before, in my Philosophical Papers, Volume II, p pages 180–184. Let me take an example which is suggested by the physics of lasers. An atom has two states: an ‘excited’ state and a ‘ground’ state. If it is excited, it may decay to the ground state; and when it does, it gives off light of a certain wave length W. When excited, it has a certain low probability per unit time of decaying spontaneously to the ground state. But when it is stimulated, by being bathed in light of wave length W, then it has a much higher probability per unit time of decaying to the ground state. An atom is stimulated and it does decay. The stimulation raised the probability of decay. But is this a case where the stimulation caused the decay, or is this a case of spontaneous decay that would have happened anyway? If stimulation raises the decay probability nine-fold, should we think that when atoms are stimulated, about 90% of the decays that occur are caused by stimulation and the other 10% are not? Now, if I’ve got the physics right, there is no known physical difference – no difference in what there is when and where – whatsoever between the case of a stimu­lated decay and the case of a spontaneous decay that happens in the presence of stimulation. Surprising, but true. The alleged difference between the two cases requires a difference-maker; there is no difference-maker known to physics. So if I believe in a difference, it seems to me that I’m letting offhand opinion override the current testimony of physics on a question where physics is authoritative. So I don’t believe in a difference. I think the question whether this particular decay was caused by stimulation or whether it was spontaneous is a mistaken question. All we can say is that the chance of decay was raised by stimulation but would have been non-zero even without stimulation. If there’s enough raising, then the stimulation probabilistically causes the decay in all cases. Therefore I reject an instance of (5B) in which, in one case, the stimulating radiation c causes a decay e, but in a duplicate case, though the stimulating radiation cʹ is present and the decay eʹ occurs, the decay is spontaneous and not caused by the stimulation. And I think that all instances of (5B) will be parallel to this one. Of course you’re very familiar with the issue in another connection: the question whether this particular atom would have decayed without the stimulation is like the question whether this particular sinner would have sinned if offered a smaller bribe (supposing that free agents are probabilistic systems). So the long and short of it is that (5B) requires a kind of generalized Molinism that I agree is commonsensical but that I nevertheless reject. Yours, David Lewis c: Peter Menzies

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101.  To Helen Beebee, 28 August 1998

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101.  To Helen Beebee, 28 August 1998 Princeton University Princeton, NJ Dear Helen Beebee, This is a letter of comment on your draft ‘Causes, Omissions and Conditions’,1 which Laurie Paul showed me. I like the way you set up the problem. Whether Smith’s not watering the plants was a cause of their death can have nothing to do with whether Smith had any duty to water them, or whether Smith could reasonably have been expected to water them, or whether it would have been in any sense normal for Smith to water them. Agreed! So we have a choice to make: either we must say that many statements of causation by omission are false although people would normally assert them, or else we must say that many statements of causation are true although people would normally refuse to assert them. Either way, willingness to assert turns out not to be a good indicator of truth. But I think you’ve made the wrong choice. Explaining why it’s not OK to say what’s true (true according to the speaker’s factual beliefs, which we may as well assume are correct) is much easier than explaining why it’s OK to say what’s false. For instance, it’s not OK to say what’s true when doing so will in no way advance our conversational purposes; and it’s not OK to say what’s true when that will mislead the hearer. I say that (CO) Smith’s not watering the plants was a cause of their death. is true regardless of whether Smith was supposed to water the plants, given that the plants would not have died if Smith had watered them. If our conversational purpose is to fix the blame for the death of the plants, and if Smith was supposed to water them, then (CO) is one premise of a sound argument for pinning the blame on Smith; so it’s OK to say it. If, on the other hand, Smith lives on the other side of the world, never heard of the plants or their owner, and so on, (CO) is still true; but this time (CO) is not a premise of any sound argument fixing the blame on Smith, and in fact in no way at all does it advance our conversational purpose of fixing the blame. What’s more, if I nevertheless do say it, then you, trusting me not to obstruct our conversation with irrelevancies, will think I thought it somehow relevant; so you’ll

  A later version of this paper is ‘Causing and Nothingness’ (Beebee 2004).

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infer that I somehow thought that Smith was supposed to water the plants; so you’ll be misled. That’s why it’s not OK say (CO), despite its truth. You and your informants feel that (CO) is false. What I have to say to that is that people are quite good at judging what it’s not OK to say, but not so good at judging why something is not OK to say. They may say ‘false’ (or they may assert the negation) and just mean that something or other has gone wrong. Here’s another example. Suppose somebody says (H) Hitler fell short of moral perfection. Outraged by the understatement, I well might say ‘Hitler did not “fall short of moral perfection” – he was a bloody monster!’; and, in the same spirit, I might say that (H) was false. But, strictly speaking, the trouble with (H) is not its truth value but something else. No news here – I’m just retailing lessons from Grice. I think Grice was absolutely right in what he said, and what he said applies very well to what we refuse to say about causation by omission. There are truths about positive causation that are out of place in an orderly conversation for similar reasons. The smash wouldn’t have happened if I’d run out of petrol an hour before. So my last fill-up was one cause of the accident. But it’s not OK to say so during a conversation in which we’re trying to fix the blame, because it’s not a premise of a sound argument to the conclusion that we should blame the petrolseller. The truth that the big bang caused all those subsequent events that wouldn’t have happened without it is out of place in almost any conversation you can imagine (except for a philosophical one). A different point. The general topic is causation by absences. Causation by omissions – absences of human actions – is a special case. Causation of harm by omissions is an even more special case. Attention to that special case, and consulting specialists on the law of negligence, invites us to attend just to contexts in which blame (or legal liability) is being fixed. But there are other quite different contexts in which causation by absences also arises, and before you dismiss it you should look at what we want to say in those other contexts. Consider the air brake (in simplified form). There’s a spring pushing the brake shoes toward the wheel; there’s a piston in a cylinder of compressed air pushing the brake shoes away from the wheel. When the train is running, there’s enough pressure in the cylinder to more than balance the springs, so the brakes are released. To stop the train, you let the air out of the cylinder; then the absence of pressure leaves the force of the springs unresisted, so the brakes are applied and the train stops. To understand the causal mechanism, you have to say that the absence of pressure (or of compressed air) causes an effect.

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102.  To Bruce Langtry, 11 September 1998

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Something similar is true of lots of mechanical, hydraulic, or electrical devices; and lots of chemical and biological systems as well. To explain these without mentioning causation by absences would require extensive circumlocution. I’m not best pleased that the network model needs to include absences in the network. (For one thing, it means that the solutions I once offered to Jaegwon Kim’s problem of non-causal counterfactual dependence are not fully general.) But I don’t think there’s any good way around it. More about this in my ‘Void and Object’. Laurie mentioned that you’d like a copy of the latest version; I’ve sent one. Yours, David c: Laurie

102.  To Bruce Langtry, 11 September 1998 Princeton University Princeton, NJ Dear Bruce, Thank you for your letter of 5 September. Good news about Barry! I’d have hoped it was platitudinous that any relation that occupies the biff-role suffices for causation – and not just because it’s platitudinous that causation itself suffices for causation, and causation occupies the role. Anyway, I doubt that caus­ ation does occupy the role, because I doubt that causation is an intrinsic relation. I think that when c causes e, that’s in virtue of the laws of nature, and (pace believers in ‘strong laws’) being subject to certain laws is not intrinsic to the pair of c and e. Your idea, I take it, is that there might be ‘fools biff’, something that occupies the role just as genuine biff does, but that isn’t the same natural relation that’s found in certain paradigm cases of causation. Then you ask how these paradigm cases are to be specified. – I reply that if so, it would turn out that in our world there are two different kind of biff; or maybe that the one biff-relation is more disjunctive and less natural than we might have guessed. Well, that might happen. (By the way, I’m less than convinced by the usual things that are said about water, gold, cats, etc. I think we would have been within our linguistic rights to respond to the discovery of iron pyrites by saying that there had turned out to be two kinds of gold, with different chemical properties; likewise I think we’d be within our rights to say that the water on twin earth has a completely different chemical

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structure. See my ‘Reduction of Mind’, pink preprint 6/93, pages 18–19; Peter Unger, Philosophical Relativity, pp. 79–104.)1 I agree with you that the struck match and death by beheading won’t do as paradigms of biff – not if I want it to be the relation of whole cause to effect in cases in which the causation is entirely positive. (Not only is it physically possible for Charles to be killed by something else after the beheading but before he has time to die from it; it’s even physically possible if he does die, the whole cause will include the absence of whatever might have saved him. If we do need paradigm cases of biff, where might we find them? Three suggestions. (1) Maybe the acceleration of a particle in response to the total (resultant) force on it would do. (2) Maybe more commonplace, macro­ scop­ic examples would do if we imagine them to be set not in this world, but in a simpler world that fits our naïve preconceptions: one in which a striking is a surefire, whole cause of a lighting, or a beheading of a death. I don’t see why reference can’t be fixed on unreal examples, especially ones which the naïve reference-fixer mistakenly takes to be real. (3) Maybe we can take a case where e is caused partly by c and partly by absences, but we can include earlier positive causes of those absences along with c in an entirely positive whole cause of e. Yours,   David

103.  To Ned Hall, 9 October 1998 Princeton University Princeton, NJ Dear Ned, On re-reading ‘Two Concepts of Causation’ (your 71-page version, undated, presumably superseded by now) I was struck by how much weight the case of Lucifer’s alarm clock was bearing. You seem unusually confident: to call Lucifer’s alarm clock a cause of the successful bombing is ‘absurd’. I don’t of course know what’s driving your intuitions, so I’ll speak for myself. I think my offhand intuitions about the case are pretty wishy-washy. But insofar as I can summon up any in­clin­ ation to agree with you, I think it comes from two disreputable sources, and it goes away when I think of how I’d dismiss parallel intuitions in other cases. Before I get to that, I want to notice how most of the alleged counterexamples to transitivity have a common structure. Like this: imagine that there’s a conflict   (Lewis 1994b); (Unger 1984).

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103.  To Ned Hall, 9 October 1998

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between Black and Red. (It could be a conflict between human opponents, or between nations; or between gods striving for one or another outcome; or just those forces of nature that conduce to one outcome versus those that conduce to the other.) Black makes a move which, if not countered, would have advanced his cause. Red responds with an effective counter-move, which gives Red the victory. Black’s move causes red’s counter-move, Red’s counter-move causes Red’s victory. But does Black’s move cause Red’s victory? – Put it like that, in the abstract, and I say ‘Of course!’ Every historian knows that actions very often have unintended and unwanted consequences, and very often turn out counter-productive. Let’s run through some familiar cases. The bomb outside the door. Black wants Red dead, Red wants to live. Black leaves a bomb outside Red’s door. Red discovers it and snuffs out the fuse. Red survives. The game of ‘Shock C’. Black is C’s friend, Red is C’s foe. C will be shocked iff the two SPDT switches are thrown alike. Black, seeing that Red’s switch is initially thrown right, throws his left. Red, seeing this, responds by throwing his left. C is shocked. The dogbite. Red wants an explosion; Black (= nature) wants peace. Black’s move: a dog bites off right-handed Red’s right hand. Red’s counter-move: difficult though it is, he sets the bomb /off/ with his left hand. Explosion. Forest fire. Black = those forces of nature that want the forest to survive; red = those forces of nature that want it to burn. Black’s move: protect the forest during the April lightning storms by raining all over it. Red’s counter-move: make the forest flammable again by gradually drying it off before more lightning comes. The forest burns in June. The deadly double dose. Black endangers Billy by giving half of the deadly double dose on Monday. Red counters by withholding the second half on Tuesday. Billy ­survives. (The fact that half of the deadly double dose cures a non-fatal illness is irrelevant, except that it turns the true statement that Black’s move somehow caused Billy’s survival into a false suggestion about how Black’s move caused Billy’s survival. We too easily mistake the falsity of what’s suggested for the falsity of what’s actually said.) Lucifer’s alarm clock. The bugler in the Black camp (or the alarm clock) summons the Black champion into battle, where he is slain by the Red forces. Without him, Black’s cause is lost. Red wins. Damned if you do, damned if you don’t. Black tries to do what God has commanded, but the Red devil interferes so that he messes it up. God accepts no excuses, so Black is damned. The idle network. Black wants neuron e to fire, Red wants it not to. Black’s move: fire c, which has a stimulatory connection to d, which in turn has a stimulatory connection

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to e. Red’s counter-move (made in advance): see to it that c also has a stimulatory ­connection to b, which in turn has an inhibitory connection to e. So e doesn’t fire. Now, my considered opinion is that in all these cases, Black’s move is a cause of Red’s victory. Whence comes such disinclination as I have against saying this? Two sources, both bad. One is what we can call the Lombard lapse: mixing up the question what caused what in the particular case with the question what sort of thing is generally conducive to what. ‘It is a bit of good common sense that heavy rains can put out fires, they don’t start them’. Or: it is a bit of good common sense that arousing Black champions to go forth into battle serves Black’s cause, not Red’s. The other is the inertness intuition: Black’s move doesn’t matter, Red would have won all the more easily without it. But that is just to say that the effect doesn’t depend counterfactually on the cause. Nobody who accepts any kind of preemption cases (unless he allocates them as you do to a second concept of causation) can possibly afford to credit these intuitions in general. I’m not denying that there may be another workable reply to these alleged failures of transitivity. I rather think there is: the sort of reply advanced in different versions by Paul and Maslen. That is to agree that Black’s move does not cause Red’s victory; but to deny that there’s really a failure of transitivity by distinguishing two versions of Red’s counter-move, one that is caused by Black’s move and another that causes Red’s victory. (The difference might be a matter of difference in explicit or implicit contrast cases.) But, while I have no objection to that sort of solution, I’m not clear how it can coexist with the solution I’ve defended here. Yours, David c: L.A. Paul, Cei Maslen, Michael McDermott, Jonathan Schaffer

104.  To Jonathan Schaffer, 9 October 1998 [Princeton, NJ] Dear Jonathan, [. . .] This is a reply to your letter of 16 September about ‘Void and Object’.1 Thanks.

  (Lewis 2004e).

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104.  To Jonathan Schaffer, 9 October 1998

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1) Your speculation is right: events, as I understand them, are spacetime regions taken in intension (equivalently, properties of spacetime regions). So, while they could happen in empty spacetime, they couldn’t happen where there isn’t even any spacetime. Hence my need for the combinatorial argument that there could be a void devoid even of spacetime itself. If I were willing to reify a void, I wouldn’t much mind calling it an ‘event’. But if I don’t first reify it, the issue of what to call it doesn’t arise. The point is that, call it what you will, there’s no such thing as a void, hence no such causal relatum as a void. There’s just the victim and nothing around him. 2) How does the counterfactual analysis escape? – By taking advantage of the fact that, whatever an absence may or may not be, the absence of an absence is just a presence. Absence of air caused Jaba to die because, roughly, if there had been air he’d have lived. More precisely, I suppose we want the bundle of counterfactuals that constitutes a pattern of influence; more precisely still, we take the ancestral of influence. No details in ‘Void and Object’ because it’s meant to be one of a pair of lectures, the companion lecture being ‘Causation as Influence’ (as yet unwritten, but you’ve pretty much heard it in the seminar).2 3) The void (as opposed to the vacuum) is the most extreme case of causation by absence, and I do think it’s a possible case. So it gives the stiffest challenge to anyone who’s reluctant to believe in causation by absence, so it’s the case I centrally use. Second reason: I’m in part responding to C.B. Martin, ‘How It Is . . .’,3 and at this point I’m picking up one of his examples. Think of my combinatorial argument this way. Premise: the relational and the substantival theories of space and time are both of them possibly true. So there are relationist worlds and there are substantivalist worlds. Well then, why not half-andhalf worlds? A relationist world, or a half-and-half world, is still interrelated by long-distance distance relations between things. So it doesn’t yet pose the problem of island universes – not even if it’s so arranged that to get from some things to some other things you have to cross a void. However I’ve been forced to reconsider the possibility of island universes by an argument of Bigelow and Pargetter: you accept that there could be a world of almost-island universes, linked only by a few wormholes? (Yes.) And you accept that each of these wormholes might exist contingently, thanks to how material things happen to be arranged? (Yes.) Well then, why couldn’t all the wormholes have happened never to be there, leaving a world of island universes?4  (Lewis 2004a).   3  ‘How It Is: Entities, Absences and Voids’ (Martin 1996b).   See ‘Beyond the Blank Stare’ (Bigelow and Pargetter 1987).

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4) It’s OK with me for you to cite ‘Void and Object’, both in agreement and in disagreement. I’m hoping it will end up in the Collins-Hall-Paul book, but it remains to be seen whether that book will really appear. In the meantime, you can write the footnote to: ‘ “Void and Object”, preprinted by the Department of Philosophy, University of Melbourne, 1998’. Yours, David Lewis

105.  To Helen Beebee, 17 November 1998 Princeton University Princeton, NJ Dear Helen Beebee, Thank you for your letter of 30 October. You say it’s false that your writing the letter caused Maite’s drinking her coffee in Mexico; you expect me to disagree, saying that it’s true but inappropriate to mention. But no: I too want to say that it’s false. What I do say is true, but normally in­appro­pri­ate to mention, is that your not going to Mexico and shooting Maite is a cause of her drinking her coffee. But I don’t identify your not shooting with whatever else you did – writing the letter, say – at the time when you might have been shooting Maite. You say about the air brake: ‘maybe there are enough positive events going on for it to count as genuine causation without the need for absences’. Your suggestion needs expansion. I say: absence of pressure was a cause of the brake being released. You say: such-and-such positive events were causes of the brake being released. I say: true, but irrelevant. It’s not as if the absence and the positive events were in competition, so that they couldn’t all be among the causes. What does the truth that there were positive causes do to get rid of the truth that there was also causation by absence? You note, and I agree, that if there’s causation by absences at all, there’s a lot of it – a lot more than we’d ever want to mention. The absence of a eucalyptus-eating griffin is part of the causal history of the growth of your sapling. Where do we stop? Well, maybe we should stop with contingent absences, and not count the absence of a round square eucalyptus-eating griffin. The growth of your sapling was caused, jointly, by the absence of all the things that might possibly have interfered. (I think, pace Kripke, that griffins, unicorns, and such are possible.)

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106.  To Ned Hall, 23 December 1998

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I’ve taken issue with you briefly in a draft paper called ‘Causation as Influence’, in very much the same terms as I did in my August letter; I’ve sent you a copy. If all goes well, ‘Void and Object’ will be published exactly at the time the Hall/ Paul/Collins volume comes out – because it will be in that volume. (As will ‘Causation as Influence’.) But we must both wait and see how the plans for that volume work out. In the meantime, you can cite ‘Void and Object’ as preprint 3/98, Department of Philosophy, University of Melbourne. Yours, David

106.  To Ned Hall, 23 December 1998 [Princeton, NJ] Dear Ned, Thank you very much for your long letter. This will be only a very partial reply. Two Concepts. Why am I opposed? Conservatism? Yeah, sure. The hypothesis that life is easy, and that we’ve been pretty much right hitherto, does have some intrinsic plausibility. But that’s not all. I think I have three other reasons. I’ve discussed the first two of them in ‘Void and Object’ (against a many-concept view which isn’t the same as yours). Jonathan1 has discussed all three, and on this question I think he and I are in full agreement. Sometimes we don’t know, and often we don’t know with certainty, which kind of causation we’re dealing with. Which concept are we using then? It won’t stop with two. There will be all sorts of mixed cases. Stepwise cases: causal chains in which some steps are steps of production, others are steps of dependence. Parallel cases: C produces D1 without dependence, D2 depends on C without production, D1 and D2 jointly produce E (or E depends on D1 and D2 jointly). You understate the problem because you think that only production is transitive; but even if I bought the rest of your two-concepts theory, I’d still think that you can cause an effect via a mixed causal chain. Once you have the entire menagerie of concepts, it will be a bit of a mystery why we have one word to cover the lot. Maybe you can say something to explain that, maybe not. (I’d guess you can.) If you can’t, that’s an unsatisfactory situation.

  Jonathan Schaffer.

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But if you can, that looks like a big step toward getting a single unified concept after all. It won’t stop with causation. We’ll have two – no, many – concepts of vision, of killing, of explanation, of rational decision, of acquaintance, of reference, and so on and so forth. Action at a Distance. Production (or biff, or process-linkage) is not one of our two (or more) concepts of causation. But it (or something in its near vicinity) is one especially prominent kind of causation.* And even if it weren’t that, it would still be a legitimate concept in its own right. So why shouldn’t I join you in enjoying the easy life? I too can say that the distinction we all had in mind – the interesting, non-trivial, contingent question which divides Newton’s physics (and maybe the physics of collapse of superpositions) from Maxwell’s and Einstein’s physics – is just the distinction between laws which do and which don’t permit production at a distance? Causation at a distance is a non-issue, say I, as witness my billiard-table example of double prevention.2 But it’s understandable that the question should sometimes get misstated as an issue about causation generally, because sometimes we focus on production and overlook the other kinds of causation. Switches and Thwarted Preventions. I agree with you about switches. But, as you feared might happen, all my Black-Red cases seem to me to have the structure of switching cases. Of course they’re not all alike in every respect, but it seems to me that they do have that much in common. I don’t think I can summon up any offhand intuitions whatever about the 100slots machine, so I’m happy to let it fall wherever my views about simpler cases would make it fall. The Idle Network. Not a slip: I was indeed looking just at the four-neuron subnetwork. But maybe if I’m looking at an example that is only part of your example, I shouldn’t call it yours. Again, thanks! Yours, David Lewis c: Paul, Schaffer

*  Well, maybe negligible amounts of process-linkage shouldn’t count as any kind of causation, at least not in everyday contexts. 2   For the description of this example, see ‘Causation as Influence’ (Lewis 2004a, 83–4).

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107.  To D.H. Mellor, 19 January 1999

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107.  To D.H. Mellor, 19 January 1999 Princeton University Princeton, NJ Dear Hugh, How about saying that causation is never a relation? It seems to me that there is a relation which, for instance, Ned’s hanging bears to his death; and if that relation between events isn’t called causation, what is it called? I’m happy to agree that not every case of causation involves instances of this relation between events; I’m happy to agree that not this relation, but rather counterfactual dependence among prop­os­ itions, is at the heart of the matter. But it won’t do to say that there’s no such relation; and it won’t do to say that there is such a relation but that it holds between true propositions as well as, or instead of, between events. I’ll fix the place that seems to ascribe the latter view to you. Thanks. I think there’s a sensible question about whether there’s action at a distance – a contingent question, which different physical theories (to say nothing of different tales of the supernatural) answer differently. But it shouldn’t be understood as the question whether there’s causation at a distance. To that question, the billiardtable example of double prevention gives an uncontroversial affirmative answer. The sensible question pertains not to causation in general, but to some important special kind of causation: ‘purely positive’ causation, ‘process linkage’, ‘biff’ – call it what you will. It’s an empirical question, about which serious theories disagree, whether that special kind of causation ever crosses a spatiotemporal gap. I approve of the efforts of those (Fair, Salmon, Dowe . . .) who try to characterize this special kind of causation. I only wish they wouldn’t call their analysandum just ‘causation’. Yours, David

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108.  To Jonathan Schaffer, 9 February 1999 [Princeton, NJ] Dear Jonathan, [. . .] Terminology. I’d like to have a term for the entire genus which includes old-style whether-whether counterfactual dependence as one species, Laurie’s when-andwhether-on-whether dependence as another species, influence as yet another species. . . . I think the best thing to do is to use ‘counterfactual dependence’ (or, for short – as when I’m trying to fit into 15 printed pages – ‘dependence’) as the term for the genus. That leaves me, or others, free to use it also for whichever species of dependence is under discussion at the moment. What I think I should not do is use it as a term specifically for influence, and I’ll go through and change any place where I use it that way. Absences. On your list of positions, (1) comes closest; but it misses the fictionalist flavour of what I say. There’s fact; there’s fiction. There’s what’s true; and there’s what we pretend is true. Since I believe that we’re within our linguistic rights in engaging in a pretence, I unapologetically do so; but also I stop to explain what I’m doing. But don’t mix what’s pretence with what’s explanation. Fact. There’s no air. There’s no such thing as an event of absence. There’s a true proposition that there’s no air. The negation of this proposition is the antecedent of a causal counterfactual.

 

Fiction. There’s an event ‘absence of air’.

There’s a true proposition that this event occurs. The negation of this proposition is the antecedent of a causal counterfactual. Necessarily, the event ‘absence of air’ occurs iff there’s no air.

Fact. Fiction. All non-fictional alterations are events; All alterations are events; some of them none of them are events of absence. are events of absence. To each non-fictional alteration there cor- To each alteration there corresponds a proposition of occurrence. responds a proposition of occurrence; and there are further propositions that we pretend are propositions of occurrence corresponding to alterations, but that are really negative existentials.

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108.  To Jonathan Schaffer, 9 February 1999

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One picture is worth a thousand words. The picture I have in mind appeared on the cover of Terry Parsons’ book Nonexistent Objects.1 It’s a picture of a nonexistent object casting an existent shadow. That’s what Terry’s book is about: the nonexistent object is, for instance, the golden mountain, and the existent shadow is a propertybundle: the set of the property of being golden and the property of being a mountain. In the present case, the existent shadows of the nonexistent events of absence are the corresponding propositions. ‘What is it to “wiggle” a negative existential?’ What are the alterations of an absence (to speak now within the fiction)? Well, there aren’t any very close al­ter­ ations of an absence – that’s why patterns of influence involving absences tend to exhibit funnelling, as I say. The not-so-close alterations of an absence are positive events, for instance an event of there being a certain amount of air (at the place in question). (Continued, 12 February 1999) Comparative Influence. Not cut, or not entirely. Page 14: ‘Influence admits of degree in a rough and multi-dimensional way’. I’ve added one item to the list of ways that influence can admit of degree: ‘How much do the Ei’s differ from one another?’ This could be subdivided into ‘How many different Ei’s are there?’ and ‘When the Ei’s do differ, how much do they differ?’ And the second also subdivides: how much on average? How much is the maximum difference? Etc. Something’s wrong with the story you tell about Ed being exploded: somebody called ‘Pam’ is mentioned later who wasn’t originally a character in your story. Pam = Sue? Or was it supposed to be Pam who placed Ed near the explosive and Sue who flipped the switch? Let’s say it was the latter: then you’re asking who had more influence, Pam whose action influenced all the details of when and how, or Sue who only made the difference to whether there’d be an explosion at all. Well, the pattern of influence from Pam has more different Ei’s; but the pattern from Sue displays a bigger difference between two of the Ei’s. I said ‘rough and multi-dimensional’, so I don’t really need a verdict about whose influence was greater. Offhand I’d say Sue, but I don’t know what general principle this might illustrate. Anyway, each had substantial enough influence that I don’t hesitate to say they were joint causes. You ask about the causal influence of the absence of a powerful demon who, had he existed, would have been able to do all manner of things. The alterations of this absence would be the event of the demon being present and using his powers this way, being present and using his powers that way, . . . . So the absence of the   (Parsons 1980).

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demon has a very great deal of influence. – I have two conflicting inclinations. (1) I might just agree that the absence of such a demon does indeed have a great deal of influence? Why not? Simply because we don’t mention this absence as a cause? – But there are lots of causes we don’t mention, for good reason. There’s the big bang, there’s the existence of air, . . . . Absence of the powerful demon might be another of those. (2) I might instead deny that the proposed alterations of the absence of the demon should count at all, being too distant from actuality. If it’s (2), there’s no problem about the absence of the demon being more of a cause of various events than their competitors. If it’s (1), maybe the absence of the demon is indeed more of a cause; but the competitors we mention are nevertheless quite enough of causes to deserve mention. When preempted Billy makes a little bit of a difference to the shattering, by way of the gravitational influence of his rock on the trajectory of Suzy’s rock, two different things are both true. One is that Billy has very little influence (because of the close similarity of the Ei’s) and the other is that Suzy has much more influence than Billy. It’s because of both these things together that it’s near enough to true that Suzy influences the shattering and Billy does not. If Billy had quite a lot of influence and Suzy had even more, Suzy would still win the competition, but in that case it wouldn’t be near enough true to say that Suzy was a cause and Billy wasn’t. Button and Dial. I’m not remembering that conversation as well as I need to in order to comment on what you say. Looking at it afresh, it seems to me that maybe my response should have been different. If I understand the set-up, pressing Suzy’s button has the same effect – maximum shock – as turning Billy’s dial all the way up. Well then, if we hold Suzy’s button-pressing fixed, and look at alterations of what Billy did, they make little difference to what happens to Lucifer: he gets the max­imum shock whatever Billy does. Whereas if we hold Billy’s initial not turning of the dial fixed and look at alterations of what Suzy does, that does make some difference to what happens to Lucifer: the electrocution gets delayed by the time it takes Billy to respond to seeing Suzy not press her button. Yours, David Lewis c: Laurie (except for ‘Business’ section)

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109.  To Nicholas White, 26 March 1999

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109.  To Nicholas White, 26 March 1999 [Princeton, NJ] Dear Nick, Thank you for your explanation paper. I’ve read it with interest, and I largely agree. On the loosening. Suppose you give some causal information about a sequence of events, say those that constitute the French Revolution, but without focusing on any one event, either the entire Revolution or some final part of it, as explanandum. I don’t at all mind calling this ‘an explanation’. I don’t much mind calling it ‘an ex­plan­ ation of the Revolution’, though I feel an ambiguity between a sense in which it deserves that name and a sense in which it doesn’t. I do mind calling it ‘an explanation of why the Revolution happened’, and this gives the sense in which I thought it wrong to call it ‘an explanation of the Revolution’. Strangely, I don’t so much mind calling it ‘an explanation of why such-and-such (listed) events happened’: it does give information about the causal histories leading up to most of those events, and if the causal history of the first event is missing – well, servings of explanatory information are normally less complete than we might wish. On the tightening. Say you tell me that the causal history leading up to a certain event was written about, in green ink, in Swedish. I agree that this shouldn’t be called an explanation of the event – not even a lousy explanation. My first thought was: but this isn’t information about the causal history. It tells you exactly nothing about the intrinsic properties of the causal history, only about one of its extrinsic properties. This is a general point about attributions of extrinsic properties. If all I tell you about the diamond is that it belongs to the Queen, there’s a good sense in which I’ve told you nothing at all about the diamond itself. (But I agree that there’s another, laxer sense in which I did give you information about the diamond.) But then I thought: the same could be said about the case where you tell me that the causal history leading up to my having lungs is of a kind with a lot of other causal histories of organisms having fitness-enhancing properties. That too is extrinsic information about the causal history, yet I think I was right to call it explanatory. So what’s the difference? – Maybe it’s this. In the second case, it seems offhand more likely that the extrinsic information will join with other information we possess, or may hope to possess someday, to give us intrinsic information about the causal history. That could happen in the first case too; but it would require a special, flukey bit of added information, not just the general advancement of science. Yours, David Lewis

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110.  To Mary Kate McGowan, 1 April 1999 [Princeton, NJ] Dear Mary Kate, The trip to Donegal (and Ulster, and England) was very successful except for one thing: cat Possum died while we were away. Not by surprise. We kept in touch with the Penn vet hospital, and they told us he was going downhill fast and there was nothing more they could do. On or near St. Patrick’s day, sessions are in the afternoon, not the evening; and, at least in the town of Donegal, they’re very crowded. So we chose sight-seeing over sessions. But, to my surprise, we later found quite a good session in Belfast. (In what was clearly a Republican pub. I don’t know whether the prots1 have sessions or not.) I hated Belfast on first sight, but came to like it a bit better as the evening went on. Having a concept (say, of causation) is having a disposition to classify possible cases in some more or less principled way. I take conceptual analysis to be the project of investigating these dispositions. Investigating my own dispositions, at least at the outset. I’d guess mine are pretty much the same as other people’s, but whether that’s so or not it’s wise to start with the case I know best. Dispositions can be interfered with by other dispositions. For instance I have a disposition to multiply correctly, but it’s interfered with by a disposition to make careless mistakes, and by a disposition to refuse to go on multiplying without ad­equate reason. So you can’t just read off my concept of multiplication from my overall pattern of multiplication-behaviour; the best explanation of my overall behaviour will say that it’s produced by an interplay of dispositions, only one of which is my concept of multiplication. So likewise with my judgements of whether various possible cases are cases of causation. My concept of causation can be interfered with by various kinds of dis­ pos­itions to get confused or make mistakes. Investigating the concept requires inference to the best explanation, and sometimes a candidate explanation for my offhand inclinations to classify cases will be that I’m getting confused or making some sort of mistake, so that my inclinations don’t perfectly fit the concept that underlies them. Sometimes such an explanation may be the best explanation, enough ahead of its available rivals that it should be (tentatively) accepted. What makes an explanation good or bad? Well, I have a prior sense of what sorts of hypotheses are more or less plausible, and I don’t know how much more I can say. An explanation that says that a certain classification is mistaken, but has   Short for ‘Protestants’.

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110.  To Mary Kate McGowan, 1 April 1999

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nothing further to say about why I make the mistake, is ceteris paribus implausible and bad; an explanation that explains why I tend to make the mistake, say because I’m misled by a certain resemblance between the misclassified case and another case, is ceteris paribus better. An explanation that says that some of my very confident classifications are wrong is ceteris paribus worse than one that says only that some of my less confident classifications are wrong, or one that says only that some of my refusals to classify are wrong. An explanation that says that my concept is not so very prin­ cipled, that it’s full of quirky exceptions that have no apparent point, is ceteris paribus worse than one that makes the concept make more sense. An explanation that posits some familiar kind of indeterminacy or ambiguity is ceteris paribus better than one that posits some unprecedented kind ad hoc. And so on, and so forth. As always, different virtues of rival explanations must be balanced off. As always, we don’t know in advance how good the best explanation will be. As always, there’s no guarantee that the best explanation is true. Suppose my classifications seem ambivalent, either because I find myself classifying the same case differently after coming at it from different directions, or because I find myself stably reluctant to classify the case one way or the other. One explanation is that there’s a right answer, but something is interfering with my dis­ pos­ition to give it. That might be the best explanation – especially if it makes the concept more principled than it would otherwise turn out to be, and especially if the alleged mistake is explicable. This is the ‘spoils to the victor’ move. It gives me license to clean up the ragged edges of my offhand inclinations to classify. But note that this is not Carnap’s sort of license to clean up: the project is still to investigate the concept I already have, not to improve on it. (Improvements might perhaps be a good idea, though I think more likely not. But surely the first step is to find out where I’m starting from!) And it should not at all suggest that the truth about my concepts is for me to make up as I please – no, what I’m making up are fallible hypotheses about an independent (mental) reality that I can’t examine directly. On the other hand, the best explanation of an ambivalence might instead be that the concept really is indeterminate: even without interferences, the disposition to classify cases one way or the other just gives out. This is the ‘respect our ambivalence’ move. I think it’s very clear that respecting our ambivalence is sometimes the right thing to do: for instance in the cases of ‘bald’, ‘flat’, and ‘know’. And sometimes not. There’s no easy rule for when it’s the right thing to do and when not – it depends on one’s judgement of how the advantages and drawbacks of the available ex­plan­ ations balance out. I hope this helps. Feel free to share it with Kate and Amelie, or others. Yours, David Lewis

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111.  To Helen Beebee, 12 April 1999 Princeton University Princeton, NJ Dear Helen, Thank you very much for your fax letter of 12 March. Your good question about the location of absences made me see that there’s an inconsistency on this point in ‘Causation as Influence’. On page 14, arguing that in double prevention we have causation at a distance (though not action at a distance) I say something very like what you say in your letter: ‘What matters, of course, is what doesn’t happen. Sometimes maybe we can assign definite locations to the prevented intermediates, and thereby locate a chain of events and absences. Sometimes not. If a preempting cause happens to work by double prevention . . . and if we cannot assign any definite location to the relevant absences, there is no saying what the intrinsic character of the comparison chain is required to match’. At that point I was thinking that the absence of the enemy interceptor was located only in the whole of the region within which the interceptor would have been. Interceptors fly fast, twist, and turn, so that’s a large region. So far, so good – except that much later, in the course of arguing that the Kim problems of non-causal counterfactual dependence would not reappear in the case of absences, I said what you spotted: ‘we can say when two absences are distinct from one another: namely, when the corresponding negative existential propositions are logically independent and pertain to non-overlapping parts of space and time’. This seems to require something more decisive by way of location of absences. In a way, the problem is easy to solve. Let’s assume that at least when worlds are not too different, cross-identification of spatiotemporal regions is easy. A prop­os­ ition, negative existential or otherwise, is entirely about region R iff, whenever the region R of one world is a perfect duplicate of the region R of another world, the proposition has the same truth value at both worlds. What would it have taken to make false the proposition that you didn’t drink any coffee on 11 March? Well, that’s false at any world where a counterpart of yours drinks coffee anytime on 11 March, anywhere. I gather you were at or near the RSSS on that day; but you could have gone to the student’s union, or flown to London, or flown to the Moon, . . . . So the answer I’m getting is number (2), on your letter – except without the restriction to not-toofar-fetched possibilities that your examples suggest.1 That’s an answer, sure enough. 1   (2) is ‘To the sum of all the localised spatio-temporal regions within which I might have drunk coffee (my kitchen at 9am, the students’ union at 1:30, the tea room balcony at 3:30, say)’. Letter from Helen Beebee to David Lewis, 12 March 1999, p. 1.

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112.  To Christopher Hitchcock, 17 May 1999

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But as you go on to explain, it’s not a satisfactory answer given what I’m trying to use it for. If the negative existentials corresponding to commonplace absences pertain to such enormous regions, they’ll usually overlap, but such overlap doesn’t seem to prevent counterfactual dependence between absences from being causal. What I’ll do for now is just to strike out the words ‘and pertain to non-overlapping parts of space and time’. That may create a risk of trouble; however it may not. I can’t really think of any counterpart of the Kim cases that would be let in. Yours, David

112.  To Christopher Hitchcock, 17 May 1999 Princeton University Princeton, NJ Dear Cricky, Laurie gave me a copy of your new version of the ‘Contrastive Explanation’ paper.1 I have some comments. I hope we disagree less than you thought. In section 4 (2nd paragraph) you distinguish a ‘strong’ and a ‘weaker’ reading of CEID.2 You say I seem to be endorsing only the weaker reading of CEID. That’s correct. Indeed, my Uppsala-Monash example is a counterexample against the stronger reading. (More about that example soon.) In section 5 (3rd paragraph) you distinguish the ‘different histories’ and the ‘different causes’ reading of what I said. I agree there’s an ambiguity; and I think it’s the ‘different history’ reading I want. If asked to find a difference between the course of events that precedes the photon going through the polarizer and the unactualized alternative course of events that would have preceded it getting stopped, I have to say there isn’t any. That’s why I can’t explain why it got through rather than getting stopped. In the next paragraph you return to my Uppsala-Monash example. You infer from my willingness to accept a contrastive explanation that I take the case to be deterministic. Not so! I think (and thought then) that very likely almost no thisworldly processes are deterministic. All you should infer, given what I said, is that I don’t think my going to Monash and my going to Uppsala would have been ‘one

  ‘Contrastive Explanation and the Demons of Determinism’ (Hitchcock 1999).   CEID is short for Contrastive Explanation Implies Determinism.

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outcome rather than another’ of the very same chance process. I think rather that their histories would have differed – namely, with respect to the invitation from Monash. Later in the same paragraph, you quote me as saying that according to the standard resolutions, counterfactuals don’t backtrack. Right; and that means that a causal counterfactual – if the cause had not been, the effect never had existed – mustn’t be a backtracker. But the counterfactual now in question – if I’d made the other choice, there’d have been a different previous history – is not a causal counterfactual, so my prohibition against backtrackers doesn’t apply. Indeed, this counterfactual is a backtracker. In short: what I had in mind was the ‘different histories’ reading plus a backtracker, not the ‘different causes’ reading plus a ‘standard’ counterfactual. Thus my example is a counterexample to the strong but not the weak CEID. So, with regard to the choice of sacrifices you offer me at the end of the section, all I have to sacrifice is a blanket prohibition against backtrackers in all contexts – which I never accepted in the first place. The Lipton point at the beginning of section 6 again requires the ‘different causes’ rather than the ‘different histories’ reading. Lipton’s ‘reformulation’ seems to be just what I meant, so I’m glad you approve of it! Maybe what disagreement remains between us can be illustrated by a branching conversation. Student: Why did the photon get stopped by the polarizer? Lewis, Hitchcock, and everyone else you mention: Well, given the previous history, it had some chance of getting stopped and some chance of going through – and it just happened to get stopped. Student: Yes, I know that. But why did it get stopped rather than going through?  

Lewis: There’s nothing more to say.

Hitchcock: The way the polarizer was set, the photon had a much higher chance of getting stopped than of going through. Student: Yes, I know that. But why did the more probable thing happen rather than the less? Hitchcock: There’s nothing more to say.

I really want to insist that we reach ‘nothing more to say’ in the end, but I don’t think you disagree with that. I just think you delay reaching it by first giving information that isn’t really information about how the effect was caused, though indeed it’s

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113.  To James Coley, 21 October 1999

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information that (had it not been stale news) well might have been of interest to the student. Yours, David c: Laurie

113.  To James Coley, 21 October 1999 [Princeton, NJ] Dear James Coley, I assume that in your letter you wish to mean what I, and various others, have meant by ‘truthmaker’. If you wished to mean something new and different it would of course be up to you to decide what you meant, and you well might decide to mean something on which it’s a non-trivial truth that an unactualized possible world, say the closest P-world, in which Q is also true, is the truthmaker for the counterfactual that if it were that P, then it would be that Q. If not, and if you mean what I do by truthmaking, then what makes it true at this world that if P then it would be that Q is whatever feature of this world makes this world resemble W more than it resembles any other P-world. This could be something about the thisworldly laws of nature, or the thisworldly past history, or both. Call these L and H. But it wouldn’t be the existence of W. Strictly speaking, W doesn’t exist at all in this world, so can’t be a truthmaker in this world for anything. But we needn’t be so strict. It might be, or it might not, that W exists in the sense of having a counterpart Wʹ here. If there is no such counterpart, again there’s no way for W to be a thisworldly truthmaker. But even if it did, Wʹ would not be a truthmaker for the counterfactual. It is not so that necessarily, if Wʹ exists, then the counterfactual is true. If we have H and L, we have the counterfactual even without Wʹ. If we don’t have H and L, we may not have the counterfactual even with Wʹ. Now you might think (though this would be a departure from what I meant by truthmaking) that it is the otherworldly existence of W, never mind whether it has a thisworldly counterpart, that makes the counterfactual true. Well, under this conception of what it means to say that another world exists, it will be necessary that if W exists, then ---, where --- is any necessary truth whatsoever. And it will be necessary that if H and L exist here in this world, and also W exists elsewhere in logical space, then the counterfactual is true. But this is trivial: the same would be true if we replaced

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W by any other world whatsoever, or if we left it out altogether. It’s H and L that do the work. W is just going along for the ride. Sincerely, David Lewis

114.  To Peter Godfrey-Smith, 3 December 1999 [Princeton, NJ] Dear Peter, Has my metaphilosophy changed? How come I find Jonathan Schaffer’s Merlin-and-Morgana story a convincing counterexample? Well, here’s what I’d say now. I think it fits the letter but maybe not the spirit of those earlier lines of mine that you quoted with approval: ‘far-fetched cases . . . go against what we take to be the ways of this world; they violate the presuppositions of our habits of thought’.1 (Emphasis added.) We find ourselves disposed to classify possible cases: as cases of causation or not, as cases of knowledge or not, or what have you. Sometimes we’re disposed to classify confidently, sometimes only hesitantly, sometimes not at all. The main desideratum for an analysis is to fit our dispositions to classify confidently. (If it can also explain dispositions to hesitancy, so much the better.) Confident classifications are where we find them. Still, we’re more often disposed to make confident classifications of cases that fit our preconceptions of how the real world is, or how it might have been. So far-fetched fantasies are likely to yield cases we can’t classify confidently, therefore cases that are not good test cases for an analysis. But our dispositions to classify grew up ori­gin­ al­ly on the basis of a naive conception of the world, not on the basis of our best scientific knowledge. So it may happen that real-world examples, say from quantum mechanics, violate the presuppositions of our habits of thought; and it may happen that some overtly magical examples do not. Yours, David Lewis c: Schaffer   ‘Postscripts to “Causation” ’ (Lewis 1986d, 203).

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115.  To Daniel Dennett, 26 June 2000

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115.  To Daniel Dennett, 26 June 2000 [Princeton, NJ] Dear Dan, Thank you and Christopher Taylor for your ‘Who’s Afraid of Determinism’.1 I think I agree with the two of you pretty completely. But instead of doing running comments on your paper (time is short, this is my first day back in my office after about 11 days in hospital) let me tell it my way, and you can compare. Austin can sink his putt iff no obstacle prevents him. An obstacle is a state of affairs nomologically incompatible with success – but by no means every such state of affairs is an obstacle. Handcuffs would be an obstacle. Paralysis would be an obs­ tacle. Lack of a club would be an obstacle. The ball being spiked to the ground would be an obstacle. A compulsion to fail would be an obstacle. Maybe trying too hard to succeed would be an obstacle (so it may be false that he can do it iff he’d succeed if he tried). Preferring not to is not an obstacle. A combination of micro-causes which together predetermine failure is not an obstacle. In general it’s not true that a world with an obstacle differs only in delicate, microscopic ways from one without. An obstacle is a robust sort of preventer. Yours, David Lewis

116.  To D.H. Mellor, 26 February 2001 Princeton University Princeton, NJ Thank you for ‘For Facts as Causes and Effects’.1 I’ve read it with interest, and with more agreement than I might have expected. Once the ‘facts’ that are truthmakers are distinguished from the ‘facts’ that are just the truths themselves, and once you draw the conclusion that sometimes there is causation without causal relata, some of my resistance to causation between facts evaporates.   (Taylor and Dennett 2002).

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  (Mellor 2004).

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Our disagreement over transitivity remains, of course. It’s ironic that the ex­amples of which you say ‘no one really believes that the first causes the last’ are exactly the sort of examples that convinced me that causation was transitive! (Indeed, ‘for want of a nail’ is one of the examples I had in mind.) I draw the predictable conclusion that most of your surviving ‘connotations’ are features not of causation in general but of the kind of causation that is easiest and most useful for us to know about. I wonder what’s going on here? I think that you, and others who confidently reject causation via long and unforeseeable chains (for instance, Gil Harman), are within your legitimate rights. And I think I am too. That suggests an ambiguity. But I’ve never come across anyone, except maybe myself, who wants to say that in one sense these are cases of causation and in another sense not. Two small matters. (1) You quote me about the deadly void; whereas I borrowed it, with citation, from C.B. Martin. I think he should get a mention; not on general principles, but because he can be touchy about such things. Indeed, I think quotations directly from Martin might serve your purpose at least as well as quotations from me: suppose . . . a void is travelling toward Alfred. He would, rightly, fear for his very life . . . It seems that the void has . . . terrible causal powers. (AJP 74 (1996): 62).2 (2) How old is Lowe? I was surprised to see him cited as the source of ‘for want of a nail’, which I knew in childhood. Yours, David

117.  To Jonathan Bennett, 26 February 2001 Princeton University Princeton, NJ Dear Jonathan, I’m sorry; it’s taken me much too long to get around to your letter of 29 December! I fear you may have thought I’d accepted your invitation to ‘please feel free to leave [the pages] unread’.1 Part of the problem was that I thought I’d answer it   ‘How It Is: Entities, Absences and Voids’ (Martin 1996b).

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1   The pages are selections from a draft of A Philosophical Guide to Conditionals (Bennett 2003). The two selections discussed below relate to pages 153–5 and 288–301 respectively.

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117.  To Jonathan Bennett, 26 February 2001

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all at once, and that would be a big job. I’m afraid I’m going to put off the first part, the part about robustness, a bit longer: it’s tricky stuff, I haven’t thought at all about it for a long time, and there’s a limit to how many things I can have on my mind at once. But I’ll take up the second and third parts now. First, a little about the second part, pages 111–12 – a little, because a little is all I can add to what I said in Plurality. --To your ‘expansion of Lewis’s remarks’ I say that it isn’t far off, but it somewhat runs together different questions. (1) Should one’s moral thinking be biased in favour of one’s worldmates, and should it likewise be biased in favour of one’s conspecifics, one’s contemporaries, one’s compatriots, or one’s relatives? No, in all cases. One should judge good and evil accurately for what they are, wherever in space or in time or in the pluriverse they may be located. (2) Should one’s moral feelings be biased in favour of one’s worldmates, and should they likewise be biased in favour of one’s conspecifics . . . or one’s relatives? If ‘feelings’ mean judgements, no in all cases, as I just said. But if ‘feelings’ mean emotional responses – say, joy or sorrow – evoked by goods or evils, then yes in all cases. The more remote the goods or evils are, and the less we could possibly do about them, the less we ought to heed them and the less we ought to respond emotionally to them. (3) Should one’s moral choices be biased in favour of one’s worldmates, and should they likewise be biased in favour of one’s conspecifics . . . or one’s relatives? Yes, but to a limited extent, in all cases where the issue arises; that is, in all cases where one has the opportunity to benefit someone at someone else’s expense. But in some cases the issue never arises. Just as one never has the opportunity to benefit past people at the expense of present people (though a time traveler might be able to affect which are past and which present), so likewise one never has the opportunity to benefit people in one world at the expense of those in another (though one often has the opportunity to affect which are actual and which not). So when I separate the questions, I say that one sort of bias is impermissible; another sort is permissible, but the difference between bias in favour of worldmates and other parallel biases is one of degree; yet another sort of bias in favour of worldmates concerns an issue that cannot arise. Something different. Can we describe, compare, and contrast possible worlds as well with abstract states of affairs as with agglomerations of space and rock? I think not. We are not describing, comparing, or contrasting the abstract objects themselves. We are describing, comparing, or contrasting the agglomerations of space and rock that exist according to these abstract objects.

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Now, on to the third part, pages 212–24. That has the advantage of being about something that’s been on my mind recently, and also it’s the part you especially wanted to get my reaction to. Before getting on to the main business, I’ll comment on your Stevenson example. ‘If Stevenson had been president, he would have been elected’. Maybe; there are other ways it might have happened, as it did with Bush. I don’t really know whether an honest election or a coup requires the lesser or the later divergence miracle. As you say, it’s a backtracker that works (under determinism), not by special standards of comparative similarity but because a small divergence miracle requires a long ramp. Anyway, I say as you expected that this is not one of the counterfactuals that matter to the asymmetry of openness or to the asymmetry of causation. You’re right that the line I take about causal relata and the line I take about time’s arrow are connected. And there’s a sore spot: I say there is causation by absences, and I want to say that causation by absences has the same asymmetry as other causation. But I do not (now) say that absences are events. (But neither do I say that causation by absences is causation by facts. Rather, I say that sometimes there is causation with no causal relata at all.) So I don’t see how my usual reason for being unworried by this kind of backtracker applies to causation by absences. --Now for the main business of this letter. We’re considering your 1984 ex­ample2 about three worlds, W0 (alias alpha), W1, and W2. I won’t yet say which one is actual. But I will suppose that W0 is ‘a world like ours’, whatever that means. W1 has a small miracle, at a time we’ll call ‘the present’; W0 and W2 are perfectly lawful. That is to say, they obey the actual laws, which are the laws of W0 and W2 and the almost-laws of W1. Because of its miracle, W1 must not be actual. I assume these laws are invariant under time-reversal: the reversed mirror image of any lawful process is itself lawful. I also assume that the laws are deterministic. Therefore the laws are two-way deterministic, so that either divergence or convergence takes a miracle in one or the other of the two worlds involved. (Seriously proposed deterministic theories normally are two-way deterministic.) Thanks to its small miracle, W1 diverges from W0 and converges to W2. W1 and W0 are exactly alike throughout the past. Likewise W1 and W2 are exactly alike throughout the future. We know there is such a world as W2 because we can take the future history of W1 and run it backward in accordance with the laws. This settles that there can be convergence at the cost of a small miracle. The ‘asymmetry of miracles’ is not an exceptionless feature of lawful worlds. No worries: I didn’t say it was an exceptionless feature, I said it was a feature of worlds like ours. In my 1986 postscript3 on Bennett worlds, I say that W2, though   ‘Counterfactuals and Temporal Direction’ (Bennett 1984).   ‘Postscripts to “Counterfactual Dependence and Time’s Arrow” ’ (Lewis 1986d, 52–66).

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lawful, is not a world like ours because it is deceptive in a way that W0 is not. Why so? W1 diverges from W0; the miracle that allows W1 and W0 to diverge is localized, so most of the near-future records to be found in W1 are very like those to be found in W0; W0 is ex hypothesi a world like ours; W0 is non-deceptive, so the records to be found in W0 justify accurate partial retrodiction of the past of W0; so most of the near-future records to be found in W1 likewise justify partial retrodiction of the past of W0. And such retrodiction is accurate, since W1 and W0 are alike in the past, so W1 also is non-deceptive. Now, W1 and W2 are alike throughout the future; so the future records in W2 are just like those in W1; so the near-future records in W2 also justify partial retrodiction of the past of W0. But we have no reason to think the past of W2 is anything like the past of W0. (Later I’ll give a rather weak reason to think not.) If not, the near future of W2 deceives us about its past. (Why near-future? After a while, the small divergence miracle has big, widespread effects. In Kit Fine’s example, W1 differs from W0 by having a nuclear holocaust starting about fifteen minutes after the divergence miracle – that’s how long it takes the intermediate-range missiles to hit their targets. A nuclear holocaust destroys lots of records, so afterward the state of W1 justifies much less retrodiction.) At this point you disagree. I said that W2 is deceptive about its past and W1 is not; you say it’s the other way round. Your reason is that the future state of W2 lawfully implies the past of W2, and so is not deceptive; whereas the future state of W1, being exactly the same as the future state of W2, likewise lawfully implies the past of W2 rather than the past of W1, and so is deceptive. Well, deceptive to whom? To a Laplacean demon, with unlimited powers of observing the most minute detail and unlimited powers of calculation? Or to the likes of us, who retrodict fallibly on the basis of limited information and limited powers of calculation? To the Laplacean demon, W1 is indeed deceptive and W2 is not, for exactly the reason you say. For the likes of us it’s the other way round, as I argued above. Neither of us is mistaken. But it was deceptiveness to the likes of us that I meant when I said that W2 was deceptive in a way W0 was not, and therefore was not a world like ours. The traces to be found (by the likes of us) in W2 are such as to record a past exactly like that of W0. Now, if ‘recording a past’ meant that those traces couldn’t possibly have been produced except by such a past, what I’ve just said would indeed be a mistake. But it doesn’t have to mean that (though I suppose it might). Some Christians say that to try our faith, God in 4004 BC created a world containing a false fossil record of an unreal past going back hundreds of millions of years. Those traces could have been produced otherwise than by the past they record – ex hypothesi they were – but what they record is their purported history, not their real history. Not for nothing is this allegedly deceptive feature of the world called a fossil record.

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Now, how does this discussion of the asymmetry of traces and of miracles bear on the asymmetry of counterfactual dependence? Suppose that W2 is the actual world. (That’s the case I had in mind in my 1986 postscript. I thought then that it was the case you had in mind in your 1984 paper, but on re-reading I’m less sure.) What if it had been that W1 Ú W0? W1 matches the actual world W2 perfectly throughout half of history at the cost of a small miracle; W0 has neither the match nor the mir­ acle. By the standards of CFD&TA4 that means that W1 is closer to W2 than W0 is. So if it had been that W1 Ú W0, it would have been that W1. So if (the vicinity of) the present had been different, the future would have been the same and the past would have been different. So the asymmetry of counterfactual dependence also goes haywire at W2. No worries: W2 is not a world like ours, and the asymmetry of counterfactual dependence also was only said to be a feature of worlds like ours. If you lived in W2, you’d be deceived into thinking you lived in W0; so you’d think that if it had been that W1 Ú W0, it would have been that W0. And you’d think that if it had been that W1 Ú W2, it would have been that W1. And you’d have been wrong about both of these. But it figures that if you live in a deceptive world, you’ll be wrong about which counterfactuals are true. We shouldn’t ask an analysis of counterfactuals to agree with our judgements even if we live in a deceptive world. So far, no trouble for CFD&TA. But trouble is not far away. For years I didn’t see it. I think Hartry Field tried to tell me about it a few years ago, but unfortunately I didn’t understand him at the time. What convinced me was a recent paper by Adam Elga (graduate student at MIT, joining our department next fall): ‘Statistical Mechanics and the Asymmetry of Counterfactual Dependence’, forthcoming in Philosophy of Science.5 To see what the trouble is, let’s look more closely at the deceptive world W2. How can it be that W2 fakes the records of a past like that of W0 without benefit of a miracle, even a small miracle? (Fakes the records well enough to fool the likes of us, though not well enough to fool a Laplacean demon.) Well, there are two known ways to fake traces, and the trouble with CFD&TA is that I only considered one of them. One way to fake records, the brute force way, the way I did consider, is by a big, widespread miracle that alters traces of lots of different kinds in lots of different places. (Or, if it gets in quicker, maybe it blocks traces of many kinds in many different ways right at their origin.) That’s not how W2 fakes the records. There must be another way. There is. Another way to fake records is through counter-entropic processes: that is to say, lawful processes in which the ‘law’ of increasing entropy is violated. It’s because such processes are only very scarce (hereabouts), not unlawful, that the ‘law’ of increasing entropy is only an almost-law, not really a law. What goes on in Popper’s  (Lewis 1979b).   5  (Elga 2001).

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pond is an example both of decreasing entropy and of deception. Vibrations in the earth near the edge of the pond are remarkably coordinated, in such a way that they start ripples which in turn are remarkably coordinated, in such a way that the ripples converge at the center of the pond, pick up a stone that’s lying on the bottom, toss it out of the pond, and leave the surface of the pond completely calm. (And that’s less than the half of it. There are also remarkably coordinated sound and light patterns coming in, and there are remarkably coordinated neural firings in the brain of the chap standing by the pond in whose hand the stone ends up, and . . . .) The state of the pond at the moment the stone is tossed out is a lower-entropy state than the previous state of the pond; and the smooth surface of the pond is deceptive, since it looks for all the world (to anybody less acute than a Laplacean demon) just as if the pond had been calm all along, with no funny business going on. Here’s another example, chosen to show the connection with thermodynamics. All there is to the world is a big impenetrable spherical shell with some gas inside. (And somehow there are observers who can observe the gas without causally interacting with it. Don’t ask me how.) At present the gas is not uniform. The gas near the center of the sphere is very hot, the rest is very cold. The likes of us read that as a record of some sort of recent event, we know not what, that released a lot of heat at the center of the sphere. But that’s not what really happened. For a very long time, the gas was near enough uniform. Nothing much was happening, at least on a macro­ scop­ic scale. On a microscopic scale, of course, the molecules were constantly zipping around and colliding with one another. But it so happened that the motions of the molecules were coordinated in just such a way as to produce the concentration of heat that we now observe. That was a counter-entropic process: the entropy of the non-uniform state is lower than the entropy of the uniform state. It was a lawful process: it is the time-reversal of the unquestionably lawful process by which the non-uniform gas will subsequently turn into higher-entropy uniform gas, and we’ve assumed the laws are time-symmetric. And, as already noted, it produced a deceptive record. Deceptive to the likes of us, I mean; not to a Laplacean demon, who can observe the most minute details of the molecular motion and run the laws backward to find out what really happened. In both cases, Popper’s pond and the gas, the counter-entropic history of the present state is very different, in macroscopic as well as microscopic ways, from the normal history that the likes of us would have mistakenly retrodicted on the basis of our limited information. I should think – I’d like to have a general argument rather than just a couple of typical examples – that this is a general feature of counterentropic fakery. I should also think that counter-entropic fakery is the only alternative to brute-force big miracles as a way of faking traces. My only reason is that I can’t think of any third way and I’ve never heard of one.

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Now let’s get back to W2. W2 has faked records – deceptive to the likes of us, though not to the Laplacean demon. They weren’t produced by any sort of miracle. The only other known way to produce them is by a highly deceptive counter-entropic process, starting with exactly the right coordinated pattern of minute details. I conclude, modulo the unproven points noted in the previous paragraph, that W2 must be an instance of counter-entropic fakery. It’s what I’ll call a C-N world, meaning that it has a counter-entropic (near) past followed by a normal future. For the future of W2 matches the future of W1; the future of W1 is normal, since it’s the sort of future we think would have followed if there had been some slight difference from W0 in the vicinity of the present, and we think that what would have followed is a normal future, not a bizarre counter-entropic future. Picture the legible part of the near-future state common to W2 and W1 as a small circle. For the Laplacean demon, that circle would contract to a point, but for us it’s a good deal bigger. Picture a truncated cone extending backward from that circle, fairly narrow in the recent past and wider as it goes farther back. The great majority of lawful histories that pass through the circle lie within that cone. W0 is one of that great majority. W1 isn’t, though it does lie within the cone, because it isn’t a lawful history at all. W2 isn’t, though it is a lawful history, because it doesn’t fall within the cone. It’s one of the small minority of lawful histories that come from far away and nevertheless manage to swerve into the circle. The cone contains the his­ tor­ies that conform to what we, fallibly and with limited accuracy, retrodict. That’s how W2 is deceptive and W1 is not – for the likes of us. For the Laplacean demon, nothing is illegible. The circle contracts to a point. The only lawful history that passes through it is W2. What he retrodicts can and does fall outside the cone. So for him, W1 is deceptive and W2 is not – which is what I said before. W1 is what I’ll call an N-M-N world: normal past, small miracle, normal future. So what we have is that a C-N world can converge to an N-M-N world. Now if two worlds can converge at the cost of a small miracle, why should it matter which world has the miracle? It seems – and this is what Elga argues much more fully – that an N-N world and a C-M-N world could equally well converge at the cost of a small miracle. W0 is an N-N world; let it be actual (contrary to our earlier supposition that W2 was actual). Suppose we do indeed have a C-M-N world, call it W3, that converges to W0 at the cost of a small miracle, and that closely resembles W0 in the vicinity of the present. Now, if it had been that W1 Ú W3, which would it have been? W1 matches W0 throughout the past and diverges from it at the cost of a small mir­ acle; W3 matches W0 throughout the future and converges to it at the cost of a small miracle. By the standards of CFD&TA, W1 and W3 are equally close to W0. So by the standards of CFD&TA it’s not true that if it had been that W1 Ú W3, it would have been W1. It might just as well have been W3. But that’s not what we think: we think

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it would have been that W1. Since W0 is not deceptive, a correct analysis needs to agree with us about what counterfactuals are true there. So CFD&TA is refuted. But I hope it’s easy to fix. W3 is deceptive, just as W2 is, because of its counterentropic past. W1 and W0 are not. So what we need to tilt the balance of comparative similarity in favour of W1 and away from W3 is to give weight not only to the respects of similarity I mentioned in CFD&TA, but also to similarity in respect of non-deceptiveness. That’s the correction I favour. Now we get the right answer: what’s true at W0 is that if it had been that W1 Ú W3 it would have been that W1. Someone might worry that the non-deceptiveness that matters is nondeceptiveness about the past, so that time-order is now built into my standards of similarity. I don’t want that, because I want to leave it open that there might be exceptional cases in which the past depends counterfactually on the future; and because I want it to be a substantive thesis that causation goes predominantly from past to future. Or someone might worry that the nondeceptiveness that matters is non-deceptiveness about the causes, rather than about the effects, of present events. I don’t want that, because I want a counterfactual analysis of causation not to be circular. My reply to both these worries is that W3 is much more deceptive about the past than W1 is about either half of history. At the end of CFD&TA, I said with regret that I didn’t know how to connect the several asymmetries I’d been discussing with the famous asymmetry of entropy. Some people have thought I was hinting that my asymmetries were independent of the asymmetry of entropy. But no – I meant what I said. I thought that probably there was a connection, I just didn’t understand it. Now, thanks to Elga, I think I do. Yours, c (part): Adam Elga

118.  To Jonathan Bennett, 6 June 2001 Princeton University Princeton, NJ Dear Jonathan, This is a belated reply to your letter of 13 March. I’m sorry about the delay. Your quotations from my letter are OK with me. [. . .] ‘. . . if it’s right to hold that two lawful worlds that are slightly unalike at T are increasingly unalike as we move further back into their pasts’. That’s what I believe, but with two qualifications. (1) At some distance back into their pasts, they might

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already be so different that we couldn’t find any greater difference by looking further back. (2) Maybe if their difference at T is infinitesimal, their difference throughout the past could be infinitesimal too. That’s a case Elga raised in his 23 April letter to me, with copy to you; I agree with him about it in the attached letter. Here’s why I think worlds couldn’t differ negligibly throughout all past time and then suddenly diverge (without a miracle). The world as we know it – other possible worlds are different, for instance a world you might meet in an example, where there are only two particles in the void – is full of amplifiers: things that turn little differences into much bigger differences. For want of a nail . . . the kingdom was lost. If two people hadn’t happened to meet a few hundred years ago, none of the people who actually live now would have lived. And so on, and so forth. I can’t believe that two worlds dodge all the amplifiers for billions of years and then finally hit one! There are mufflers too: things that turn big differences into littler differences. – Yes; but these generally muffle differences in only one respect, so they do not do enough to counteract the amplifiers. So I think that histories that are only slightly (but more than infinitesimally) different at one time will usually, in worlds like ours, be much more different at nottoo-very-much-later times. I expect that’s a consequence – maybe even an equivalent formulation? – of increasing entropy, but I don’t know enough to show that it is. Could a small divergence miracle be undone by a small convergence miracle if it came soon enough? A photon hits a photocell, and one nanosecond later the causal chain starting from that hit is snapped. ‘That is not enough time for many other effects to radiate out from the impingement of the photon, requiring to be stuffed back into the bag if perfect reconvergence is to be achieved’. Well, they won’t radiate out very far: a light-nanosecond is just under a foot. But they’ll be varied, and they’ll have had time to become more varied by impinging on other things – even empty spacetime, if that’s all there is – within that 1-foot radius sphere. The reconvergence mir­acle doesn’t need to be very spread out spatially, but it does have to be multifarious. Better make the interval still smaller . . . But the smaller you make it, the less clear it is that the event mentioned in your antecedent has really had enough time to happen at all. Probably the best move is to make the reconvergence miracle simultaneous with the hit: it’s a special supernatural kind of hit that doesn’t even start to radiate traces. Then did the photon really hit the photocell? Or did it just vanish the moment before it would otherwise have hit? The part of your revised text corresponding to page 4, lines 8–9, of your letter probably ought to read ‘And from T onwards w1 is indiscernible from w2’. We’re off to Cambridge, Canberra, Hobart, and Melbourne in a few days – that’s why I’m catching up on letters. Back here mid-July. Yours, c: Elga

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119.  To Adam Elga, 6 June 2001 Princeton University Princeton, NJ Dear Adam, This is a belated reply to your letter of 23 April. The really tiny miracle. OK, this is a third way to get convergence, with only a small miracle and no counter-entropic fakery. The reason it works is that there’s no lower bound on how small a present difference it takes to make your antecedent true. So we don’t face the question how it’s possible for two worlds that have been only negligibly different throughout history to suddenly diverge in a non-negligible way. (Still, I’d like to understand Belot’s argument that the existence of such pairs of histories follows from continuity of the dynamical laws.) But I don’t think it should worry me. The object of the exercise is to predict the right truth values (in non-deceptive conditions) for the counterfactuals people really do have opinions about, and in particular for the ones that enter into a counterfactual analysis of causation. The supposition ‘If the position of the particle had been different by any non-zero amount whatever . . .’ is not such a counterfactual. (‘And we certainly do not want counterfactuals saying that if a certain event had not occurred, a barely different event would have taken its place. They sound false; and they would make trouble for a counterfactual analysis of caus­ ation . . . quite generally’ [Φ Papers II, p. 211]. ‘When asked to suppose counterfactually that C does not occur . . . we imagine that C is completely and cleanly excised from history, leaving behind no fragment or approximation of itself’ [‘Causation as Influence’, JΦ version, p. 190].1 The need for such a stipulation was pointed out by Bennett.) Gold worlds. The Gold world is deceptive. Not to a Laplacean demon; maybe not to a cosmologist who has come up with a theoretical case for it. But certainly to the or­din­ary folks whose opinions in non-deceptive conditions we’re trying to predict correctly. Loewer’s ‘laws’. I want to insist that a law, rightly so called, should be a universal generalisation, preferably about what follows what (where a differential equation can be a limiting case). But that’s just a terminological dispute. I’d be willing to agree that if boundary conditions figure as axioms in the best theory, as I agree might   (Lewis 2000a).

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happen, then they should share at least some of the privileges of laws: in particular, they should be held fixed (or almost fixed) at all (or almost all) costs in evaluating counterfactual suppositions about what would happen if something were different later on in history. See you here soon. We’re off very soon to England and Aus; back in mid-July. Anna didn’t know when you were arriving. Yours, c: Bennett

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PART 2 Modality

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120.  To Jerome A. Shaffer, 17 October 1965 [Cambridge, MA] Dear Jerry, Thank you for the copy of ‘Persons and Their Bodies’.1 As you expected, I can’t swallow such a line, so I had to look it in the mouth to find a way out. (Dig the metaphors!) Thus – Let’s say mental event E (at time T) happened to person P who either occupied or was body B. You say, and I agree, that E could not have happened to any person other than P. You say, and I still agree, that some person other than P, call him Pʹ, might have occupied or been body B (at time T). You infer that if event E happened to body B, then E might have happened to (the body of) Pʹ, contrary to the first premise. I don’t accept this inference. I agree that if a scratch happens to body B, that scratch could not have happened to any body other than B.  But I think it’s different for a mental event: E might have happened to a body other than B, call it Bʹ, if P had occupied or been Bʹ (at time T), and E could not have happened to B itself if Pʹ had occupied or been B (at time T). That is, I think your proof turns on a false third premise: an event which happens to a body must happen to just that body if it happens at all. The premise is true for scratches, but false for mental events which happen to those bodies which are persons. Event-identity cannot be covered by both person-identity and b ­ ody-identity because person-identity and body-identity can diverge; ordinarily event-identity is governed by body-identity, but in the case of mental events considered as such, event-identity is governed by person-identity. (In the case of mental events which are neural or ectoplasmic events, I take it there are two different relations of ­event-identity, just as in the case of chunks of water which are rivers or in the case of bodies which are persons there are two relations of identity.) The relations I have been calling relations of identity are not the relation of strict identity. Nor are they the relation of identity through time, i.e. the relation which different time-slices of one temporally extended object bear to one another. Rather, they are cases of the relation which something in one (actual or) possible world bears to its counterpart (under some definite correlation) in another. It is because there are different possible worlds that there are different relations of identity. Rephrasing the premise I am contesting in terms I would prefer: you are claiming that if event E happens to body B in a possible world W (viz. the actual world),

  (Shaffer 1966).

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and event Eʹ happens to body Bʹ in possible world Wʹ, then if Eʹ is to be the eventcounterpart of E, Bʹ must be the counterpart of B. I claim that Eʹ may be the mentalevent-counterpart of E although Bʹ is not the body-counterpart of B, in case Bʹ is the person-counterpart of B. For your multiplicity of entities I wish to substitute a multiplicity of counterpart-relations correlating the parts of different possible worlds. Here I am applying an idea I believe is due to Hintikka, though he mainly discusses it in an obscure Scandinavian journal I haven’t been able to find.2 (Though also briefly in Knowledge and Belief.)3 He calls it referential multiplicity; i.e. a referring expression refers at once to something and to all its counterparts in all those possible worlds in which it has counterparts. The idea is that there are two conceptual ingredients in quantified modal logic (i.e. in the notion of modal properties of things – just things, not things-qua-…): there is consistency, i.e. possibility of completely described worlds, and there is the (or, some salient) counterpart relation. Thus X has the property of being possibly P if some possible world includes something Xʹ which is a counterpart of X and which is P; X has the property of being necessarily P if every counterpart Xʹ of X, in every possible world in which X has any counterpart, is P. The uneasiness we feel about modal properties reflects the openness and cluster-character of the counterpart relation. But insofar as there is some one definite salient counterpart relation, there is a clear sense to what Quine calls ‘Essentialism’, which, as he argues, is required to interpret quantified modal logic. Maybe we can replace all this talk about parts of possible worlds by talk about definite descriptions occurring in maximal consistent sets of sentences; if so all the better, but that’s a somewhat different issue. Enough philosophy. I’m sorry I used your present for a target. Things are going very well for us, though we’re kept busy. I’m supposed to be working on my thesis, and I’ll get down to work on it almost any day now. Unfortunately there are some interesting courses which require work that I can ill afford. We have a stack of grad. school forms for Steffi, so that whenever I hear about a job at __ she can apply to the grad. school at __ or next door the next day. I hope, however, that we can stay here; Harvard’s good, and Harvard plus MIT plus Brandeis is unbeatable. I assume we’ll see you at the A.P.A.; I suppose you have to attend on behalf of your Council. Is there any chance you’ll be up here? Best wishes, David Lewis

  ‘Modality as Referential Multiplicity’ (Hintikka 1957).   

2

  (Hintikka 1962).

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121.  To Dagfinn Føllesdal, 6 March 1966

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121.  To Dagfinn Føllesdal, 6 March 19661 Irving Terrace Cambridge, MA Dear Professor Føllesdal, I have been spending some of my time recently working on a way of treating the modal operators, and I would be very interested and grateful to hear any reactions you might have. The idea was suggested to me by some informal discussion in a paper Saul Kripke wrote for a seminar his senior year;2 but it turns out that I took a somewhat different turn from Kripke (at least from his ‘Semantical Considerations on Modal Logic’ in Acta Philosophica Fennica fasc. 16 (1963), which is the only one of his papers I’ve read carefully). My treatment is of the same family as yours, Kripke’s, Hintikka’s, and Kanger’s, but I hope it may differ from them somewhat. Suppose we have a formalized language Lc, based on standard quantification theory with identity and without eliminable singular terms, in which the variables are taken to range over a universe including many possible worlds and the things in them. We need not say that everything is in some world – perhaps God, numbers, universals, sets with elements in several worlds, wholes with parts in several worlds, or worlds themselves might best be taken as not in every world. However – contra Kripke – things are in at most one world. And there is a world which contains just those things which are in the actual world. So Lc contains these three predicates – Wx . . . . . . . . . x is a possible world x in y . . . . . . . x is something in world y; world y contains x Ax . . . . . . . . . . x is something in the actual world governed by at least these postulates – x in y ⊃ Wy x in y & x in z .⊃ y = z ( $x )[ Wx &("y ) ( y in x º Ay )].

Nothing is in more than one world. But in place of saying that something in one world is strictly identical to something in another world, we may say that one is a counterpart of the other. This is to say, roughly, that the two are similar in content and context to a high degree in important respects. So Lc contains another predicate – x C y . . . . . x is a counterpart in x’s world of y in y’s world   From the W.V. Quine Papers, MS Am 2587 (644), Houghton Library, Harvard University. Courtesy of Houghton Library, Harvard University. 2   1961–2. ‘Quantified Modality and Essentialism’. Recently published: (Kripke 2017). 1

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governed by at least these postulates – x C y ⊃. (∃z) (x in z) & (∃w) (y in w) x in z & y in z. ⊃. x C y ≡ x = y by which only things in worlds are or have counterparts and anything in a world is its own unique counterpart in that world. For the sake of generality, let us not postulate that the counterpart relation is symmetric or transitive; nor that everything in a world has a unique counterpart in any other world; nor that everything in a world is the unique counterpart in that world of something in any other world. We may give the name counterpart theory to the apparatus just described; Lc is thus an arbitrary formalized language containing counterpart theory. Before going on, let us define some abbreviations – ȼxy ……… (℩z)(z in x & z C y); the unique counterpart of y in world x Eȼxy …….. ( ∃w)(w = ȼxy); y has a unique counterpart in world x @ ………... (℩x)[Wx & ( ∀y ) (y in x ≡  Ay)]; the actual world (existence and uniqueness of @ are guaranteed) (∀x: Φx) … (∀x)(Φx ⊃ __); for every x such that Φx, ___ ( $x: Fx ) ¼( $x )( Fx & __); for some x such that Φx, ___. Now suppose we have a second formalized language Lm which contains the modal operators □ and ◇. Let variables in Lm range only over things in the actual world; and let Lm not contain the four predicates of counterpart theory. Otherwise, let Lm be like Lc. I claim that the translation scheme from Lm to Lc which I am about to describe preserves our intended interpretation of the modal operators in Lm. Given a modal-free sentence Φ (closed) or Φy1 . . . yn (open), the sentence obtained from it by replacing all unrestricted quantifiers by corresponding restricted quantifiers of the form (∀x: x in w) or (∃x: x in w) – its restriction to world w – may be written as Φw or Φwy1 . . . yn. To translate from Lm to Lc, start by repeatedly applying the following substitutions, which remove innermost modal operators – i.e. modal operators whose scopes do not contain other modal operators. At every step, let w be a variable which does not yet occur in the sentence under translation. If Φ is a modal-free closed sentence – ___□Φ___ → ___(∀w : Ww) (Φw)___. ___◇Φ___ → ___(∃w : Ww) (Φw)___. And if Φy1 . . . yn is a modal-free open sentence with free y1 . . . yn – ___□Φy1 … yn___→___(∀w: Eȼwy1 & … & Eȼwyn) ( Φw ȼwy1 … ȼwyn)___

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121.  To Dagfinn Føllesdal, 6 March 1966

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___◇Φy1 … yn ___→___(∃w : Eȼwy1 & … & Eȼwyn) (Φw ȼwy1 … ȼwyn) ___.

(Since Eȼwy ⊃ Ww, it is unnecessary to include Ww explicitly in the restriction on the quantifier.) After all modal operators have been removed in this way, restrict any remaining quantifiers to things in the actual world by the substitution – F ® F@ . (Notice that restricted quantifiers may not be expanded by the definition above until translation of a sentence is complete; otherwise they will be restricted over again.) For instance, take the sentence ‘There must be somebody who might have been mayor but is not’. Writing ‘P’ for ‘is a person’ and ‘M’ for ‘is mayor’ we would presumably render this sentence in Lm as – □( ∃x) ( Px & ◇ Mx & ¬Mx);

That would be translated into Lc as – (∀u : Wu)(∃x : x in u)(Px & (∃v : Eȼvx) (Mȼvx) & ¬Mx) which we can read as ‘In every possible world, there is somebody whose unique counterpart in some possible world is mayor, but who is not himself mayor’. I claim that this sentence in Lc is a correct analysis of the original English sentence, and a fortiori of the corresponding sentence in Lm. It is nothing new, of course, to think of the modal operators as quantifiers over possible worlds. Kripke also suggests that they are restricted quantifiers, but for him they are restricted in a different way: to worlds ‘possible relative to’ a world under discussion in a context immediately surrounding the modal operator, rather than to worlds containing unique counterparts of the things denoted by variables free within the scope of the modal operator. (We might combine the two approaches by taking a modal operator as a quantifier over possible worlds which is restricted in both ways.) The difference is shown, for instance, in the fact that Kripke gets a coun­ter­ exam­ple to the converse Barcan formula – □(∀x) (Φx) ⊃ (∀x)□(Φx)

and, as will be seen, I do not.

Another difference between my treatment and Kripke’s is that Kripke is providing a truth-definition for known modal logics; I am providing an alternative ap­par­atus which, I claim, can take the place of modal logic. Therefore it is not essential for me that the laws for modal operators which are available as translations of theorems of counterpart theory should be those of a known modal logic – though it is, of course, an interesting question whether they are. If they are not, so much the

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worse for that system of modal logic; not, so much the worse for my translationscheme. Unfortunately, I do not have enough familiarity with systems of modal logic to make the comparisons. If we translate the controversial sentence of Lm – (∀x)(∀y)(x = y ⊃ □x = y)

we get this sentence of Lc –

(∀x : x in @) (∀y : y in @)(x = y ⊃ (∀w : Eȼwx & Eȼwy) (ȼwx = ȼwy)) which can be shown to be true. Hence the sentence of Lm ought to be an axiom or a theorem of modal logic. If we translate these four sentences of Lm – □(∀x)(Φx) . . .…. . . Necessarily everything is Φ* (∀x)□(Φx) . . .…. . . Everything is necessarily Φ □(∃x)(Φx) . . .…. . . Necessarily something is Φ (∃x)□(Φx) . . .…. . . Something is necessarily Φ

we get these four sentences of Lc – ("w : Ww )("x : x in w )( Fx )  . . .…. . .       Everything, in every possible world, is Φ (∀x : x in @)(∀w : Eȼwx)(Φȼwx) . . . . Every unique counterpart of any actual   thing is Φ ("w : Ww )( $x : x in w )( Fx )  . . .…. . .  Every possible world contains some   thing which is Φ ( ∃x : x in @)(∀w : W ȼ wx)(Φ ȼ wx). . . . There is some actual thing, every unique   counterpart of which is Φ. By considering the implications between these translations, we get the following table of implications which ought to hold in modal logic between the original four sentences in Lm –  * . . . holds if everything, in any * □(∀x)(Φx) (∀x)□(Φx) world, is the unique counterpart in its world of some actual thing. * and #  # . . . holds if every actual thing has a unique counterpart in every world. #   □(∃x)(Φx) (∃x)□(Φx) *  In this paragraph and the next, Φx is to contain no modal operators, no quantifiers, and no free variables except x; however it may have truth-functional structure.

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121.  To Dagfinn Føllesdal, 6 March 1966

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If we translate this sentence of Lm – ◇□□(∀x)(Φx) we get this sentence of Lc – ( $u : Wu )("v : Wv )("w : Ww )("x : x in w )( Fx ) in which all the modal operators except the rightmost have been translated as vacuous quantifiers. If, on the other hand, we translate this sentence of Lm – (∀x)◇□□(Φx) we get this sentence of Lc – (∀x : x in @)(∃u : Eȼux)(∀v : Eȼvȼux)(∀w : Eȼwȼvȼux)(Φȼwȼvȼux) in which the quantifiers are not vacuous. (A free variable which occurs in a sentence as an argument of a ȼ-term or within the restriction-clause of a restricted quantifier is to be treated just like any other free variable in that sentence. A ȼ-term may be the second argument of another ȼ-term.) So a string of iterated modal operators should not collapse in general, but should collapse when it governs a closed sentence. It is clear that this treatment of the modal operators involves essentialism. The essential properties of something are just those of its properties which it shares with all of its unique counterparts, in all the possible worlds in which it has a unique counterpart. I do not claim that essentialism is entirely clear; however, on my treatment the unclarity of essentialism is resolved into two distinct components. There is unclarity over the question of what worlds are possible; this is the question of what purported descriptions succeed in consistently describing worlds, and thus it runs into the usual difficulty about analyticity etc. (Plus difficulty about the distinction between empirical laws and other truths, if by possible worlds we mean physically possible worlds.) There is also an independent unclarity in our notion of the counterpart relation. We certainly have some such notion, but it is very vague. We should expect that if it can be made precise at all, it can be made precise in several incompatible and equally artificial ways (perhaps leading to different additional postulates for counterpart theory). We might tamper with counterpart theory in order to cut down the basis of primitive predicates and the ontology. If we had another predicate – x with y..x and y are in the same possible world we could use it to eliminate ‘in’ and ‘W’. If Lc contains set theory (or the calculus of individuals) we can say that a world is a maximal set (or whole) whose elements (or parts) are related pairwise by ‘with’; if so, ‘in’ would be replaced by ‘ε’ (or ‘ Cardinality (W). You say that DG is not well-founded. (You say this may be acceptable – not to me.) Why? I think you think I think that G is some sort of set-theoretic construction out of, inter alia, DG. Not so. G is an individual, not any kind of set. DG is not, and many of its members likewise are not, built into G as any kind of constituent, urelement, part, . . . Now consider the predicate ‘contains a David Lewis counterpart’. You present this predicate to me here at this world; so I assume that as it’s actually meant, it applies only to worlds that contain counterparts of the thisworldly David Lewis. Also, since your point doesn’t have to do with the vagueness of similarity and the multiplicity of counterpart relations, I hope I can fairly assume that somehow, per impossibile, we’ve fixed determinately on one definite counterpart relation. Right, now we have a subset WDL of the worlds. The members of WDL are exactly those worlds that satisfy the predicate. You say that for any Wʹ ⊆ W, there is a world where the set of things worlds(?) that satisfy the predicate is Wʹ. Not so. Once and for /all/, that set is WDL. It’s not

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176.  To Alan McMichael, [Fall 1985]

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c­ ontingent which worlds satisfy the predicate. A world satisfies that predicate (under the fixed meaning we’ve given it) at all worlds, or at none. Yours, David (July 29 until AAP week: c/o Philosophy Dept, Melbourne Uni)

176.  To Alan McMichael, [Fall 1985] Princeton University Princeton, NJ Dear Alan McMichael, This is a very tardy reply to your letter of 26 October 1984 about my paper and Peter van Inwagen’s reply at last year’s Chapel Hill conference.1 Much of your letter concerns what I call a hybrid form of ersatzism. Peter mentioned it somewhat approvingly, but I don’t think you’re right that he committed himself to it; rather, he agrees with me that it leads indirectly back to the same problem – if indeed it is a problem – that pure and simple magical ersatzism faces. In pure and simple magical ersatzism, we have abstract entities (whatever that means) with no relevant inner structure, which might be given various names; I called them elements, but someone on more friendly terms with them might call them ways for a world to be, or perhaps properties that the entire concrete world might have. A world may select, or exemplify, these entities. In hybrid ersatzism, we have maximal consistent sets of sentence-like abstract objects: parseable structures, with a recursive semantics. But the basis of the construction won’t be words; rather, in place of words we have abstract entities, with no relevant inner structure, which I would again call elements but which someone on more friendly terms with them might call ways for a thing to be, or perhaps properties that a thing might have. A thing may select, or exemplify, these entities. The truth or falsity of the sentence-like constructions is explained ultimately in terms of the selecting by things of elements that occur in the constructions, or if you prefer the exemplifying by things of properties. 1   Lewis read ‘Possibilities: Concrete Worlds or Abstract Simples?’ at the UNC-Chapel Hill Philosophy Conference, 7 October 1984. It was based on §3.4 Magical Ersatzism of On the Plurality of Worlds. Van Inwagen’s reply became ‘Two Concepts of Possible Worlds’ (van Inwagen 1986b).

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In pure magical ersatzism, we hit upon the selecting of elements right away; in hybrid ersatzism we hit upon it after a couple of steps of construction, first building up the sentence-like constructions and then collecting those into max­ imal consistent sets. Either there is or there isn’t a problem about understanding the selection of elements by things, world-sized or smaller. If there is a problem, why are we better off if we reach it after the two steps of construction, and why are we better off if we have it for things in general rather than just for world-sized things? If there isn’t a problem, why not keep life simple by by-passing the two steps of construction? (Those questions aren’t entirely rhetorical. I can think of a view that answers them as follows. In a very few special cases, cases involving for instance the fundamental physical properties of very small things, exemplification of properties is comparatively unproblematic: it’s just a matter of the presence of a certain multiply located individual at the right spatiotemporal position. If so, then we need the construction steps so as to get the complex properties of big things – worlds, say – from the few fundamental properties of little things. This leads to the view I called Lagadonian linguistic ersatzism; and the dilemma about internal vs. external selection in the Chapel Hill paper wasn’t meant to apply to that proposal. Indeed I think it’s a fairly promising one, though I fault it both for requiring primitive modality and for conflating alien possibilities (also I think there’s a less important fault about conflating indiscernible possible individuals, say in the different epochs of a world of eternal recurrence). But suppose you don’t want just a sparse few elements. Then I think it’s quite incredible to think of them being literally present within the world or lesser thing that exemplifies them. Now my dilemma gets going. You choose the second horn: selection is an external relation. Then, as you say, the issue about acquaintance with ‘representational’ properties of elements does not arise. That was an issue for those who choose the other horn. You say that my objection to the external horn may be right if it’s the whole world that selects elements – in other words, exemplifies ways for a world to be – but not if it’s lesser things that select elements – in other words, exemplify ways for lesser things to be. I don’t see why the size and abundance of the things that do the selecting should make the slightest difference. You say that my argument against the external horn (in the case where the whole world does the selecting) ‘begins with the observation that the selection relation must be necessary . . . In contrast, the exemplification relation is not necessary (except in the case of essential properties . . .)’. No. In the first place, where’s the contrast? – The whole world also has its accidents.

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176.  To Alan McMichael, [Fall 1985]

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My objection wasn’t that the selection relation is necessary, in the sense that if a world or lesser thing selects an element, then it cannot possibly not select that elem­ent. Rather, my objection was that the selecting of elements was necessarily connected with, for instance, whether the selecting world does or doesn’t consist partly of a talking donkey; or whether the selecting lesser thing does or doesn’t consist partly of diamonds. Here are two elements, with no relevant structure and no relevant differences in their intrinsic nature. One of them must be, and the other one cannot be, selected by things that consist partly of diamonds. Why is there any such constraint? Why couldn’t it have been the other way around? If there were an internal relation of selection, and the elements had relevant internal structure, my question could have an answer in terms of some sort of match of structure between the thing with the diamonds and one but not the other of the differing elements. But that was not the horn you chose. It’s no good saying that the constraint obtains because one element is the property of consisting partly of diamonds and the other one is the property of having no diamonds as parts. To answer thus is to ‘solve’ the problem by presupposing that it has been solved already. I want to know: what makes the two elements deserve those two names? --On the matter of alien possibilities. You say that the ersatzer in the simpler world can describe our world by existential quantification: it is a world where there are six extra fundamental physical properties which do thus and so. OK; he has one Ramsified description. But he doesn’t have 720 descriptions, one for each permutation of the six extra fundamental properties. I say there are 720 possibilities, not one; but there’s only one description, which describes all 720; so the doctrine that possibilities are their descriptions leads, in his case, to the conflation of 720 different possibilities. ‘He can acknowledge that any such world would have permuted relatives’ – sure he can. But how does that help him? He ought to have acknowledged that there are 720 different possibilities, and instead he says there is only one (though if it were realised, then there would be 720). He’s right about how many possibilities there would be, but that doesn’t make him any less wrong about how many there are. When the Plurality of Worlds book is out, which should be very early 1986, you’ll find some further discussion of just about everything touched on in this letter. Sincerely, David Lewis cc: Lycan, van Inwagen

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177.  To Margery Naylor, 14 January 1986 [Princeton, NJ] Dear Margery, Thank you for showing me your note.1 I agree: your parallel to my argument is indeed a reason – defeasible, perhaps, but strong – to accept impossible worlds. That is: a reason to accept some sort of entities suitable to play a theoretical role which includes getting quantified over in saying, e.g., that being blue and red is only one of countless ways the chair couldn’t have been. But the question is: shall we have genu­ ine or ersatz impossible worlds? It is easier to make ersatz impossible worlds given genuine possible worlds than it is to make ersatz possible worlds given only (what I take to be) the resources of actuality. I had two main worries about Linguistic ersatz worlds; both go away if we’re making ersatz impossible worlds given the resources of genuine possible worlds. One was the problem of alien natural properties: I think there’s reason to think there might have been natural properties alien to actuality, but no reason to think also that impossibility contains yet further natural properties alien to possibility. The other was the need for primitive modality in order to distinguish ersatz pos­ sible worlds from other linguistic constructions and in order to say what’s implicitly true according to an ersatz world; however the first job no longer needs to be done at all, and the second can be done by using the possible worlds to define modality. So the drawbacks of ersatzism in the step from actuality to possibility don’t reappear in the additional step to impossibility. Also, I deny that genuine possible worlds lead to trouble, apart from the sheer disagreement with common opinion. But genuine impossible worlds do lead to ­trouble: I don’t think you can describe what goes on in the contradictory world without simply contradicting yourself, whereas you can describe what goes on in the unactualised world without telling falsehoods. (First footnote in Section 1.2 of Plurality of Worlds – note that the point doesn’t go against ersatz impossible worlds.) So here too, for impossible worlds the balance tips in favour of ersatzism. Yours, David Lewis

  ‘A Note on David Lewis’s Realism About Possible Worlds’ (Naylor 1986).

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178.  To John Bigelow, 30 May 1986

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178.  To John Bigelow, 30 May 1986 [Princeton, NJ] Dear John, Thank you for the ‘Real Possibilities’ paper.1 I liked quite a lot along the way quite a lot, but I’m afraid I’m convinced that the main idea is too good to be true. I know just where I get off the bus. It’s something that starts happening on page 14, no worries at that point, and then blows up in my face at the top of 17. Page 14: ‘we may say that, in general, a possible combination . . ., [F, a], will entail another, [G, a], just when F contains G . . . This link . . . will be the cornerstone’. So far, so good. But the link expands when we’re not watching. And then when it reappears, at the top of 17, it’s ‘if something entails everything, then it contains everything’. No longer must the entailer and the entailed be ‘possible combinations’; indeed, if the entailer is [P & N, a] with P and N incompatible – maybe they’re the universals of positive and negative unit charge – then that exactly isn’t a possible combination. You think your opponent will be a relevantist who doesn’t believe that an inconsistency entails everything. But no; I grant you, indeed I insist, that an inconsistency entails everything; but you never showed me why that kind of entailment had to work by mereology, and I don’t believe it. Well – believe it as a hypothesis, justified by its fruits? No; because it gets in the way of standard mereology, and I hold that pretty sacred. You say with regret on 16 that you adhere to standard mereology when it comes to unrestricted composition. But look: unrestricted composition doesn’t allow you to sum together P and N and get the universe. For we may well suppose that there’s some third universal, a mereologically atomic simple universal, which is entailed neither by N nor by P. Let it be a universal Q of quark colour. Is Q part of the mereological sum of N and P? Yes, according to you. N and P are incompatible, we’re supposing; so N & P entails everything; so N & P entails Q; so Q is part of N & P. (Or: N and P are incompatible; so N & P is the universe; and anything, for instance Q, is part of the universe; so Q is part of N & P.) So Q shares a part either with N or with P, by definition of mereological sum; but Q is mereologically atomic, we have supposed, and has no parts except itself; so Q itself is part either of N or of P; in which case either N or P entails Q, contra hypothesis; which completes the reductio. Now, I have made some hypotheses here; but you remember that you offered to handle whatever modal intuitions the customer brought you, and I say it’s at least as possible that the situation with three universals might be as I supposed.   (Bigelow 1988a).

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Suppose the problem of incompatible simples goes away – we know a priori that simple universals are never incompatible – as DMA often thinks. That removes one problem for your expanded, unqualified entailment-is-containment link – at the price of forcing modal intuitions to fit the machinery. But now there’s another choice. Tractarian alternative: there are simples a priori, and enough that all else supervenes on the combination of simples. Technically workable, but again in­tu­ itions are forced to fit the machinery. Open-minded alternative: maybe we have simples, maybe not. Suppose the latter; then it’s structures all the way down, we have to do the combinatorial program of structures because what else have we got? Then there’s a new kind of entailment: the kind from combination [S, a] and [F, b] where a ≠ b, S is a structural universal involving the simpler universal F, and b is part of a. (Simplest case, DMA’s: S is the universal consisting of two different F’s.) Now, to make the expanded entailment-is-containment link work, you have to make the pictorial conception of structural universals work: S has to contain as a part the simpler universal F that it involves. On that score, you and I have an unfinished argument. Lesser matters. Page 20: the theory of possible worlds ‘does not explicitly exclude universals; but it is nominalistic in spirit’. That surprised me, as a possible world enthusiast who remains neutral about universals. As I see it, possible worlds solve one problem for one variety of nominalism: the problem that accidentally coextensive properties come out as the same class, but should still be two properties. Possible worlds also solve one problem for immanent realism: we don’t have to worry about whether to believe in uninstantiated, but instantiable, universals; there aren’t any; the ones we say are contingently uninstantiated are just the ones instantiated only off in other worlds, no worry any more than the ones instantiated in New Zealand but nowhere in Australia. So: the helping hand is extended even-handedly to both sides. Page 2: truth-making is not what it used to be, if the question ‘what is the truthmaker for this claim?’ can be paraphrased as ‘what things must there be, and how arranged, in order for this claim to be true?’ Why not ‘what things must there be, and how related . . .’, since arrangement is after all a matter of spatiotemporal relations? (I remain somewhat sympathetic to the view that maybe, in the last analysis, spatiotemporal relations are the only irreducible relations.) Or even ‘what things must there be, and how propertied . . .’ since properties are the monadic case of relations? Consider a claim which is exactly the claim that certain things are arranged (or, more generally, related, or propertied) in a certain way. The three stars are arranged in a triangle. What things must there be, and how arranged, to make that true? – the stars, arranged in a triangle. No facts required, just stars! Your real old-time true-blue truthmakerist might reckon you’re just a Melbourne ostrich after all.

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179.  To Graeme Forbes, 23 June 1986

351

Steffi and I definitely intend to be at the AAP, and I assume you’ll be there. I’ll probably turn up in Melbourne earlier in the winter as well. But maybe for only a short time, maybe without Steffi, and I don’t know quite when. Anyway, see you in August! Yours, David [. . .]

179.  To Graeme Forbes, 23 June 1986 [Princeton, NJ] Dear Professor Forbes, Thank you for the advance copy of your TLS review of Plurality . . . .1 It strikes me as a good review, in both senses: favorable, and also a good job of informing the educated but non-specialist reader what the book is and how it fits into the scene. Thank you. Comments. Page 3, lines 5–6 up. I wouldn’t quite agree with ‘same kind of explanatory fruitfulness as does the positing of unobservable entities in empirical sciences’; because the unobservable particles, fields, etc. afford causal explanations of what we observe, and the possibilia don’t. (I think of scientific explanation mainly as a matter of information about how things are caused, rather than as a matter of subsuming things under big systematic theories.) But what follows the colon gets the point right. Page 4, line 7. Not clear whether your dissatisfaction is with the ‘trouble construing apparent invocations of crossworld spatiotemporal relations’ or whether it’s with ‘the epistemological question’. If the former, are you suggesting that the counterpart-theoretic solution won’t do? If the latter, no dispute. Indeed, I wouldn’t mind if one effect of the book was to embarrass my fellow mathematical Platonists! But ‘everybody’s problem is nobody’s’ – I don’t owe an alternative epistemology for mathematics in order to say that it refutes a thoroughgoing causal theory of knowledge. Sincerely, David Lewis

  ‘World Enough and Time: On the Plurality of Worlds by David Lewis’ (Forbes 1986).

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180.  To Alvin Plantinga, 18 November 1986 [Princeton, NJ] Dear Al, Thank you for the new draft of ‘Two Concepts . . .’.1 I’ve looked at it from page 16 on (since you said the first half was little changed). Yes, I find this version more to my liking. But can it really be to your liking? Now you stake your point on the premise that it’s not just true but wholly obvious that no set is either true or false, that no set represents anything as being thus and so, that no set is believed, and so on. I say it’s nothing of the sort. Whatever may be so in general, it sure ain’t obvious that this is obvious! In Webster, ‘obvious’ means ‘easily discovered’ – can you make it easier for me to discover the obvious? By the way, what about a set of propositions? (Propositions as you conceive of them, I mean.) It seems natural to say that the set is true iff all its members are, other­ wise false; is believed by anyone who believes all its members; and represents things to be the way its members jointly represent things to be. Is this wrong? Is it wholly obvious that this is wrong? – I think this is no objection to what you intend to say, just a quibble about formulation. On my proposing of models: what you say suggests unintended models, whereas I claim to be proposing intended models. Conditionally intended, and perhaps not uniquely: we intend that such words as ‘proposition’ and ‘property’ denote entities capable of filling certain theoretical roles – roles which on my view do not include not being sets – and if there is a plurality of maximal objects, then one way our intentions can be fulfilled is that these words should denote certain sets. But if you did mean to suggest that I was proposing unintended models, that would be fair if you were again classifying my position with the aid of premises which I reject but which you find wholly obvious; for instance, the premise that no model can conform to our intentions if it makes ‘propositions’ turn out to be sets which are then classified as true or false. So my only comment is that when you discuss how to classify a theory, and what disputed premises may be used in doing so, you might do well to make it explicit that this discussion applies not only to the classification ‘realist/antirealist’ but also to the classification ‘semantical reductionist’ or ‘modelling’. I thought you might be interested in the enclosed letter from me to Barry Taylor.2 I think it demonstrates the extent to which we agree at least about the   ‘Two Concepts of Modality: Modal Realism and Modal Reductionism’ (Plantinga 1987).   Letter 283. To Barry Taylor, 5 August 1986, Volume 1: Part 3: Ontology.

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181.  To John Coker, 5 February 1987

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­ etaphilosophy, if not about what’s wholly obvious. The background is that Barry m had written a paper3 in which he quickly dismissed the view that antirealists about X’s are those who deny the existence of X’s; because ‘the most jejune antirealist phenomenalism has ready a tale explaining how the primeval forests existed in the absence of human observers’. I reply that the jejune phenomenalist may or may not deny the existence of the p.f., and he may or may not be an antirealist about the p.f., but in no case is he an antirealist about the p.f. who nevertheless asserts that the p.f. existed. Yours,

181.  To John Coker, 5 February 1987 [Princeton, NJ] Dear John Coker, Thank you for your letter and your paper. Of course there’s a lot to agree or disagree about, and I hope you’ll excuse me if I don’t comment fully. I did want to say, however, that I agree with what I found to be much the most interesting point you make: that your belief in God, maker and cause of all things, gives you a good positive reason for disbelieving in my thesis of the plurality of worlds. I don’t remember hearing this said before, but now that you say it I think it’s clearly right. What I can and do believe is that many worlds have their gods; and, in some cases, a world has a god that makes and causes all else that is part of that same world. (This is why Peter Forrest has said, correctly, that I am a polytheist.) But as many more worlds have no gods, still less gods that make or cause the rest. I believe that we inhabit a godless world (and in this sense am an atheist – I hold that among my worldmates there is no god). But at no world whatever is there any god who does the impossible. For instance, at no world is there any god who makes contra­ dic­tions be true. Likewise, at no world is there any god who is involved in any way in trans-world causation; for on my view that too is impossible. So neither at this world nor at any other is there a maker and cause of all things – I mean, of all things without exception, without any tacit restriction. But at some world (though if I am right, not this one) there is indeed a maker and cause of all (other) things that are part of that world.

  ‘The Truth in Realism’ (Taylor 1987).

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A believer who also accepted my thesis of plurality of worlds (complete with its prohibition of overlap and its principle of recombination, which says that if there are two distinct things, say a god and his creation, then at some world there’s a duplicate of the second unaccompanied by any duplicate of the first) could say that he believed in a maker of all things; but he would have to say this under a tacit restriction of quantifiers and mean maker of all things that are part of the same world. It would be fair to say this; it might be true – what is true under a tacit restriction is, nevertheless, true. So the problem is not that this believer couldn’t square plurality of worlds with the truth of his creed, suitably interpreted. (But literally interpreted, since I think restriction of quantifiers should not count as a departure from literal meaning.) But I think he still has a problem: he may rescue the letter of his creed but not the spirit. The thesis of plurality of worlds belittles god – belittles any god, the god of any world that has a god – by portraying him as only one among equals, a minute part of reality, his power limited also to a minute part of reality. You might well defend the claim that such a being satisfies, and arguably in a literal sense, the description that is written into the believer’s creed. But what I think you cannot do is to make such a being seem like a fit object of religious worship. A fit object of fear and loyalty, as a king might be; of veneration, as a wise teacher or a saint might be; of amazement, as a sorcerer might be; . . . But worship was supposed to be something else. In the middle sections of Chapter II of PoW, I answered arguments urging that although modal realism did not lead to outright paradox, it did demand momentous changes in the way we think and live. Were I a believer, as you are, I think modal realism would demand a momentous change: though I might retain the opinion that there was a god among my worldmates, I do not see how I could go on regarding this as a fact of supreme importance. (Just as I do not regard the fact that there are gods not among my worldmates as something of great importance.) As I am an atheist, and likely to have been one no matter what I had believed about the metaphysics of modality, I count this no drawback whatever of modal realism. But I agree that believers have no business following my lead. Sincerely, David Lewis cc: Plantinga

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182.  To Philip P. Hanson, 27 March 1987

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182.  To Philip P. Hanson, 27 March 1987 [Princeton, NJ] Dear Phil, A world is a ‘maximal object’ – an object which includes anything spatiotemporally related to its parts, and which does not consist of two parts not spatiotemporally related to each other. No modal primitive yet, OK? Which of these worlds are possible? – all of them! (Here I mean possible simpliciter, disregarding restricted modalities like physical possibility etc.) Still no modal primitive. No need to divide the possible from the impossible worlds because none of the latter, therefore no need for a modal primitive to make the division. If I thought I needed to posit impossible worlds, then I might need a modal primitive to make the division. But I don’t need or want to posit impossible worlds. Because (1) impossible worlds are less clearly useful than possible worlds; (2) impos­ sible worlds, at least the downright contradictory ones, are more problematic than possible worlds – see PoW, footnote on page 7; (3) it’s more feasible to be an ersatzer if all we want is to make ersatz impossible worlds given all the genuine possible worlds than if we want to make all the ersatz possible worlds given only the actual world. Your statement of the principle of recombination is modal, sure enough; but not primitively modal. Stated without primitive modality, it becomes a conditional about the existence of maximal objects. For instance, if some world has a head and some world has a horn, then some third world has a duplicate of the horn attached to a duplicate of the head. Working in the ‘shape and size permitting’ part is complicated; it may force us to have recourse to mathematical structures – which I don’t mind – but I think not to primitive modality. (Phil Bricker has gone much beyond me in exploring exact formulations of the principle of recombination. You might get in touch with him at Yale.) I wanted to say how much I liked your review.1 Not just because it’s so fa­vor­ able, though of course that’s nice too; but also because of how well it tells the reader what the book does. Some of the other forthcoming reviews have rather distressed me that way – they’re more a pretext to display the reviewers’ wares than any sort of account of the book. I was glad you made a point of how  ‘the sheer momentum of the system seems to be taking over ’ the case against haecceitism. I think it’s important that this  issue shouldn’t be settled on the basis of intuitions about haecceitism itself,   (Hanson 1986).

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i­ntuitions which can anyway be accommodated by haecceitist and antihaecceitist alike, but rather by longer arguments which turn on other issues. If there were no problem of accidental intrinsics there would be no need to reject overlap, and if there were no need to reject overlap there would be no need to reject haecceitism. Or if there were no problem of alien properties and no problem of primitive modality (or if primitive modality were everybody’s problem as you suggest) then there would be no good reason not to be an ersatzer, in which case again we might as well be haecceitists. Sincerely,

183.  To Jaegwon Kim, 31 March 1987 [Princeton, NJ] Dear Jaegwon, Thank you for your paper on supervenience, which I’ve read with great i­ nterest.1 I discuss weak and strong supervenience in On the Plurality of Worlds, pages 14–17. Not under those names: I portray strong supervenience as supervenience simpliciter, weak supervenience as a distortion engendered by the wrongheaded idea that any modal idiom of ordinary language has to be expressed by means of boxes and diamonds. I agree with you in wanting to express strong supervenience without departing from the original idea that one difference requires another: there could be no difference in the supervenient without difference in the basis. I think the difference between McLaughlin’s way and mine of stating this is not important. It comes from difference over the underlying metaphysics of modality (maybe McL holds a contrary view to mine, maybe he just wants to be more neutral) rather than any difference about supervenience itself. Page 10 is a bit misleading so far as I’m concerned. You say that some philo­ sophers have looked to global supervenience as a mode of ‘determination without reduction’; for example, those who characterise materialism in terms of global supervenience; e.g. Lewis. But disowning reduction was not any part of my aim. See ‘New Work’ page 358: ‘A supervenience thesis is in a broad sense reductionist . . . but unencumbered . . . It captures what the cautious reductionist wishes to say’.2 I’m interested, in a different connection, in the sort of partial or approximate supervenience that appears toward the end of the paper. If a statement entirely about   ‘ “Strong” and “Global” Supervenience Revisited’ (Kim 1987).   

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  (Lewis 1983c).

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183.  To Jaegwon Kim, 31 March 1987

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a subject matter is one whose truth value supervenes on the state of that subject matter, what is a statement partly about a subject matter? Various answers are possible, depending on what you take to be partial. But could it, inter alia, be the supervenience that’s merely partial? I was surprised by the examples of global supervenience without strong or weak supervenience. However, I don’t think I believe the point you’re making by means of these examples. The examples succeed on their own terms, of course. However I think that sometimes – maybe always? – they work by violating what I call the Principle of Recombination. Sometimes – always? – you can get strong supervenience back from global supervenience plus Recombination. Recombination is, roughly, the principle that anything can coexist with anything else; less roughly, that an intrinsic duplicate of anything can coexist with a wholly distinct intrinsic duplicate of anything else; for something a bit less rough, see PoW, pages 86–92; and for something better yet, await some not-yet-published work by Phillip Bricker. Here’s a rough idea of how my reply works. Supposedly we have a world W1 which is physically just like our world W0 except for some silly little atom on Saturn, yet in W1 the rocks are conscious. Strong supervenience fails but global supervenience doesn’t fail! I reply: but if there’s such a W1, surely there’s also a W2 in which Saturn is as it is in W1 but the rest – including the unconscious rocks – is just as it is in W0. Why can’t the two alleged possibilities be patched together? Now W2 and W0 give the expected failure of global supervenience, even if W1 and W0 didn’t. I can’t apply Recombination to your formal mini-examples as they stand, because I need to build in a distinction between intrinsic and extrinsic properties. For mnemonic purposes only, let’s talk of ‘mental’ and ‘physical’ instead of F and G. Let’s avoid commitment to trans-world identity, as opposed to trans-world similarity. And let’s roll the two examples, Petrie’s of global without strong supervenience and yours of global without weak supervenience, together into one.3 Now let P1 and P2 be alternative total physical natures – maximally specific combinations of intrinsic and extrinsic physical properties. Let M1, M2, M3, and M4 be alternative intrinsic mental natures – maximally specific combinations of intrinsic mental properties. (It isn’t really required that M4 should be different from each of the other three. The other differences do matter.) Now we have two mini-worlds, each with two things as described. (Maybe there are some trans-world identities – I’m not assuming anything one way or the other.) World 1: P1a & M1a & P1b & M2b. World 2: P1c & M3c & P2d & M4d.

  ‘Global Supervenience and Reduction’ (Petrie 1987).

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So a and c are a counterexample to strong supervenience; a and b are another, and also they are a counterexample to weak supervenience; but since these two worlds aren’t physically alike, we don’t yet have any counterexample to global supervenience. But that, I say, is because we have ignored Recombination. Given worlds 1 and 2, we have two more worlds, patched together in the way suggested by their names. World 2/1: P1e & M3e & P1f & M2f. World 1/2: P1g & M1g & P2h & M4h. Taking World 1 versus World 2/1, we get one counterexample to global supervenience; taking World 2 versus World 1/2, we get another. How did I do the recombinations? First consider World 2/1. Let e have the same intrinsic physical and mental nature as c; likewise let f have the same intrinsic phys­ ic­al and mental nature as b; and let e and f stand in the same external physical relations as a and b. (This ought to be possible: e has the same intrinsic physical nature as c, which in turn has the same total physical nature as a, so e has the same intrinsic physical nature as a; and ex hypothesi f has the same intrinsic physical nature as b; and if e and f have the same intrinsic physical nature as a and b respectively, what could stop them standing in the same physical external relations?) If e and f have the same intrinsic physical natures as a and b respectively, and also stand in the same physical external relations, that should be enough to settle that e and f have the same total physical natures as a and b respectively – namely, P1 both times. Ex hypothesi they have the same intrinsic mental natures as c and b respectively – namely, M3 and M2. The case of World 1/2 is similar. Let g have the same intrinsic physical and mental nature as a; likewise let h have the same intrinsic physical and mental nature as d; and let g and h stand in the same external physical relations as c and d. (This ought to be possible because g and h have the same intrinsic physical natures as c and d respectively.) That should settle that g and h have the same total physical natures as c and d respectively, namely P1 and P2; and ex hypothesi they have the same intrinsic mental natures as a and d respectively, namely M1 and M4. This falls short of a full reply to you, for several reasons. One reason is that in order to handle the examples in this way, I needed to take the M’s as intrinsic; whereas really we’re interested in supervenience of the mental generally, intrinsic and extrinsic alike. I don’t offhand see how to extend the treatment just given to the case of extrinsic M’s. Another shortcoming is that my discussion of Recombination in PoW didn’t really cover how to patch things into a structure of external relations; in the above discussion, I was to some extent improvising as I went along. (See PoW page 181 for another place where it would have been nice to have a statement of what Recombination means in the presence of hypothetical external relations.)

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184.  To Jack Copeland, 22 June 1987

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But the main caveat is that none of this applies at all to nomic supervenience – supervenience restricted to worlds that obey the actual laws. Those worlds certainly do not obey Recombination – rather, by recombining elements of law-abiding worlds we can generate a law-breaking world. To my mind, a thesis of psychophysical nomic supervenience is an empirical thesis for dualists – not a form of materialism at all. True, I do see minimal materialism as a restricted supervenience thesis; but the restriction I have in mind isn’t nomic, rather it’s to worlds without alien natural properties, and this restriction does obey Recombination. Yours, David Lewis cc: McLaughlin, Petrie (I don’t know where Petrie is. Could you please forward the enclosed copy to him? Thanks.)

184.  To Jack Copeland, 22 June 1987 [Princeton, NJ] Dear Jack, Congratulations on the promotion! Where is ‘Logic on the Australian Plan’?1 I’d missed it. Sorry to see Martin signing up once again for a share of Meyer’s rhetoric. I’d have thought he knew better. I asked Roz Chast to let me use her ‘Parallel Universes’ for the cover or frontispiece. She said no, because it was going to be on the cover of her own collection Parallel Universes.2 Blackwell then got interested in surrealist paintings for the cover, which would have come out looking just like up-market science fiction paperbacks 15 or so years ago. Then I suggested some painting out of Locomotives that Never Were, a book of paintings of 20th century British locomotives that were designed but never built;3 Blackwell didn’t like that. In the end, I was quite happy to settle for the plain cover, which I think looks quite handsome. Chapter 7 is very nice, so far as I can tell without having paid much of any attention to the Chinese Room in the first place!4 [. . .]

  (Meyer and Martin 1986).    2 (Chast 1984).   3  (Barnes 1985).   Artificial Intelligence: A Philosophical Introduction (Copeland 1993).

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I’ll be in Aus most of August and September, including the AAP. Steffi will be with me for three weeks in the middle. No NZ side trip this year, but maybe next. Am I right that next year the NZ conference will be in August? Where? A good op­por­tun­ ity – I’ve never been to an NZ conference, because I’m normally not free to travel in May. Last August, Steffi and I got a 4WD and drove in various directions from Alice – no crocs, but some terrific scenery, by no means limited to the official sights. This year, I was thinking about high country east of Melbourne, thinking we might go further if we hired a 4WD again than we dared to go with cars in previous years. Not outback in the ordinary sense, but (if we keep away from the ski slopes) just as empty. In what sense are you ‘kind of coming round to Graham Priest’s ideas’? Myself, I think his view is certainly false; but as you say it’s a real view, not evasion, and I think he plays fair. [. . .] In which connection: will I see you in two weeks in Brisbane? Or at the AAP? I’m off quite soon; Steffi, who has only three weeks off, will join me on 9 August. Sydney, Canberra, and Melbourne mostly; and some sort of drive in August, maybe farther north in Aus than we’ve gone previously. Yours,

185.  To Robert C. Stalnaker, 28 July 1987 Princeton University Princeton, NJ Dear Bob, Thank you very much for the draft review.1 I did find it surprising: we differ more radically than I had realized about ontological seriousness. I think all the issues you raise amount to parts of this one big issue. I am the fundamentalist Platonist, or near enough. I don’t definitely think that numbers have shape, or exist in a physical space; but maybe they do, and certainly I take these to be meaningful and wide-open questions. Certainly I’m far closer to the fundamentalist than to the liberal. I never would say anything close to what he said: ‘The existence of numbers is just constituted by the fact that there is a legitimate practice . . . and that certain of the products . . . meet the standards of correctness’.2   ‘Critical Notice of On the Plurality of Worlds’ (Stalnaker 1988a).   

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  (Stalnaker 1988a, 119).

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186.  To E.J. Khamara, 21 September 1987

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I resist the temptation to comment at length. The general comment is that I found it very good and illuminating. A specific comment is that lines 7–9, page 2, look to be backward: isn’t it the explanations and analyses that presuppose the hypothesis? I haven’t read most of ‘Vague Identity’ yet,3 but I did want to comment on footnote 1. For all its caution, I think this still gives a misleading suggestion about what Evans was doing. My understanding, which Evans confirmed emphatically in a letter,4 was that he was displaying an argument against vague identity statements which, in his own opinion, was fallacious and led to an absurd conclusion. His main point was that the vague-objects-in-the-world man was in trouble for not having a diagnosis of the fallacy and a way of dodging the conclusion. So a supervaluationist diagnosis of the fallacy supports Evans (because it puts the vagueness in language, not the world); and supports the main argument of Evans’ paper,5 though not the argument prominently displayed in the middle of that main argument. I have congratulated one or two traveling techies on their good fortune. Since the fact that you made the decision to go is evidence that it was the right decision to make, congratulations now to you as well. Yours, David

186.  To E.J. Khamara, 21 September 1987 Australian National University Canberra, Australia Dear Edward, I’ve now read ‘Indiscernibles . . .’1 with great interest, though only partial agreement. I like it very much. One thing to say is that I fully agree with your footnote 31: ‘What leads Lewis to leave the question [of indiscernible worlds] open is his realism . . . But if we think of possible worlds as creatures of our own powers of conception . . . what distinguishes one . . . from another must always be some difference in their intrinsic natures’. I’d think of conceptualism about worlds as one form of linguistic ersatzism, in which  (Stalnaker 1988b).   4  Letter from Gareth Evans to David Lewis, November 1978.   ‘Can There Be Vague Objects?’ (Evans 1978).

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  ‘Indiscernibles and the Absolute Theory of Space and Time’ (Khamara 1988).

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world-descriptions (in this case, descriptions in the medium of mental representation) go proxy for worlds; in which case there’s no distinguishing of worlds with the same description. (I think I say something about this in Plurality of Worlds, but I don’t have a copy here.) Even given my modal realism, there’s a principle I accept which could serve as a substitute for inter-world identity of indiscernibles. That is my anti-haecceitism. I reject haecceitistic differences between qualitatively (‘purely’) indiscernible worlds: that is, differences in which things are which that hold without benefit of qualitative differences between worlds. But a difference by spatial or temporal translation between two worlds would be a haecceitistic difference. So I reject that no less than you do, despite leaving open the question of indiscernible worlds. Maybe there are qualitatively indiscernible worlds; but if there are, I say they are entirely alike and don’t disagree about where the eastern boundary of the material universe is, or about when its beginning is. My disagreement with Leibniz and with you concerns the first inference in the translation arguments: if the material universe occupies a certain finite ìperiodof time in AW, then there’s a different world PW in which it occupies a simí îregion ìperiod . I reject this. If in AW the material universe MU ilar but numerically different í region î ìperiod occupies í R, and in PW likewise MUʹ occupies Rʹ, and we have exact qualitaîregion tive similarity, I say this makes Rʹ the counterpart of R; so there’s no sense in which PW differs from AW by translation. (Likewise, mutatis mutandis for reversals.) So though I wouldn’t object to their final steps – the appeal to inter-world PII.3, or else to anti-haecceitism – I nevertheless wouldn’t endorse Arguments I, II, Iʹ, IV, V, or Vʹ. Some further comments. You don’t say that every relational property is either positive or negative, but I think a reader might get that impression. It isn’t so, because there are mixed cases: the property of owning a cat and no dog, or the property of being either a bachelor or a bigamist. Likewise for pure versus impure: the property of being either a pupil of Plato or a pupil of a fool is a disjunction of impure and pure. (See my ‘Extrinsic Properties’, Philosophical Studies approx. 1983, for a problem that arises because the positive extrinsics and the negative extrinsics fail to exhaust the extrinsic properties.)2 I thought the definition of a pure (positive) relational property on pp.10–11 might have drawn the line at the wrong place. Consider the group of individuals: Edward Khamara, the Sydney Harbour Bridge. I have the property, pure by the   (Lewis 1983a).

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186.  To E.J. Khamara, 21 September 1987

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­ ef­in­ition, of reading a paper written either by EK or by the SHB. Also I have the pure d property: not reading any paper written by a bridge. Also, I suppose, the SHB is essentially a bridge. So from my ‘pure’ properties plus a necessary truth about the essence of the SHB, it follows that I have the impure property of reading a paper written by EK. That should not have happened; and I think the false step came at the beginning. The group of EK and the SHB wasn’t the proper sort of ‘group’; it should have been a group specifiable by a shared pure property. If this introduces circularity, I can only say: better to leave purity undefined than to get the line in the wrong place. Should you say ‘kinetic’ rather than ‘dynamic’ universes, since nothing was said about any forces that make the spheres move? Also, I thought that even if the universe of moving spheres sometimes went into isosceles or equilateral configuration, the spheres could be discerned even then by cross-time spatial relations. Let’s suppose the cycle is

Can’t I say that at t1 the spheres are discernible because one has the property: being such that later it will be 3 units from one sphere and 4 units from another which the other two lack; and likewise for the other two. (Of course, I still need a scalene configuration sometimes.) On page 26 you say that relations between two worlds supervene on their intrinsic natures taken separately. Well, maybe – I am inclined to believe it. But it seems to me more of an open question than your statement suggests. For one thing, there’s Pargetter’s theory of laws of nature: an interesting rival to fancy regulatory theories, avoiding some drawbacks of both, which posits a relation of nomic accessibility* which doesn’t supervene on the natures of the two worlds taken separately.3 The statement of Argument Iʹ (page 30) confused me, until you said it was supposed to parallel Argument IVʹ (page 32). I first thought we were assuming that in AW the material universe was infinite, and occupied an infinite region R, but nevertheless R was only a part of space, whereas in PW it occupies Rʹ, again only part of space, with Rʹ different from R. (Everything north of Melbourne, including the sky, is an infinite region in the sense of extending an infinite distance, yet is only part of space.) But first, this wouldn’t parallel IVʹ. Second, it wouldn’t fit your division of cases on * 

I forget whether this is P’s name for it.   ‘Laws and Modal Realism’ (Pargetter 1984).

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page 27: (i) space partly occupied by the M.U.; (ii) space fully occupied by the M.U.; (iii) space entirely unoccupied, no M.U. exists. So I thought maybe the distinction between proper parts of space that are finite and infinite in size was a red herring, and more likely Argument Iʹ was supposed to be like this. In AW, an infinite M.U. fills space completely; likewise in PW; but for each finite part x of MU, x occupies different finite regions in AW and in PW. (Let matter fill all space; but to get from AW to PW, displace every bit of matter one mile southward. All the matter will still fill all the space, but each finite bit of matter will fill a different region.) Finally, two typos [. . .] Yours, David

187.  To Paul Tappenden, 21 December 1987 [Princeton, NJ] Dear Paul Tappenden, There’s no explicit mention of Everett’s many-worlds quantum theory in my book, but I did say some things that were meant to apply, inter alia, to it. See the discussions of branching versus divergence, and of many world-like parts of one big world versus many worlds: 70 ff. and 206 ff.1 I see Everett as offering not a theory of many worlds in my sense, but rather a theory of branching within one world: our world is bigger than we think; it consists of a superposition of many world-like parts, not altogether isolated because they grow out of a common past. I have mixed feelings about this theory. It’s very elegant to have quantum mechanics with Schrödinger evolution only, and no reduction of the wave packet; but, unlike my sort of many worlds, this really is the sort of theory that makes nonsense of wondering what one’s future will be. And I wonder (following Hilary Putnam, in conversation) in what sense Everett is right that he predicts what standard quantum theory does? The idea is that in most of my futures, the stat­ is­tics will come out in the way standard quantum theory tells me they probably will. But ‘most’ has to be explained in terms of amplitude in the superposition, and what has that to do with reasonable expectation? If Everett tells me that I will have many futures, some with A and some with not-A, and also tells me that the A-futures have   On the Plurality of Worlds (Lewis 1986c).

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188.  To Charles Huenemann, 1 February 1988

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the lion’s share of the amplitude, why is that a reason to expect A rather than not-A? However the amplitude splits up, surely I ought to expect both, not one rather than the other; but of course not both together. And if Everett is really telling me to expect both, then why should I think that observing A confirms Everett’s prediction and observing not-A doesn’t? Having two futures that are equally mine makes nonsense of our ordinary way of expecting one thing rather than the other, and therefore makes nonsense of our ordinary way of deciding that a prediction turned out true. No such thing happens with my sort of many worlds, since I have only one future, the other futures belong at best to my otherworldly counterparts. In view of the Principle of Recombination, I don’t think there could be strong physical constraints on what’s possible in the broadest sense; but there might well be unexpectedly strong constraints on what’s compossible with what. Maybe if you want both strong and simple laws and conditions permitting any form of life, there are surprisingly few possible ways to combine the two. That would mean not that there were few possibilities, but rather that most possibilities are either lawless or lifeless or both. Sincerely, David Lewis

188.  To Charles Huenemann, 1 February 1988 [Princeton, NJ] Dear Charles Huenemann, Thank you for your letter. The answer to your main question – do I believe that the denial of a necessary truth entails a contradiction? – is yes and no. By that I mean only that there are various notions of entailment. My favorite one is strict implication: A entails B iff it is impossible that A without B. Now if A is the denial of a necessary truth, then it is just plain impossible that A; so it is no less impossible that A without B. So on that understanding, the answer is yes. But there are other notions, and I don’t want to deny that it’s OK to use the word ‘entailment’ for those instead. The word doesn’t have a firmly settled meaning. For instance, there’s logical – ‘narrowly’ logical – entailment: A entailsL B iff, no matter how we reinterpret any non-logical words that may occur in A or B, still even under the reinterpretation it remains impossible that A without B.  On that understanding, the answer is no. ‘Not all bachelors are unmarried’ is the denial of a

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necessary truth, sure enough, and it does entailS every contradiction (and everything else); but it doesn’t entailL any contradiction, because it can be true without any contra­dic­tion being true under the reinterpretation that makes ‘bachelor’ mean ‘cat’ and ‘married’ mean ‘striped’. You are right that ‘There exists a plurality of worlds’ is, for me, necessary: true at every world if it’s true at any world – and it is. So its denial entailsS everything, and in particular every contradiction. But you can’t see it entailing a contradiction! – Right; a priori knowledge of what entailsS what is no easier than a priori knowledge of what’s possible and what’s necessary. If there are unknowable facts about modality, there are unknowable facts about what entailsS what. ‘There does not exist a plurality of worlds’ does not entailL any contradiction – look at what happens under the reinterpretation that makes ‘plurality’ mean ‘army’ and ‘worlds’ mean ‘giraffes’. But it does not follow that there exists a world where this proposition is true. Not anything that entailsL no contradiction is a way a world could be. Of course you can invent still other notions of entailment but these two may be enough. Talk to Fabrizio about this, I suggest. Sincerely,

189.  To Alexander Rosenberg, 7 June 1988 [Princeton, NJ] Dear Alex, At last I’ve had time to turn to the paper you sent me in March.1 I’m sorry it’s taken so long! I have trouble even beginning to share your worry that there’s something unintelligible about disconnected spacetime. I know of no argument against that isn’t premised on verificationist or idealist doctrines I’d reject in any case. So whatever problem remains seems to be just that I can’t imagine that there are two place-times with no spatial or temporal distance between them. But it seems to me that I can imagine that perfectly well; or, if there’s a sense in which I can’t imagine it, that’s a sense in which I likewise can’t imagine all sorts of other things that are perfectly intelligible and possible and actual.   ‘Is Lewis’s “Genuine Modal Realism” Magical Too?’ (Rosenberg 1989).

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I have some running comments as well. Page 3, 2/3 down: Perhaps Lewis endorses intra-world PSC ‘not really because he believes it, but only because it is required . . .’. I hope I don’t endorse things I don’t believe! But what’s true is this. I believe and endorse it not out of spontaneous in­clin­ ation, but as the conclusion of an argument that outweighs spontaneous inclination. The argument is that modal realism needs something to delineate one world from another, and letting spatiotemporal relatedness do the job seems to be the most plaus­ible hypothesis because it dispenses with a mysterious primitive worldmate relation. Page 4, 1/3 down: ‘What is the difference between nonmaximal regions and maximal ones?’ I don’t get this question. Are you asking for a definition? A maximal region simpliciter is a region that is not a proper part of any other region; a maximal connected region is a connected region that is not a proper part of any other connected region; I’m not sure which one you have in mind. Or are you asking why a maximal region, unlike a nonmaximal region like Syracuse + Riverside, can’t be disconnected? If it’s maximal simpliciter then it can be disconnected, indeed I say it must be; whereas a maximal connected region is connected by definition. I don’t think any of these easy questions I’ve just answered can be the question you meant to ask, though. Page 5, middle: Right you are; ‘like Space in certain formal respects’ is not what’s wanted. Sometimes otherworldly space differs in interesting ways from thisworldly space, but sometimes not – consider, for instance, a world where one dust mote is minutely displaced, and which is otherwise as like this world as can be. Same place. ‘Space’, or better ‘Spacetime’, as a proper name for a particular could be a proper name for all of thisworldly spacetime, in which case I say it’s a name for a particular that’s far from unique; or it could be a name for all the spacetime of all the worlds, in which case there’s only one such thing, but it’s disconnected. Page 6, top. Quinton’s story needn’t involve transworld identity in the objectionable sense of overlap; the man who lives partly in the waking world and partly in the dream world could survive by perduring, that is by having some stages entirely in one world and others entirely in the other. But it does involve transworld causation, for instance when the man remembers in the waking world his life in the dream world, and I do object to that. But Quinton’s argument is, I think, addressed to verificationists: they thought the hypothesis of two spaces (within actuality) was meaningless because unverifiable, Quinton answers by showing how it might be verified. Myself, I’d answer them by rejecting verificationism. So I don’t need Quinton’s argument. Page 7, middle. No, unimaginability is not a good criterion of impossibility. For if what’s required is a sketchy, schematic sort of understanding, then I can

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imagine the impossible; whereas if what’s required is imagining in full detail, then I can’t even imagine what’s actual. And besides limits of detail, there are other limitations on what I can imagine that are equally irrelevant to possibility. It’s true (no matter how many false claims get packaged with it) that I can’t imagine having a bat’s sonar sense-experience, but that doesn’t make it impossible. Anyway, I think that probably I can imagine spatiotemporal disconnection. The only problem, if it is a problem, is a general difficulty about what it means to imagine a negative existential. I imagine a man, and fail to imagine him having a home anywhere – have I imagined a homeless man, or is my imagining incomplete? What’s the difference? I imagine odd goings on, and fail to imagine them being at any spatiotemporal distance from here and now – have I imagined spatiotemporal disconnection, or is my imagining incomplete? What’s the difference? To the extent that imagining is like making a mental picture, there’s a general problem about picturing negative existentials. (Except when it’s clear where the so-and-so would go if there were one – I can picture an earless man well enough.) To the extent that we can im­agine negative existentials, I suppose the moral is that imaginative representation is not all that picture-like. Page 8, bottom. The cases aren’t parallel. I’m not asking you to grasp some extra primitive notion that you might have hoped to dispense with, and that you find mysterious. You understand ‘distance between x and y’ and you understand ‘there isn’t any’ and I’m not asking you to understand anything more, just to put together those two things you understand already. Page 9, middle. The idea of an otherworldly spacetime that isn’t spatiotemporally related to ours because it’s abstract has two problems. One is that if ‘abstract’ just means ‘not bearing spatiotemporal relations’, then nothing has been done to explain why some things don’t bear spatiotemporal relations, so the ‘because’ is wrong. The other is that otherworldly spacetimes have parts that do bear spatiotemporal relations to one another, if not to us. So those parts, at least, aren’t abstract. But one wouldn’t have thought that an ‘abstract’ whole could be made of ‘concrete’ parts. Page 10, bottom. Some worlds may have what are merely analogically spatiotemporal relations; but others will be exact duplicates of this world, except for a minute displacement of a dust mote, and those worlds, at least, will have the same spatiotemporal relations as our world does. So even if your problem had a solution involving merely analogical spatiotemporal relations, that couldn’t be a general solution. (You say this later, without very much emphasis. But I think it’s enough of a problem to sink the approach decisively.) Page 13, middle. A problem with taking causal isolation as sufficient for two things to belong to different worlds is that it rules out chaotic possible worlds

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190.  To Murali Ramachandran, 18 October 1988

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wherein there’s no causation at all. Each part of such a world would be isolated from each other part, so the chaotic world wouldn’t be all one world after all. --I’ll probably see you next year. At present I’ve tentatively agreed with Carl on a date in late April for a two-day visit, which may or may not fit my teaching schedule for the spring. But if that doesn’t work, or if it takes too long to find out whether it will work, it should be possible to find a fall or early winter date instead. Sincerely, David Lewis

190.  To Murali Ramachandran, 18 October 1988 [Princeton, NJ] Dear Murali Ramachandran, Thank you for your nice ‘Alternative Translation’ paper,1 which I’ve now read with much interest. I do hope Analysis accepts it. So far as I can remember, it’s a new proposal. The only thing it reminds me of is my colleague Stephen Neale’s use of ‘neutral’ definite descriptions – neutral between singular and plural – in which ‘Fred beats the donkey/donkeys he owns’ is symbolized as ‘Fred beats (Nu x: x is a donkey and Fred owns x)’ and translates to ‘There is at least one donkey Fred owns, and Fred beats every donkey he owns’. That means that your ‘Ft’ is F(Nu x: x is a counterpart of t). When I wrote ‘Counterpart Theory . . .’, I probably would have said that your translation scheme wouldn’t do, exactly because it gives you a form of the strong interpretation. We were taught that the box was supposed to correspond to the English ‘necessarily’; and sometimes, to the naïve and uncorrupted ear, it sounds correct to treat ‘necessarily’ and ‘essentially’ as interchangeable, even when the thing that has properties essentially is not something with counterparts at every world. But nowadays I think that what we were taught doesn’t give us any unequivocal guide to how to interpret quantified modal logic. It is not a language that has any clearly defined intended interpretation. Therefore no counterpart-theoretic translation, whether mine or yours or any other, ought to be put forward as capturing the intended interpretation of quantified modal logic. See my remarks in On the Plurality of Worlds, pages 12–13. What’s true is that many conflicting translations, each

  ‘An Alternative Translation Scheme for Counterpart Theory’ (Ramachandran 1989).

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­sounding right some of the time, may together capture the extent to which we never did give quantified modal logic a determinate meaning. It’s to this that your alternative scheme seems to me to contribute. In exploring your scheme, I looked at this example. Let us say ‘twins’ for short to mean two people at the same world who are so much alike that if either one of them is my counterpart then both are; and who are not included in any larger set (at the same world) of which the same is true. Let us call someone who is one of a pair of twins ‘twinned’. Twins need not be born at exactly the same time. Let us call someone who is the younger member of a pair of twins a ‘junior’. I can say in English: (1) I might have been a junior or (1A) I might have been the younger one of two twins. And maybe I can say the same in modal logic thus: (2) Possibly: I am a junior. or (2A) Possibly: for some y and z, y and z are twins, and y is younger than z, and y = me. or (2B) Possibly: for some z, I and z are twins, and I am younger than z. I think you translate these into (equivalents of): (3) For some world w, for some x in w, x is a counterpart of me; and for all x in w, if x is a counterpart of me, x is a junior. or (3A) For some world w, for some y and z in w, y and z are twins, and y is younger than z, and (for some x in w, x is a counterpart of me) and (for all x in w, if x is a counterpart of me then y = x). or (3B) For some world w, for some z in w, (for some x in w, x is a counterpart of me) and (for all x in w, if x is a counterpart of me then x and z are twins) and (for all x in w, if x is a counterpart of me then x is younger than z). Have I got that right? (1) and (1A) strike me as true whereas (3) and (3A) and (3B) are false. But that needn’t mean that your translations won’t do; the fault might lie rather in the translation between English and modal logic. Given my view that quantified modal logic has no determinate interpretation, I think there’s no determinate fact of the matter about whether the modal logic sentences are synonymous with the English or with your translations; what’s clear, though, is that the English sentences aren’t synonymous with your translations. But you never said they were; you said nothing about how to translate from English to counterpart theory. Also, I can say in English:

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(4) I might have been twinned. or (4A) I might have been one of a pair of twins. And maybe I can say the same in modal logic thus: ( 5) Possibly: I am twinned. or (5A) Possibly: for some y and z, y and z are twins and y = me. I think you translate these into: (6) For some world w, for some x in w, x is a counterpart of me; and for all x in w, if x is a counterpart of me, x is twinned. or (6A) For some world w, for some y and z in w, y and z are twins, and (for some x in w, x is a counterpart of me) and (for all x in w, if x is a counterpart of me then y = x). This time, (4) and (4A) strike me as true, and (6) is true – so far, so good – but (6A) is false. My remarks are as before: something’s wrong somewhere, but whether it’s your step from modal logic to counterpart theory or whether it’s the prior step from English to modal logic is entirely up for grabs. This case illustrates the same point that your discussion of special predicates does: it matters a lot whether you say something in a long-winded way or whether you say it by means of an atomic abbreviation. That disturbs me. One likes to be free to substitute synonyms for synonyms, even if one synonym is atomic and the other compound, without having that make a difference to truth conditions. (A language doesn’t have to meet this condition; it’s one way that a language can be nice; but who said quantified modal logic had to turn out nice?) I thought of one general device you might introduce, which subsumes the introduction of special predicates at the end of your paper. You could introduce an abstraction operator that converts arbitrary formulas into predicates, binding one or more variables; and you could treat any predicates formed in this way as though they were atomic, even though they aren’t. Then you could at least freely substitute abstracts for atomic predicates, though what you couldn’t do would be freely interchange subject-predicate sentences using abstracts with synonymous sentences resulting from putting the subject in place of the variable of abstraction. Example: [x: –Fx]t would behave like your F*t, rather than like –Ft. You could always interchange the synonyms [x: –Fx] and F*, though you couldn’t always interchange the synonyms [x: –Fx]t and –Ft. Example: [x: for some y and z, y and z are twins and y is younger than z and x = y] or [x: for some z, x and z are twins and x is younger than z] would behave just like the atomic predicate ‘junior’ which I introduced above by way of abbreviation. Example: [x: for some y and z, y and z are twins and x = y] would behave just like my atomic predicate ‘twinned’.

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I think Allen Hazen (University of Melbourne, Parkville, Vic 3052, Australia) and Stephen Neale (Princeton) might find your paper interesting and might want to comment on it. My greetings to Martin, if you see him. Best regards, David Lewis

191.  To Phillip Bricker, 2 February 1989 [Princeton, NJ] Dear Phillip, Thank you for the new draft of the plural de re paper.1 I liked it very well before, and now it’s even better. I think Max Cresswell would find it very interesting, and it fits closely with what he’s working on. Address: Department of Philosophy, Victoria University of Wellington, Private Bag, Wellington, New Zealand. I have Jubien’s new ‘Magic’2 and haven’t read it yet. I’m hoping for time to catch up on reading this semester after admissions and hiring are done. For some while it’s been ‘Don’t read, write’ – first on ‘Parts of Classes’, now almost to a complete draft, and then on an ethics paper that was due 1 December and sent 28 January.3 Last time I was at U.Mass. (when Jubien was still there) we had some long and rather confused discussion of internal and external relations. It was clear at that point that he didn’t want to mean what I did by the distinction; not so clear what he did want to mean. Some sort of hybrid between my sense and the sense in which a relation is internal if it’s essential to its relata? Yes, identity and part-whole are meant to come out external. (This is one thing Jubien and others don’t like.) I don’t mind restricting the internal/external distinction to ‘fundamental’ relations. Those are the ones I mainly have in mind, let the rest fall where they may. And I have some sympathy with setting the mereological relations, including identity, aside as some sort of a special case. Graspable, of course; but somehow quite unlike the spatiotemporal relations. Armstrong sets them aside

  ‘Quantified Modal Logic and the Plural De Re’ (Bricker 1989).   ‘Could This Be Magic?’ (Jubien 1991). 3   Parts of Classes (Lewis 1991), and probably ‘Dispositional Theories of Value’ (Lewis 1989a). 1 2

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192.  To John Martin Fischer, 27 April 1989

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as a special case – they don’t get to be genuine universals – but for reasons that look to me like special pleading. If it were just identity, I might say ‘not fundamental because of definability using plural quantification’; but that doesn’t extend to the rest of the mereological relations, and I want to treat those all together. There’s a certain amount about this in ‘Parts of Classes’, which is now one section short of a complete draft. When that’s done, or before if it drags on, you’ll get a copy. Yours,

192.  To John Martin Fischer, 27 April 1989 Princeton University Princeton, NJ Dear John, Thank you for the papers you sent.1 I’m writing now in reply to the question you raise in footnote 16 of ‘Freedom and Actuality’.2 Right you are: I have not con­ sidered such a position explicitly. What might I think of it? The condition is the combination of my indexical possibilism with the idea that God’s omniscience is limited to knowledge of world-indexed, necessary truths: He knows that at world W17 Adam freely falls, while at world W137 Adam withstands temptation. But does He know how Adam chooses at the actual world? Certainly He doesn’t know how Adam chooses at the absolutely actual world, because according to indexical possibilism no world is absolutely actual. So does He know how Adam chooses at the relatively actual world? Distinguish two cases. (First, let me restrict myself to worlds where there exist God and Adam. I’ll pretend to take for granted that we inhabit such a world.) Case 1. Each world contains its own God, and likewise its own Adam. The several Gods are wholly distinct, but are counterparts of one another; likewise the several Adams. One of all these Gods, the this-worldly one, is the one we may just call ‘God’; likewise the this-worldly Adam is the one we may just call ‘Adam’. If God knows which of all the Adams do and don’t fall, and which of all the Gods do and don’t have fallen Adams as their worldmates, He may yet fail to know which God He is, which world He lives in, and whether His worldmate Adam is one of the Adams

1   Fischer sent three papers, two of which were ‘Responsibility and Failure’ (Fischer 1986) and ‘Freedom and Actuality’ (Fischer 1988). 2   (Fischer 1988).

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who falls or one of the Adams who doesn’t. In short, God doesn’t know whether Adam falls. Then He doesn’t have the sort of foreknowledge that would threaten Adam’s freedom. But then it seems to me that He is too ignorant to count as omniscient in anything remotely resembling the traditional sense. So this does not seem to me to be a successful reconciliation of omniscience and freedom. It just gives up the former in aid of the latter. God could have known which world He lived in, and if He doesn’t then He’s just plain ignorant. Case 2 is more interesting. Suppose the method of counterparts applies to the Adams as before. But suppose God is an exception: He is wholly present at each world, a common part of all the worlds. Then He can’t be called ignorant for not knowing which world is His, for not knowing which world He’s at, for not knowing which world is relatively actual relative to Him, for not knowing whether His worldmate Adam is an Adam who falls or an Adam who doesn’t. Because all worlds alike are His, all worlds alike are worlds He’s at, all worlds alike are actual relative to Him, all Adams alike – the fallen and the unfallen – are His worldmates. (If God is sempiternal, and not by having time-slices at different times but by enduring identically, He cannot be called ignorant for not knowing, at 2:30 pm on 30 April 1989, what time it is. All times alike are present to Him. Likewise, mutatis mutandis, if He is common to many worlds just as He is common to many times, then He cannot be called ignorant for not knowing, at world W17 with its fallen Adam, which world He’s in. All He can truly say when asked the time, or when asked how the contingent facts are, is ‘It’s all times’ or ‘They’re all ways’.) What would I think of having God be an exception to counterpart theory, something wholly present in all worlds? My main general objection to such things is that they can’t have any accidental intrinsic properties. (Plurality of Worlds, section 4.2.) I think that’s totally absurd for you and me, or Adam, or even an electron – obviously we have plenty of accidental intrinsic properties. But nothing’s obvious about whether God has accidental intrinsic properties. One must consult the theologians. If one does, I’m sure one will come away mightily confused. Yours, David Lewis

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193.  To Michael Jubien, 14 June 1989

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193.  To Michael Jubien, 14 June 1989 [Princeton, NJ] Dear Michael, The semester is over, and at last I have time to catch up with reading before I set off on my vacation travels (to points east: Swansea, Perth, Melbourne, New Zealand, San Francisco, Princeton). The delay had one good effect: I’m reading ‘Could This Be Magic?’ in its latest version.1 I’m making running notes as I go – Footnote 6. I think I did have mereological sums mainly in mind – though if somebody had preferred sets or ordered pairs, I wouldn’t have fussed. (But now I think I would fuss, because I’ve come to wonder what if anything the intrinsic character of a set may have to do with the intrinsic characters and external relations of its members.) I don’t get your problem about the sum. Here’s the sum S of you and me, a scattered object with two parts separated by about 3000 miles (If you’re in Davis now, if we ignore other times). Any intrinsic duplicate of S, in this or another world, also will be a scattered object with two parts separated by about 3000 miles. There’s the supervenience of the external relation on the intrinsic character of the composite. What’s the problem? Is it this: that the distance holds in virtue of the amount of space between us, and the space between us is not part of the mereological sum? – If that analysis of distance were true, then I say distance wouldn’t be an external relation, because it wouldn’t be an intrinsic relation at all. But I don’t think that analysis has a hope of working, because some prior notion of distance would be needed in explaining which parts of space are the ones that are between us. Page 3. How do you know that propositions aren’t spatiotemporal? (I’ve been wondering how people think they know that classes aren’t spatiotemporal, and it’s a parallel issue about propositions.) I suspect the famous headless woman: you don’t see that she does have a head, so you think you see that she doesn’t. Pages 4–5. OK in principle, but what are the ‘outward manifestations’ of the ‘makes-true’ relation? Aren’t the propositions usually alleged to be causally inert? When you speak of ‘isolation’ that runs together our epistemic isolation from the causally efficacious microstructure of things and our causal isolation from the alleged intrinsic properties of the propositions. The latter matters, the former not. Page 7. Same issue as with footnote 6. It seems to me that your two alternative theologies of mathematics both make perfect sense if we take the composites as mereological sums – the classification of the relation doesn’t depend on the ‘unsettled

  (Jubien 1991).

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question of the exact nature of Lewis’s composites’. There’s something you’re presupposing that I don’t believe, and I’m not getting quite what it is. Page 7. I don’t agree that a part-whole relation between abstract things is an ‘abstract part-whole relation’. Part-whole, like identity, is a topic-neutral notion applicable to all manner of things. Pages 7–9. Sure, I classify identity and part-whole as external. Where’s this ‘natural inclination’ to say otherwise? Maybe it comes out of a different usage from mine, one on which ‘internal’ means, roughly, essential to the relata. (That would mean that similarity wasn’t internal but identity well might be.) Historically, and even today, I think that both currents of usage are around, and not always very well separated. I’ve tried to stick with the supervenience-on-natures part, and let the rest go off and seek some other name of its own. Page 9. I think the numbers are the Zermelo numbers, so succession is the member-to-singleton relation, a special case of membership. And I do think there’s a big problem about how we could possibly grasp the membership relation, though it’s just unbelievable to solve that problem by saying we don’t. Van Inwagen’s tu quoque is right (or near enough). The two frying pans – claiming to somehow grasp the makes-true relation, claiming to somehow grasp membership – are equally hot (or near enough); the difference is in the respective fires. Modal realism is cooler than the first frying pan, so in that case go for the fire; mathematical ‘nominalism’ is hotter than the second frying pan, so in that case stay in the pan. Page 9. Even ‘in the realm of the concrete’ I don’t agree that part-whole has much to do with a more fundamental spatiotemporal relation. E.g. we can know that three quarks are parts of the proton without knowing whether they’re side by side or whether they’re exactly superimposed, at the very same location. Pages 10–11. Right, the lack of necessary connection between the external relations of something and its intrinsic nature wasn’t meant to hold just as a consequence of the definitions of ‘external’ and ‘intrinsic’. Rather it’s an aspect of the principle of recombination (PoW, top of page 181). Compare the lack of necessary connection between the intrinsic characters of two particulars side by side – not a mere consequence of the definition of ‘intrinsic’, but intuitively compelling all the same. Page 11. The modality in question is necessity simpliciter, not nomological necessity. Of course there isn’t a principle of recombination for nomological necessity. In fact, that’s one of the main things recombination is for: to show that lawful connections are not necessary simpliciter. Page 12. Replaced the definition? – No, not everything true has to be true by definition. Page 15. Of course I agree that ownership involves not just the owner and the owned, but much in the surrounding society. You point this out as if scoring a point – I don’t see why.

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193.  To Michael Jubien, 14 June 1989

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On my view of things, the Eiffel tower relation is either internal, or else is grounded partly in external relations. Case 1. You mean ‘each has the actual shape of the Eiffel tower’. Then it’s internal. Case 2. More likely, you mean ‘each has the shape that the Eiffel tower has in its world’; that is, on my view, ‘each has the shape of the Eiffel tower that is its worldmate’; and worldmate is an external relation, maybe a spatiotemporal relation. It still looks to me as if an extrinsic relation is going to be based on external relations, perhaps to quite a large hunk of the surroundings (e.g. enough to contain the social setting of ownership). Page 16. I mentioned that van Inwagen’s tu quoque wasn’t quite perfect. The failure of the parallel comes at the point you’ve just reached, in taking the membershipis-external horn of the dilemma. I said: there’s got to be an unintelligible necessary connection between the intrinsic character of the concrete world and which propositions it bears the alleged external relation of making-true to. Van Inwagen echoed this: there’s got to be an unintelligible necessary connection between the identity of the member and which classes it bears the alleged external relation of membership to. But the echoing isn’t exact. Necessary connections of identity can be explained by counterpart theory, which isn’t applicable to necessary connections of character because there’s no de re modality involved there at all. Page 17. ‘We’ think that one of the intrinsic features enjoyed by x is its haecceity. Speak for yourself! By me, haecceities are definitely not intrinsic, because they differ between duplicates. Once again, some undercurrent having to do with essence is getting mingled with the idea that an intrinsic property of x flows entirely from the character of x itself – the qualitative character, not the identity. Mean what you will the rest of the time, but if you’re talking about my argument or parallels to it, you’d better mean what I meant by ‘intrinsic’. Be that as it may, you might think that membership could be explained in terms of haecceities. I agree; except now the action shifts from the member-of relation to the haecceity-of relation, which gets us no further forward. Indeed, it may leave us in the exact same spot, since I suspect x’s haecceity and x’s unit class are identical. Page 21. What you, and many others, seem to be saying strikes me as peculiar. Nothing is identical with anything that doesn’t exist. If I identify A’s with B’s, and believe in the B’s, that settles that I believe in A’s! (Of course, I don’t believe in ir­re­du­ cible A’s, having just accepted a reduction, but that’s a different question.) ‘Evince non-trivial belief’? Well, if I identify A’s with B’s, then I suppose I must believe in A’s exactly as non-trivially as I believe in B’s. Or so it seems – but really I don’t know the difference between believing in A’s trivially and believing in A’s non-trivially. Here’s something I can understand, though: A’s loosely speaking exist and are identical to B’s, whereas A’s strictly speaking don’t exist. (Because the B’s are a mediocre

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candidate to play the role of the A’s, not clearly good enough and not clearly not good enough.) Sometimes maybe it’s this that lies behind apparent doublethink over whether the A’s got identified or whether they got eliminated. Pages 22–23. I don’t at all understand this business about creating new relations, if it isn’t just a metaphor for renaming old relations. Page 26. Fine to say that propositions have relevant complex inner structure – in fact that’s my own view, since I took them to be classes of ‘concrete’ worlds. (I could, and maybe should, have bypassed the mystery of membership by taking them to be mereological sums of worlds instead.) My stipulation that propositions are ­simples was not a substantive thesis, it was just a matter of considering alternative the­or­ies one at a time. That’s it. Thanks very much for showing me the paper. Plenty of interest in it, and plenty worth discussing. Eventually you’ll get a draft from me called Parts of Classes, which is of some relevance to some of these matters.2 Yours, David Lewis c: Bricker, van Inwagen

194.  To Charles Pigden, 22 September 1989 [Princeton, NJ] Dear Charles, My Christchurch conference paper consisted of much of Chapter 3 of Parts of Classes, a short book now in close-to-final draft, with a new introduction tacked on. I’m sending you a copy of PoC separately,* and I enclose a copy of the new introduction. I keep finding that McCloskey1 has been one place or another ahead of me. Does that mean it would be rewarding actually to read McCloskey? Well, if somebody would just edit a 250 page selection, I’d read it like a shot. But as is . . . . Thank you very much for the references. I don’t see that Freedom and Reason pp. 48 ff. helps Hare a whole lot.2   (Lewis 1991).

2

*  Pages 20 and 60 have traded places, thanks to the photocopy shop trying to make copies of the draft look like books. 1  H.J. McCloskey.   2  (Hare 1963).

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PoW has little to say against primitive modality, except that the primitive ap­par­atus would have to be something a good deal more than just that of standard modal logic, or even modal logic with an ‘actually’ operator added. I bet that however it’s done, if the primitivist’s modal apparatus is adequate to say the things we do want to say, it will turn out to look like quantification very thinly disguised. Max Cresswell is writing a book that argues this. But suppose primitivism could get by with just a primitive box or diamond. Then would it be worth the ontology to get rid of that primitive? I think so, but I can’t say why. Well then, would it likewise be worth the ontology of sets to get rid of primi­tive plural quantification? I think not, but I can’t say why not. Fortunately, the issue doesn’t arise. The second question is as hypothetical as the first. (1) Even if you have plural quantification, even if you have it on top of mereology, you still need sets. The system of plurality and composition yields only a fragment of mathematics. It’s a strong enough fragment to be /of/ interest, maybe strong enough to tempt revolutionary hotheads to dump the rest of math, but in the end I say it’s not enough. Not enough for the literal truth of the mathematics we were taught, I mean. (For all I know, it might be enough for the scientific applications of mathematics.) As you say, it’s a matter of putting off the evil day, not avoiding it forever. But how much is mere postponement worth? (2) Even if you have sets, even if you have proper classes besides, you still need plural quantification to say all the things you ought to want to say, such as that whenever there are some things eligible to be members, even if they are not all and only the satisfiers of some formula, there is a class of them; and if in addition there is an upper bound on their rank, there is a set of them. By the way, why did you say it’s an extensionalist prejudice that militates against plural quantifiers? What’s unextensional about them? This seems like guilt by as­so­ci­ ation: they’re associated with second-order logic, which in turn is associated with quantification over properties. But if (monadic) second-order logic is understood as plural quantification, that’s an alternative to taking it as quantification over properties. Right, I deny that ‘Lutheranism’ is true at any possible world.3 More simply, I deny that ‘God exists necessarily’ is true at any possible world. What’s more, I deny that ‘Some grandfather is childless’ is true at any possible world. Right, we have consistent counter-possibles. Put another way: narrowly logical ‘possibility’ goes beyond possibility: it applies to sentences that, though not possibly true on their intended interpretations, are possibly true on unintended reinterpretations of all

3   A Luther world is a world in which the theology of Martin Luther (which includes the idea that God foreknows each thing necessarily and immutably) is true. The apparent problem for Lewis is that if there is such a world, then it is the only world that exists. See (Pigden and Entwisle 2012, 162).

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but the logical vocabulary. Narrowly logical ‘possibility’ is dual to narrowly logical truth; the notion that Quine accepts when rejecting analyticity. (See ‘Carnap and Logical Truth’.4) In a first-order language, narrowly logical ‘possibility’ means satisfiability in the usual model-theoretic sense, and turns out to be the same thing as deductive consistency in any of many sound and complete deductive systems. So I don’t define modalities in terms of consistency, if consistency means narrowly lo­gic­al ‘possibility’. What’s the problem? How do I define possibility? – Truth at some world. How do I exclude Lutheran worlds? If there is one, then there isn’t also a world where God foreknows differently, let alone a Godless world – but there are such worlds, ergo there’s no Lutheran world. The interesting thing about the Entwistle (et al.) objection is that if it’s anything at all, it isn’t a special problem for Lewis on modality, but rather a whole new paradox of analysis. For it applies quite generally, even to the most trivial and uncontroversial analyses imaginable. Did you think geometers had managed to eliminate the primi­ tive notion of circularity, when they defined a circle as the region consisting of all points at a given distance from a given point? Not at all! For how did they test this proposed new definition to see whether they should accept it, if not against a primi­ tive notion of circularity which they’d kept in the back room to await this use? Yours,

195.  To Richard B. Miller, 28 March 1990 [Princeton, NJ] Dear Professor Miller, Thank you for your letter. I agree: modal statements are not part of the description of any one world, rather they are about the many worlds. The Luther-world description, insofar as it describes a world, describes this world; and then it goes on to misdescribe the rest of the worlds by falsely saying that there aren’t any, or at least there aren’t any that differ from this world. We could say that it’s an extrinsic description – or rather, misdescription – of this world; but then we should say in general that an extrinsic description of something is not entirely about that thing. So that’s how what you said and what I said fit together.   (Quine 1960a), reprinted: (Quine 1976a).

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196.  To Catherine Z. Elgin, 4 April 1990

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But while I agree with you, I have a problem about agreeing. The problem is that I hold a certain modal theory of aboutness, which, while it works fine for contingent subject matters, doesn’t work well for noncontingent subject matters. The system of all the worlds, however, is a noncontingent subject matter. I think I know in a general way how to extend my theory of aboutness to noncontingent subject matters – namely, by admitting impossibilities, about which I’d be some kind of ersatzer – but I’m far from knowing in detail how this extension ought to work. I enclose something about this.1 Sincerely, David Lewis

196.  To Catherine Z. Elgin, 4 April 1990 [Princeton, NJ] Dear Catherine, [. . .] Armstrong. Thank you for the review.1 It’s interesting to compare notes, since I’ll be reviewing Combinatorial Theory for the Australasian JΦ.2 Nothing written yet, but it’s due in September. I see that Bill Lycan will contribute a piece about Combinatorial Theory to a Festschrift-like book on Armstrong.3 I don’t know if he’s written it yet. According to his abstract, he’ll argue that there’s no treatment of fictions that would meet Armstrong’s needs. I’ll be interested in seeing whether what Bill says about Armstrong and fictions resembles what I plan to say, which is as follows. I couldn’t tell (not from drafts – maybe the final version settles it) whether Armstrong had in mind many little fictions, each one a different fiction about how the one world is; or whether it was one big fiction about the many worlds. If it’s the many little fictions, then I ask what en­tities that Armstrong believes in these many fictions may be; for almost none of them are fictions that have ever actually been told. If it’s the one big fiction – this would be the line that Gideon Rosen explores, plus some Armstrong doctrines about what a world is made of – then there’s no problem saying what the fiction is, since it   ‘Relevant Implication’ (Lewis 1988b). See also ‘Statements Partly About Observation’ (Lewis 1988c).

1

  ‘Review: D.M. Armstrong, A Combinatorial Theory of Possibility’ (Elgin 1991).   ‘Armstrong on Combinatorial Possibility’ (Lewis 1992). 3   ‘Armstrong’s New Combinatorialist Theory of Modality’ (Lycan 1993). 1 2

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has been told; it consists of some printed books, On the Plurality of Worlds plus several books by Armstrong. But in that case I say (1) Armstrong doesn’t solve the problem of demarcating worlds from one another (that is, of saying when it’s true according to the fiction of the many worlds that things are worldmates) unless through appeal to facts of totality; and (2) if facts of totality are included, the fiction is an impossible fiction. It says that there exists a fact Fa & Gb & Total(Fa & Gb) – that is, there’s a world consisting of the facts Fa, Gb, and nothing else – but in addition there exist other facts, Hc or whatnot, namely the facts of other worlds. This coexistence is supposed to be impossible. Mind you, I’m not sure Armstrong has to mind admitting that the fiction of many worlds is impossible. Truth according to an impossible fiction needn’t collapse into vacuity. Also (3) I think the notion of truth according to fiction counts as a modal primitive, so whether it’s the many little fictions or the one big fiction, I don’t think Armstrong analyzes modality in non-modal terms. He needn’t mind that, I think. His aim of finding the truthmakers is very different from the usual aim of cutting down on primitives. I think Armstrong has only gradually realized how different his aim in analysis is from the usual, and that’s the main reason why he’s done less than could be wished to help others see what he’s up to. I find nothing ‘hideously wrong’ in your review, nothing much wrong at all, in short I like it a lot. But I do have comments at a couple of points, mainly the paragraph at the bottom of page 2 and top of page 3. You say ‘. . . we might suppose . . . Plainly this won’t do’. I wasn’t sure whether you meant ‘We might suppose it’s true that . . . but plainly this isn’t true’ or whether you meant ‘We might suppose Armstrong thinks that . . . but plainly this isn’t what he thinks’. Anyhow, it’s clear what Armstrong does think. There is not a universal for every predicate; and only if science has discovered all the universals, which may not have happened yet and may never happen, will there be a predicate for every universal. Logical relations of inclusion and exclusion between predicates are beside the point, not a problem. Exclusion or inclusion between genuine universals would be a problem; and then only if they’re atomic, not structural, universals. As you say on page 5, charge threatens to be an embarrassing example. You say straight out that positive charge excludes negative charge. But on this, I think Armstrong would be more open-minded. I’d expect him to say: Science teaches that positive charge at least nomically excludes negative charge, but never says whether the combination of positive and negative charge on a single simple particle is absolutely impossible. Science is also silent, as yet, on whether charge is reducible to a structure of extensive magnitudes. This leaves some room for his position that positive and negative charge are absolutely incompatible only if they are reducible to structures.

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(Still, I think Armstrong does have a problem in this vicinity. His account of nomic exclusion in his book on laws of nature depends on incompatible universals: the way you have a law that no F is G is that for some specific positive H, F lawfully necessitates H, and H is absolutely incompatible with G. So taking the teachings of both books together, it seems you couldn’t have even nomic exclusion between atomic universals.) Again, on page 3 you say straight out ‘two material objects can’t be in the same place at the same time’ and conclude that ‘material objects don’t qualify as particulars’ in the combinatorial scheme. Again I’d expect Armstrong to be more openminded and follow where his theory leads. I think he’d say that if particles are genuine atomic particulars, then they can be at the same place at the same time; if that’s excluded, the exclusion is merely nomic. So I think Armstrong escapes your conclusion that his logical atoms ‘turn out to be utterly unfamiliar’. But he gets out of this at the price of acknowledging some pretty weird possibilities; or rather, being prepared to acknowledge them if that’s the way the scientific cookie crumbles. The atomic particulars might be electrons and quarks; the atomic universals might include unit positive and negative charge; but if so – and it’s up to science to say if it’s so – then combinatorialism says it’s possible to have two particles at the same place at the same time, and possible to have a particle that’s charged both ways at once. Myself, I think these things are not obviously pos­ sible but not obviously impossible. I might have more trouble swallowing some of the weird possibilities Armstrong might be committed to if the atomic particulars turned out to be spacetime points. First paragraph, last line: Armstrong used to be very insistent that for professional purposes he was ‘D.M.’, not ‘David’. I think he may have mellowed, but play it safe. Parts of Classes. Something surprising has happened. See enclosed.4 You can have all of orthodox set-theoretical mathematics without any set-theoretical primi­tive. Mereology and plural quantification do it all. There’s still a hefty ontological, as opposed to ‘ideological’, commitment: there have to be an infinity – a strongly inaccessible infinity! – of atoms. And there are still some first principles that are not as evident as old-time logicists would wish. But nominalism in exactly the sense Nelson asked for, so it seems to me, is triumphant. I’m not perfectly convinced we ought to want nominalistic mathematics, but anyway it’s there for the asking. I think that at the time of my MIT talk last fall, I mentioned that Allen Hazen had shown how to translate quantifiers over relations of atoms within the framework   Presumably, material related to the Appendix to Parts of Classes (Lewis 1991).

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of plural quantification and mereology. Hazen (with a hint from Quine) then saw how his trick could be extended to cover relations of arbitrary things – atoms, fusions of atoms, even atomless gunk or gunk+atoms fusions (provided there are enough atoms available as well). Independently, and near enough simultaneously, John Burgess found a rather different way to do the same thing. Once you can, in effect, quantify over relations (and hence functions) within the framework, you can ‘Ramsify out’ the singleton function and take set-theoretical sentences to be generalizations over suitable functions. Take any sentence in which the primitive predicate of membership occurs: . . . x is a member of y . . . u is a member of v . . . becomes the Burgess or Hazen translation of For all s, if s is a function that satisfies such-and-such axioms [namely, those that characterize a singleton function] then . . . s(x) is part of y and y is a fusion of values of s . . . s(u) is part of v and v is a fusion of values of s . . . Yours,

197.  To Sydney Shoemaker, 17 September 1990 [Princeton, NJ] Dear Sydney, Thank you for your 22 July letter. I was away over the summer vacation and the letter wasn’t forwarded, so I found it only when I returned to Princeton. Recombination. Agreed, the argument runs either way: some recombinations would violate the actual laws, so we’re forced to choose between combinatorial possibility and strong laws. I’m not sure what to say to someone who faces that choice squarely and chooses the latter. I’ve also reached a standoff with Armstrong, who by my lights chooses a compromise: a limitation on combinatorialism, and laws not altogether necessary but only necessitated by a lawmaking relation of universals. He doesn’t really see it as a limitation on combinatorialism, though, and I don’t understand why not. Your Tu Quoque. I complain that the theory of identical endurance through time turns temporary intrinsic properties of things into relations to times. You consider how somebody might complain that realism about universals turns intrinsic properties of things into relations to universals. But I don’t worry about the latter ­complaint,

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do I? (I’m undecided whether to believe in universals, but don’t make this complaint against them.) So why worry about the former? Well, I do worry about the latter complaint. A theory of universals is in danger of misclassifying intrinsic properties as relational, at least if it’s the wrong kind of theory of universals. I take it that when Armstrong says Is it not clear that a’s whiteness is not determined by a’s relationship with a transcendent entity? Perform the usual thought-experiment and consider a without the Form of Whiteness. It seems obvious that a might still be white. So a’s being white is not determined by a’s relation to the Form. (Universals & Scientific Realism, Vol. I, p. 68) he is complaining, correctly, that a theory of transcendent universals does turn intrinsic properties, like whiteness, into relational properties. With this I agree. But Armstrong goes on to say that the argument . . . would fail against the view that the Form is something present as a whole in a (as well as present as a whole in other particulars). And with that I also agree. Having a certain (qualitatively unique) thing present in it as a part is an intrinsic property of a. A theory of immanent universals ought to escape the complaint. The irony, though, is that I’m not sure Armstrong’s own system escapes the complaint. Goodman’s does; I mean the main system of Structure of Appearance, on which color-qualia are present as parts of particular color-spots, and one quale may be wholly present as part of many particular spots. (For all that Goodman calls his system ‘nominalistic’ because it abjures set theory, it is of course a theory of immanent universals.) Goodman’s particulars are mereological sums which include their universals as parts. But in Armstrong, clearly in recent writings though not so clearly in Universals & Scientific Realism, the universal is not present as a part in the particular. The particular (the ‘thick’ particular) consists of states of affairs; a simple state of affairs Fa has the universal F as a ‘constituent’ (along with the ‘thin’ particular a); but being a constituent isn’t the same as being a part. The state of affairs Fa has no parts; it is a mereological atom. So the universal gets into its particular instances by constituency, that is by some sort of unmereological composition. (Armstrong has good reasons to insist that constituency in states of affairs isn’t mereological. Otherwise (1) we’d have the state of affairs Fa automatically existing if F and a do, regardless of whether F instantiates a; (2) we’d lose the distinction between states of affairs with the same constituents, say (Fa & Gb) versus (Fb & Ga), or Rab versus Rba.)

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Armstrong certainly thinks of constituency as a variety of composition, but for myself, I’m not prepared to grant that unmereological ‘composition’ is any kind of composition at all. It seems to me that mereology is the general theory of composition. I think Armstrong has some sort of unexplained primitive relation between the state of affairs and its constituents. Without some reason to think of this relation as if it were composition, I’m not sure he’s entitled to say that the universal is ‘present in’ the particular instance. If not, his realism is transcendent rather than immanent; and then it’s right to turn his own complaint against him and say that he treats intrinsic properties as relational. (Back to Goodman, then? Well, I’m much attracted to that; but there are things I’d want a theory of universals to do that Goodman’s system just can’t handle. For instance, if we grant Armstrong his unmereological ‘composition’, then he can make sense of structural universals that are in turn ‘composed’ of simpler structural universals that are in turn . . . and so on ad infinitum without ever any simples. There’s no way Goodman’s system can make sense of that, yet it does seem like a genuine epi­ stem­ic possibility. Now you see why I’m so undecided about universals. See ‘Against Structural Universals’, enclosed.1) Sorting Intrinsic and Relational. So I’m unappeased by the tu quoque. I still say that your theory of persistence as identical endurance makes all temporary intrinsics into relations to times; I still say that overlap of worlds makes accidental intrinsics into relations to worlds. I agree you can draw a line that falls in the place where we’d have expected the intrinsic-relational line to fall. But if you tell me that this is the intrinsicrelational line, and therefore you haven’t misclassified intrinsics as relational, I won’t agree. I’ll decide whether it is the intrinsic-relational line not by seeing where it falls, but rather by seeing what your theory says about it; and when I see how your theory explains it, I reckon it is after all a line that divides some relational properties from others. (I say this briefly in ‘Rearrangement of Particles’, enclosed.2) The better argument against overlap. The ‘better argument’ is, roughly, that overlap messes up the demarcation of worlds by spatiotemporal interrelatedness. This argument doesn’t seem to me to work against all kinds of overlap. I already say that worlds could have universals in common, if there are universals. We might suppose that worlds share some other things in the same way that they might share universals. Like this. Suppose we have substantival spacetime, in each world, and suppose the spacetimes of two worlds never overlap. Then a maximal spatiotemporally inter­ related portion of spacetime is the spacetime of one world. Suppose also that we have some sort of occupiers of spacetime. A world consists of a maximal interrelated portion of spacetime, together with all the things that occupy regions of that portion of  (Lewis 1986a).   2  (Lewis 1988a).

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spacetime. Occupiers may be shared between worlds: the same occupier (the whole of it) occupies two regions, one a part of the spacetime of world w1 and the other a part of the spacetime of w2. (Like universals? Maybe, maybe not: there’s more to being a universal than just being multiply located. Presumably there never are two duplicate universals, but for all I said there might be two duplicate occupiers.) Occupiers have spatiotemporal relations to one another in a derivative and worldrelative way. If Ithaca and Princeton are occupiers, they are 300 miles apart in w­1 iff the regions of the spacetime of w1 they occupy are 300 miles apart; 29 miles apart in w2 iff the different regions they occupy in w2 are 29 miles apart. The demarcation of worlds by spatiotemporal interrelatedness applies to spatiotemporal relations of regions (or maybe just spacetime points), not spatiotemporal relations of occupiers. This is not the same as my official line in the book, of course, but it preserves the idea of spatiotemporal demarcation while allowing a good deal of overlap. If I wanted to allow more overlap – if I were as unworried about the problem of accidental intrinsics as you think I ought to be – this might be the way to go. Almost-isolated worlds. However, I’m less happy with spatiotemporal interrelatedness as a principle of demarcation for worlds than when I wrote Plurality, thanks to an argument by John Bigelow and Robert Pargetter. (‘Beyond the Blank Stare’, Theoria, recent or forthcoming.)3 Think of a world whose spacetime is divided into two almostisolated halves, connected by just a few temporary wormholes. Suppose further that the opening up of wormholes is causally dependent on what happens beforehand: the inhabitants of one or both of the halves must build a spacewarp machine, or cast a spell, or whatever. So for any one of the wormholes whereby the two halves are connected, it’s true in the world in question that if things had gone a little differently, that wormhole wouldn’t have been there. In fact, it seems that if things had gone not so very much differently, none of the wormholes would have been there, and then . . . . Do you say: . . . and then the two halves would have been completely isolated? Or do you say: . . . and then the world would not have included the other half at all? My position commits me to the second, but doesn’t the first sound better? This illustrates a general recipe for arguments against a position that says X can’t happen. First step: it’s granted that almost-X can happen. Second step: further, almost-X can happen in such a way that the details of the departure from X depend counterfactually on something that could easily have been different. Third step: then it seems true, from the standpoint of the world where almost-X happens, that if things had been a little different then X would have happened. We have a double counterfactual: Almost X ⁄ (Slight difference ⁄ X)   (Bigelow and Pargetter 1987).

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Barring vacuity, a counterfactual can’t be true unless the consequent is possible; so a double counterfactual can’t be true unless the consequent of the consequent is pos­ sible. Bob Adams uses this pattern against identity of indiscernibles. Bigelow and Pargetter use it against the alleged impossibility of spatiotemporally disconnected worlds. You could use it against the alleged impossibility of a universal freeze. (It wouldn’t be quite as neat as the argument you actually gave, though.) You could use it against a Rylean who says it’s impossible for a complete and incurable paralytic to have a mental life. Etc. Of course it’s just a recipe; there’s no guarantee it always works. I could deny the counterfactual about what would have been the case if the spacewarp machine had never been built. Maybe on the whole that’s how I should go, but I’m certainly uncomfortable. Yours, David Lewis c: Armstrong

198.  To Peter van Inwagen, 20 December 1990 [Princeton, NJ] Dear Peter, The one page from your talk on critical studies arouses my interest in the rest. Maybe it’s none of an unbeliever’s business, but if you don’t mind such nosiness and can send a copy, I’d quite like to read it.1 Yes, it’s crossed my mind that my ‘follies of philosophers’ passage in Parts of Classes might put readers in mind of the countless other-worldly donkeys.2 And good on the readers if it does! – I do think the stare is outweighed, but I certainly don’t think it’s weightless. However I’d distinguish two kinds of weird tales from the philosophers. Some incredible tales say there’s less to reality than we usually think: no motion, no time, no beliefs, no evidence, no tree in the quad, no Taj Mahal or Mount Everest, no numbers, . . . . It would seem that if we believed the philosophers who tell us these tales, then we should change our ways not just inside the philosophy room but outside as well. It would seem so – but I understand that the philosopher may have more to add (additions that I take to be much more plausible in the case of the   ‘Critical Studies of the New Testament and the User of the New Testament’ (van Inwagen 1993).   (Lewis 1991, 59).

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Taj Mahal and Mount Everest than in the other cases) about why the disagreement with common opinion is less than meets the eye, and why there’s no call after all to change ­our ways. Other incredible tales say there’s more to reality than is dreamt of in commonsensical philosophy: uncountably many other-worldly donkeys, inaccessibly many simples of whose whereabouts and nature we know nothing (except maybe a via negativa), Mr. abstract Pickwick and Tom abstract Sawyer, . . . . These tales aren’t as bad as the others. They don’t, by and large, ask us to change our mind about the things we take to surround us, and they don’t ask us to change our ways outside the philosophy room. I can believe in the many worlds and carry on just as before. So sections 2.5–2.7 of Plurality . . ., on why I needn’t ‘change my life in extreme and eccentric ways to suit my philosophy’, are essential to support my defiance of the incredulous stare in 2.8. I can believe in the many worlds and carry on just as before. I’m not so sure you could. I once got a paper from a student of Al’s3 which argued that modal realism was atheistic: OK, there are many gods in many worlds, each one causally isolated from the other worlds, but none of them is a necessary being, none is (speaking unrestrictedly) omniscient or omnipotent, so none of them is God. I’m inclined to agree. As to the first point, I’m pretty happy to think that God’s alleged necessary existence has little to do with religion; it’s more a theologians’ and metaphysicians’ fancy than a serious article of faith. The second point is better. Of course I can tell a theist who is also a modal realist to restrict his quantifiers and say ‘allmighty’ and just mean ‘allHis-own-worldmates-mighty’; I can say that no theist who ignored the question of modal realism ever intended that his quantifiers should not be so restricted. It strikes me that the many godlings of the many worlds are not what the believer had in mind, and none of them, whether or not He’s your worldmate, is an altogether appropriate object of worship. What do you think? – it’s not for me to put words in the believer’s mouth. Yours, PS. I recommend, not without reservation but still enthusiastically, David Stove’s The Plato Cult, just out from Blackwell.4

  John Coker. See Letter 181. To John Coker, 5 February 1987.   

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199.  To Peter van Inwagen, 14 January 1991 [Princeton, NJ] Dear Peter, Well, I did so read it with interest.1 If ever you write on the methodology of Tibetan archaeology, I’d quite like to see that too. Being interesting has more to do with the author than with the subject. Anyhow, your paper does touch, briefly but importantly, on one of my ‘interests of record’: having reason versus having a winning strategy in debate, having reason although debate is deadlocked. The Denier – Argle,* Berkeley, van Inwagen – says: ‘Distinguo! The vulgar, and I myself outside the philosophy room, say A; I deny A+ but I affirm A–; I myself intend (henceforth) to say A and just mean A–; and when the rest of the vulgar say A, heedless as they are of the distinction, who’s to say they mean A+ and not just A–?’ (When the vulgar say there are holes in it, who’s to say they mean more than just that it’s perforated?) The defensive move works the same way in different cases, but sometimes it strikes me as fair and convincing, and sometimes not. In Argle’s case it’s OK, in Berkeley’s not. But I don’t understand how the cases differ. And I don’t know whether to put you with Argle or with Berkeley. Who’s to say whether the vulgar are committed to A+? – Not the vulgar, anyway. You can’t just ask them. They like fantastic philosophy and they’ll rise to the occasion. That’s why I’ve sometimes left the rest of the vulgar out of it, and concentrated on the requirement of honesty which says that I myself should be able to believe my own philosophy even outside the philosophy room. But that retreat loses something that I don’t really want to lose. Even if I can defy settled general opinion honestly and consistently, out of the philosophy room as well as in, there’s still something mad about doing so. So it still matters whether a given Denial really does defy the opinion of the rest of the vulgar. Point taken – I think that what Al’s student said was atheistic was the whole shebang: maddog realism, denial of overlap, principle of recombination and all. (Sorry: I should be crediting this student by name, but I’ve forgotten the name.2 Since I file letters alphabetically that means I can’t easily look up the exchange of letters.)   ‘Critical Studies of the New Testament and the User of the New Testament’ (van Inwagen 1993). Argle in the first half of the paper, before he changes position. 2   John Coker. 1

* 

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200.  To William G. Lycan, 26 June 1991

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I don’t think there was supposed to be any problem about omniscience – the problem was with necessary existence and with omnipotence. Yours, PS Did I ever show you my letter to Dick Cartwright about having reason when debate is deadlocked? Copy enclosed.3

200.  To William G. Lycan, 26 June 1991 Sydney, Australia Dear Bill, You might be interested in this draft review of A Combinatorial Theory of Possibility, which includes a certain amount on alternative ways to be a fictionalist about possibilities.1 (By the way, I highly recommend Gideon Rosen’s paper2 cited therein.) It’s meant for the AJP, but it’s so seriously overdue and overlength that it remains to be seen whether they’ll want it. On kettle-biting.3 A world is a mereological sum of worldmates. Correct as it stands, no amendment required. It’s also true that a world is a sum of self-identical worldmates – because there’s no other kind, everything (here the quantifier is absolutely unrestricted) is self-identical. But though the amended definition is correct, the amendment is unnecessary; the unamended definition which didn’t drag in selfidentity was already correct. Likewise, a world is a sum of worldmates each of which either is or isn’t purple. The amendment is permitted but not required, it makes no difference. It should not be said, just because the amendment is permitted, that world-hood is defined in terms of colour. Likewise, a world is a sum of possible worldmates. Since everything every worldmate (unrestricted!) is possible, again the amendment makes no difference. It is

  Letter 701. To Richard Cartwright, 4 September 1989, Volume 2: Part 6: Epistemology.

3

  ‘Armstrong on Combinatorial Possibility’ (Lewis 1992).   ‘Modal Fictionalism’ (Rosen 1990). 3   ‘Pot Bites Kettle: A Reply to Miller’ (Lycan 1991). See also ‘Review of On the Plurality of Worlds’ (Lycan 1988). 1 2

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permitted but not required. It should not be said, just because the amendment is permitted, that worldhood is defined in terms of possibility.* You also suggest that there’s need of a circular restriction to ‘logically coherent’ spatiotemporal (or at least analogically spatiotemporal) relations. I’m not sure what a ‘logically incoherent’ relation would be, if there were any. But if there are none of them (unrestricted!) then there is no need of any amendment to exclude them – again, just as there is no need of any amendment to exclude non-self-identical relations, or relations that both are and are not purple. There’s nothing there to exclude. (On the previous page4 I struck out ‘everything is possible’5 because of a point due to Hintikka. A disunified thing has two parts not spatiotemporally related to one another. Something is eligible to be a worldmate iff it is not disunified. (So Miller’s (1) needs a correction.)6 The unified parts of a disunified whole are not worldmates, so at no world is the disunified whole present in its entirety; and in that sense it is a pos­ sible thing. So although every unified thing is possible, not everything is possible. However ‘worldmates’ already implies ‘unified’. So ‘sum of worldmates’ is OK as it stands, and requires no amendment to ‘sum of unified worldmates’.) Yours, David cc: DMA, Miller

*  ‘Nothing but the impossibility of round square cupolas keeps a round square cupola from being spatiotemporally related to another object’ – Wrong. What prevents it is that there aren’t any (unrestricted) round square cupolas. 4   That is, two paragraphs above. 5   Really, Lewis only struck out ‘everything’, but his meaning should be clear. 6   Miller’s (1) is ‘Individuals are worldmates if they are spatiotemporally related’ (Miller 1989, 477).

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201.  To Charles Pigden, 13 November 1991

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201.  To Charles Pigden, 13 November 1991 [Princeton, NJ] Dear Charles, Thank you for ‘Spread Worlds . . .’.1 Haven’t got to it yet – business before pleasure! – but much look forward to reading it, and to discussing it with Rebecca.2 In the meantime, one thing to say about it and two things about your accompanying letter. Mad-Dog Modal Realism. The name is originally mine, not Lycan’s. At the Chapel Hill conference in 1984, I gave a talk mostly consisting of stuff from PoW, Section 3.4, then in press; and Peter van Inwagen gave a reply that later became his excellent ‘Two Concepts of Possible Worlds’ (Midwest Studies, 1986). Peter wasn’t best pleased to be called a magician, and by way of protest decided to make up his own pejorative name for himself: ‘I will not accept this dyslogistic name for the position I propose to defend. I will call it Unsound Abstractionism, which is an acronym for  Unscientific Naive Superstitious Obscurantist Unenlightened Neanderthal Dogmatic Abstractionism’. For the sake of peace and good humour I responded in kind. ‘Mad-Dog’ was an acronym for ‘Misguided Asinine Deluded Dopy Outlandish Gratuitous’. I’m not sure what Peter thought, but Bill, and then Miller, took it up eagerly. Pricing Policy. I think the price of modal primitivism may be higher than you think, because you need modal notions that don’t reduce to necessity and possibility, or even necessity and possibility and actuality. These notions involve – as the modal realist can say, but the primitivist cannot – comparisons between things in different worlds. In English we express them with modal modifiers that attach not to sentences but, so to speak, to particular places of many-place predicates. (They seem to crop up especially when modality is used in philosophy of math.) I think we have no theoretical understanding of these modifiers apart from what we get via modal realism. ‘If it were that A, then it would be that: if it were that B, then someone would be funnier in the latter case than anyone would be in the former case’. That is, let w be any one of the closest A-worlds to our world, and let v be any one of the closest B-worlds to w; then someone in v is funnier than anyone in w is. Conference. Maybe others besides me weren’t wild about a few days in beautiful Hamilton! However, I definitely do plan to attend the 1992 conference at Otago. Whether Steffi can accompany me remains to be seen (she can only be away about 1   ‘Spread Worlds, Plenitude and Modal Realism: A Problem for David Lewis’ (Pigden and Entwisle 2012). 2   Rebecca Entwisle.

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three weeks, so will have to choose between the NZ conference and the Aus one). Whether I can offer a paper also remains to be seen. In case I can: can you tell me who’s in charge of the program, and what’s the deadline for submissions? Thanks. Yours, c: Rebecca

202.  To Megan McLaughlin, 21 January 1992 [Princeton, NJ] Dear Ms. McLaughlin, Your ‘quasi-urgent’ letter reached me only yesterday, but I hope this will reach you by fax before your Thursday seminar meeting. Why do I postulate that nothing is in two worlds? Not the reason Loux gives on page 47 of his Introduction,1 I think. In fact, I don’t really understand what argument Loux is talking about there. And also not the problem about identity that you mention. If I did think that x was in both W1 and W2 then I suppose I’d say that x just plain has the property of existing in W1 and has the property of existing in W2; and in neither world does x lack either of those properties. Rather, my main reason is a different problem about identity. Suppose again that x is in both W1 and W2. Presumably anyone who believes in trans-world identity also supposes that things sometimes vary in their intrinsic, non-relational properties from world to world. So suppose, for instance, that x varies in shape from world to world: x is round in W1 and not round in W2. This looks like a contradiction: how can the very same thing be both round and not round? (How does saying: ‘but in different worlds!’ help?) Somebody might answer: x stands in the round-in relation to W1 and x does not stand in the round-in relation to W2. So there’s no contradiction; it often happens a certain thing stands in a certain relation to one thing but not to another, as when I’m south of Seattle but not south of Portland. – I don’t like this. It seems to me to ignore the original problem about the property of roundness, and switch attention instead to this relation. I don’t think shapes are really relations to worlds. Somebody might answer: there’s no such thing as a just plain shape property; there are just properties like round-in-W1, square-in-W2, etc. – And again I think the   ‘Introduction: Modality and Metaphysics’ (Loux 1979).

1

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original problem is just being ignored: there is such a thing as the plain, simple property of roundness, and I want to know, without contradiction, whether x has this property or not. Somebody else might answer: think of a world not as a place at which x has a shape, but as an abstract representation, perhaps a linguistic representation, according to which x has a shape. So if W1 is a true representation and so x is just plain round, then saying that it’s not round in W2 is like saying that W2 is a liar who misrepresents x’s shape. That’s no contradiction. – But I don’t buy that because I don’t reduce worlds to linguistic representations. (And this is as close as we can get to fitting Loux’s cryptic words into the picture.) My own answer is, of course, that if x is round in W1, then x is in W1 and x is just plain round; and what’s in W2, and is not round, isn’t x at all, but something else, x’s counterpart. No contradiction between one thing being round and a different thing not being round! I call this argument the ‘problem of accidental intrinsics’. You’ll find it, and also the corresponding argument about identity through time, in On the Plurality of Worlds, section 4.2. I have some less important reasons for denying trans-world identity. One is that it makes trouble for the indexical analysis of actuality. If I were in two worlds at once, saying in both at once ‘The actual world is this world that I’m in!’, I suppose I’d be saying that both the two worlds were actual; but don’t we want to think that there’s just one actual world? Another reason is that I want to say that it’s a vague and context-dependent matter which properties of things are essential. Am I essentially human? Could a robot with humanoid psychology possibly be me? – I don’t think there’s any definite answer either way. If my essence consists of the properties I share with all my counterparts, then my essence can be vague to the extent that the counterpart relation can be vague – which it certainly can be. (An otherworldly robot can be not enough like me to be definitely my counterpart, but also not enough unlike me to be def­in­ ite­ly not my counterpart.) But how can identity be vague? Finally, I want to say that I might have been twins. So here’s x in W1; and here are the twins y and z in W2; and y and z have equal claim to be x. Well, it’s easy to see how they could have equal claim to be counterparts of x; but how could they have equal claim to be identical to x? Either they are or they aren’t; and if they are both identical to x, then they must be identical to each other, which they’re not (or they wouldn’t be twins, there’d be just one of them). So, lots of reasons; but nowadays, the problem of accidental intrinsics is my main reason. I can see ways for a defender of trans-world identity to get around the other reasons: see the discussion of ‘extreme haecceitism’ in On the Plurality of Worlds.

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I certainly think there are worlds that don’t have anything just like our sort of space and time. Whether there are worlds that don’t have any sort of space and time, no matter how unlike our sort, is partly a question about what sorts of worlds there are, and I don’t claim to know the answers to all such questions. And partly it’s a verbal question about how different from our sort of space and time you could get and still have something that can be called ‘space’ and ‘time’ at all. Someone said that if he dropped out of college right now, he’d have an effect on his counterpart. What effect did he have in mind? I don’t know: but maybe he thought ‘If I do, my counterpart will have the property “being the counterpart of a drop-out” and if I don’t, then my counterpart won’t have that property’. If that was the idea, I think it’s wrong. Here’s Fred-1 in one world, staying in college; and here is Fred-2 in another world, dropping out; and there’s Fred-3 in a third world who never went to college in the first place. The Freds are all counterparts of each other. The Fred of this world – maybe he’s Fred-1 or maybe he’s Fred-2 – says: ‘whether Fred-3 is the counterpart of a drop-out depends on whether I drop out’. That amounts to saying: ‘whether Fred-3 is the counterpart of a drop-out depends on whether I’m Fred-1 or Fred-2’. Not so: either way, Fred-3 is still the counterpart both of drop-out Fred-2 and of stay-in Fred-1. By the way, there’s absolutely no apology required either for ‘warmly put’ wording or for the cartoon in your letters last year. Best regards, Sincerely, David Lewis

203.  To William G. Lycan, 4 June 1992 [Princeton, NJ] Dear Bill, To think you called me a Meinongian!1 Round squares, at whatever world or mountain* they might be, would be things about which you could only tell the (whole) truth by contradicting yourself. For they’d have corners, they’d have no corners; their sides would be straight, their sides would not be straight; etc. Agreed, I think? There are no subject matters, however marvellous, about which you can tell the truth by contradicting yourself. That’s   See ‘Two-No, Three-Concepts of Possible Worlds’ (Lycan 1990, esp. 225–7). was Plumwood Mountain I had in mind, but before I could publish, both Richard and Val had moved elsewhere. 1

*  It

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204.  To Gideon Rosen, 16 June 1992

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because no contradiction, regardless of subject matter, is true. Can I prove from something still more obvious and certain that no contradictions are true? – I doubt it very much. Your impossibilism has met with a reductio ad absurdum, it has ended in contradiction (without any effort on my part). But if that reductio doesn’t move you, I don’t see what I can say that would move you more. The standoff between me and the paraconsistentists (whom you’ve now joined) has long been my favourite ex­ample of a philosophical impasse. I enclose a copy of a letter to Richard Cartwright that says more about what I think of such impasses.2 If you were right about the existence (speaking unrestrictedly) of impossibilia, then I think you’d probably also be right about the need for a primitive modal distinction to distinguish them from the possibilia. But since impossibilia don’t exist (unrestricted), as has been shown by reductio ad absurdum, the primitive distinction isn’t needed. I’m happy enough about ersatz impossibilia, by the way. I also enclose a copy of a letter to Margery Naylor3 about why I think the balance of advantages between ersatzism and mad-dog realism tilts one way for possibilia and the other way for impossibilia. Or rather, I’m happy enough that you can have ersatz impossibilia if you want them; I’m less sure that they have any very useful applications. The problem for applications is that you’re likely to need to distinguish blatant from subtle impossibility, and I don’t have much idea how to do that. I discuss one possible application at the end of the enclosed paper (siding with Canberra against Pittsburgh).4 Off to Aus not yet, but soon: leave 20 June, stop briefly in San Francisco and Auckland, reach Melbourne 26 June. Yours,

204.  To Gideon Rosen, 16 June 1992 [Princeton, NJ] Dear Gideon, Thank you for ‘A Problem for Fictionalism . . .’.1 It’s very interesting. I think I know what I must have said to you when you told me about it, and I think I also know why you didn’t see how it helped.   Letter 701. To Richard Cartwright, 4 September 1989, Volume 2: Part 6: Epistemology.   Letter 177. To Margery Naylor, 14 January 1986.    4  ‘Relevant Implication’ (Lewis 1988b).

2 3

  ‘A Problem for Fictionalism About Possible Worlds’ (Rosen 1993).

1

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First, a small point about page 6. ‘Armstrong . . . rejects non-spatiotemporal objects, and so is chary about the employment of set-theoretic constructions in metaphysics’. Both clauses are right, but the ‘so’ is wrong. Armstrong has long thought that sets are spatiotemporal and naturalistically OK. (Maybe not pure sets, but there’s plenty of constructing we can do without those.) He’s tried on various different explanations of why sets are naturalistically OK, and the current explanation is indeed a recent development, but I think he’s thought sets were OK at least ever since the 1978 universals book. He’s chary about – I’d rather say, he’s quite hostile to – set-theoretic constructions in metaphysics for a different reason. It’s like ‘What Numbers Could Not Be’.2 All these constructions involve arbitrary choices. Armstrong thinks you can’t be ontologically serious about X’s and then say that it’s an arbitrary choice whether an X is this set-theoretic construct or that one. I’ve tried saying ‘Well OK, I’m not ontologically serious about X’s, exactly; I’m serious about each of several different settheoretic X-candidates, and I reckon the arbitrariness is just semantic indecision about which candidates deserve the name of X’s’. But he usually regards this as a very damaging retreat from seriousness about X’s. Here’s my first reaction to your point this time, and I think it must have been my first reaction before. Besides the ambiguity you mention in ‘at a world’ there’s another ambiguity: the ‘in the fiction’ prefix can come and go. I can say that Sherlock Holmes didn’t exist, and then I can say he lived in Baker Street. No worries, the first is unprefixed, the second is tacitly prefixed, and so they’re true together. As always, the right disambiguation is the one that makes the message make sense. So a many-worlds fictionalist can say ‘There are many worlds’ and ‘At every world, there are many worlds’ (tacitly prefixed), and still say ‘There’s only one world’ (unprefixed) and all he says is true by his lights. Likewise, mutatis mutandis, for a compound fictionalist. That was my answer to you. Why it puzzled you, and why it’s misguided, is that it’s addressed to a position different from yours. Suppose you said (1) modality translates into many-worlds talk in just the way modal realists say it does, and (2) modal and many-worlds statements alike are fictional, true only if (explicitly or tacitly) prefixed. Then I think what I say above would be the right answer. But I was forgetting that you’re not that kind of fictionalist. For you, the prefix is built into the analyses of modal statements, and the modal statements themselves are nonfiction. So I don’t know what to suggest for a solution; except maybe to consider converting to the different kind of fictionalist that I carelessly mistook you for. Yours, c: Armstrong   (Benacerraf 1965).

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205.  To Charles Pigden and Rebecca E.B. Entwisle, 19 January 1993

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205.  To Charles Pigden and Rebecca E.B. Entwisle, 19 January 1993 Princeton University Princeton, NJ Dear Rebecca and Charles, I’ve been reading the post-Adelaide draft of your ‘Spread Worlds’ paper,1 and it seems to me that something goes wrong starting on page 7. Either I missed it before, or it wasn’t there before. The overall plan of your paper is to present ‘a problem for David Lewis’ by arguing that I’m committed to spread worlds and then showing that spread worlds are big trouble. An obstacle to this plan is that my official principle of plenitude – namely, recombination – doesn’t yield spread worlds. A way around the obstacle would be to discover some unofficial extra principle of mine that goes beyond recombination and does yield spread worlds. Accordingly, you’d like it if I held a principle saying that any consistent description describes a being somewhere in lo­gic­al space (a world, or a less-than-world-sized individual, as the case may be). Well of course I do think this: a description is consistent iff possibly it (truly) describes something iff there’s some possible being it describes, wherefore indeed any consistent description does describe some possible being. True but trivial; useless to settle what possible beings there are; and, in particular, silent on the question of spread worlds. If a (describable) spread world is possible, then some description of a spread world is consistent; if not, not. Understanding ‘consistency’ this way, you yourselves have refuted the offhand supposition that the description of the Lutherworld (for example) is consistent. I accept that refutation happily, just as you’d expect. So far, so good for me. But what if you could find evidence that I accepted some less trivial principle of consistent describability? Some principle that gave us an independent handle on what descriptions are consistent – and in particular, told us that descriptions of spread worlds were consistent? That would be trouble for me, sure enough. I think you think you have found your evidence, namely in the polytheism footnote on page xi of Papers I. I think you think that my reference there to consistency of descriptions signals that I was appealing to some sort of non-trivial principle of consistent describability to establish the existence of a large number of possible gods. And if my supposed non-trivial principle of consistent describability can yield gods, mightn’t it yield spread worlds too? 1   ‘Spread Worlds, Plenitude and Modal Realism: A Problem for David Lewis’ (Pigden and Entwisle 2012).

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Not so. The polytheism footnote is an assertion, not an argument. But of course I did have an argument in mind. I think you think I had in mind an argument from some sort of non-trivial principle of consistent describability. Like this: there are so-and-so many goddescriptions that are in some appropriate sense consistent (or rather, so-and-so many conflicting consistent god-descriptions), ergo by the supposed principle, there are at least that many gods. – A reasonable guess, but dead wrong. Actually, the argument I had in mind was as follows. Following Quine, let a Democritean world consist of continuum many spacetime points, some or all or none of which are occupied by matter (see PoW 90–1); and let me confine my attention here to Democritean worlds of finite volume. The quantifiers below aren’t restricted to actuality. (1) There is at least one god. Premise. (2) There is at least one Democritean world. Premise. (3)  If there’s one Democritean world, there are at least beth-2 different ones. Recombination. (Beth-2 is the number of subsets of a continuum.) (4) For any god and any Democritean world, there’s a world where a duplicate of that god coexists with a duplicate of that Democritean world, and with nothing else. Recombination. (5) A duplicate of a god is a god, and a duplicate of a Democritean world isn’t a god. Premise. (6) No two Democritean worlds have identical duplicates. Premise. (7) At least beth-2 worlds contain gods. (4), (5), (6). (8) No god is contained in more than one world. Premise. (9) There are at least beth-2 gods. (7), (8). Quod erat demonstrandum. So it’s just my usual argument from recombination that there are at least beth-2 worlds, souped up to say that there are beth-2 different worlds with gods in them, hence beth-2 different gods. Consistent describability has nothing to do with it. Suppose instead I had tried an argument from some sort of principle of consistent describability. Note two things. First, most of these worlds aren’t describable by sets of sentences of finite length from a finite alphabet; because to describe a (patternless) Democritean world, you need to have a name for each point in a con­tinuum, and there aren’t continuum many different finite strings from a finite alphabet. Indeed, no matter what fancy system of description you might invent, there are only countably many finite sentences from a finite alphabet; so only continuum many sets of such sentences, so at most continuum many consistent sets; so you don’t have enough different consistent descriptions that each of the beth-2 different worlds can get one. Second, if I’d concentrated on descriptions of the gods, never mind their

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205.  To Charles Pigden and Rebecca E.B. Entwisle, 19 January 1993

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Democritean companions, there would still be only continuum many descriptions, hence at most continuum many consistent ones, so not enough to give me as many as beth-2 different describable gods. This is another reason, besides the one you mention, why ‘Lewis no doubt believes there are more things than we can consistently describe’. Indeed, even within actuality, if spacetime is a continuum, there are more things (viz. points) than we can describe. (Incidentally, your notation for infinite cardinals is screwed up. ‘2-to-thealeph’, with the ‘aleph’ unsubscripted, doesn’t mean anything. If you don’t want to use the ‘beth’ notation, you could write a double exponential: ‘2-to-the-(2-to-thealeph-null)’ is the long-winded way of writing beth-2. If you knew that the generalized continuum hypothesis was true – but alas, there’s no way of knowing – life would be easier: for in that case, beth-2 = aleph-2 = 2-to-the-aleph-1, where aleph-1 = 2-to-the-aleph-null.) But wait. If that was my argument, you ask, why did I mention consistent describability at all? Why did I, as you put it, ‘make the possibility of consistent description the criterion of existence’? – Well, I didn’t. Look again (emphasis added): ‘if . . . a being does not have to satisfy some inconsistent description to be a god, then . . .’. You paraphrase that to ‘If a god does not have to satisfy an inconsistent description in order to be . . .’. But there’s a big difference between being a god and just being! Here’s why I said that. Just by recombination (from the actual world) we can show the existence of some characters who seem plenty god-like to me, vulgar polytheist that I am. For instance there are otherworldly beings who play the Thor-role; fix on one of them (let’s pretend) and call him ‘Thor’. If indeed Thor is a god, we have Premise (1). Myself, I’m happy to call Thor a god. But I expect flak from lofty theologians who have more exalted notions than I do of what it takes to be a god. These theologians have some degree of linguistic authority. So if vulgar polytheists say Thor is a god, and lofty theologians say he hasn’t got what it takes, then I suppose it’s to some degree a matter of semantic indecision (over the linguistic community as a whole) whether he is or whether he isn’t. Now, I think that some of the things that some lofty theologians sometimes say about what it takes to be God are inconsistent. (I’ll use the singular, and capitals, to signify loftiness.) For instance, they may say that the genuine God, properly socalled, is causa sui: He causes Himself. (And He does so directly, unlike a time traveler who is his own grandfather; and the whole of Him causes the whole of Him, unlike a self-perpetuating process in which the early parts cause the later parts.) I think that’s inconsistent. And not in some interesting sense that would be needed in order to state a non-trivial principle of consistent describability – it’s inconsistent in my official and usual sense, i.e. there’s nothing anywhere in logical space that’s truly described by a description that includes being causa sui.

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Similarly, I think it may well be inconsistent to say that God is simple or changeless or outside of time and then also say that He thinks; I think it’s inconsistent to say that He’s omnipotent in a sense that involves an absolutely necessary connection between His will and the world that obeys His will; I think it’s inconsistent to say that He exists necessarily (you know the reason: because the Plantinga-world is a spread world); and so on. There might even be an inconsistency between His alleged perfect goodness and His alleged allowing of evil, though that’s the one I’m least convinced of. So my conclusion in the polytheism footnote was that either there are no Gods or else there are beth-2 gods, depending on whether we adopt an inconsistent conception drawn from lofty theology or a more vulgar but consistent conception. You’re right to think that Recombination starting from actuality isn’t enough to settle exactly what there is. It would be nice to say more; and it would be even nicer to say more in a general and positive way. But the further things I know of to say seem to me sometimes true but trivial; sometimes false, according to the modal opinions that are our starting point; sometimes too specific to be much help; sometimes too unspecific to be much help. (I’m willing, for what it’s worth, to say true things that aren’t much help – but you needn’t hope to find them very helpful.) Trivial: everything that could exist does. Trivial: every description that could pos­ sibly describe something does describe some possible thing. False: for every description that doesn’t imply a contradiction by first-order logic alone, or by logic plus a certain finite list of axioms, there is something it describes. False: for every description that strikes us offhand as possibly describing something, there is something it describes. Too specific: there exist things located in time but not in space; there exist things bilocated in spacetime. Too unspecific: there exist particles different in kind from any that are found anywhere at our world. Too unspecific: there are enough things altogether – enough things in all the spacetimes of all the worlds, plus things (if any) in worlds but unlocated in spacetime and things (if any) outside the worlds altogether – to afford a model of standard iterative set theory. Lacking satisfactory things to say, I say less than you and I both would prefer. I guess this is a problem for me, sure enough. But I don’t think it’s a very big problem. Who said I had to know everything? (It’s not that my theory is ‘unacceptably vague’, as you say near the end. If I say the train arrives sort of sixish, that’s vague. If I say the train arrives sometime after 5:45 exactly and before 6:15 exactly, that’s not at all vague, but I’ve said less than you might prefer to be told.) Yours, David Lewis

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206.  To Quentin Smith, 4 October 1993

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206.  To Quentin Smith, 4 October 1993 Princeton University Princeton, NJ Dear Professor Smith, Thank you for your forthcoming paper on anthropic explanations.1 I look forward to reading through it; but for now, let me comment without delay upon your comparison on page 8. What you say about three differences between ‘Lewis’s worlds’ and Leslie’s or Carter ‘worlds’ seems to me exactly right. Myself, I wouldn’t call the Leslie-Carter ones ‘worlds’ at all – I’d call them world-like parts of our actual world. However, I think there could be an anthropic reasoner who was betwixt and between. He might say, as I do and Leslie does not, that the many worlds are al­together unrelated spatiotemporally and causally; that they include worlds where even the most fundamental laws of nature are different, or where there are no laws at all; and that they include worlds inhabited by spirits and gods. And yet he might also say, as Leslie does and I do not, that our best reason for believing in the many worlds is that they would afford anthropic ‘explanations’ of the ‘fine-tuning’ that permits life. But though there’s a possible position here, I’m not sure I know of anyone who holds it. Sciama, maybe? – he spoke of an ‘extreme form of the anthropic principle’ which ‘invokes the existence of all conceivable logically self-consistent universes’, but whether this was modal realism or careless rhetoric I do not know. I myself have at least some sympathy for anthropic reasoning, but I don’t at all wish to rest my case for modal realism upon it. Because (1) world-like parts of this world would suffice for anthropic reasoning, and (2) I want a case that would survive even if the remarkable ‘fine-tuning’ turned out to be all a mistake, and (3) I’d rather make a case that starts from common ground rather than specialist knowledge. See On the Plurality of Worlds, pages 132–3, for a very brief discussion of point (1). Sincerely, David Lewis c: Leslie

  ‘Anthropic Explanations in Cosmology’ (Smith 1994).

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207.  To Jan Cover and John Hawthorne, 31 January 1994 [Princeton, NJ] Dear John; Dear J.A. Cover, Thank you for sending me your paper ‘Leibnizian Essentialism . . .’.1 I’ve read it with interest. I’m not qualified to comment on the question of Leibniz exegesis, except to say that I found your line interesting and plausible. I did want to say, however, that I think my own position is closer than you think it is to that of your Leibniz who accepts transworld identity of indiscernibles. Both the following two points appear in section 4.2 of On the Plurality of Worlds. First, your footnote 48 is literally true but misleading. I have no opinion about whether Armstrong-style universals exist or not. They are not ‘in my ontology’ in the sense that I am committed to their existence; neither are they outside my ontology in the sense that I am committed to their non-existence. But if they do exist, then I say they are transworld identical – unit negative charge is wholly present wherever and whenever there is an electron, whether in this world or in another. This universal, if it exists, is part of all electrons, therefore part of all electron-containing worlds. Second, my main argument against transworld identity (in the sense of overlap, something wholly present as part of two different worlds) is the problem of accidental intrinsics. I say that this argument does not apply against transworld identity of indiscernibles. A second, but far weaker, argument still does apply, at least if the transworld indiscernibles include language-users. Suppose I’m in two worlds at once, saying in both that there will be a sea fight tomorrow in ‘the’ world I’m in; then what I say suffers from indeterminacy of reference; and if there’s a sea fight the next day in one of the two worlds I’m in but not the other, it suffers also from in­de­ter­min­ acy of truth value. Myself, I regard this as an unwelcome conclusion and a drawback of the supposition; but of course there are many who’d welcome it! Yours, David Lewis

  ‘Leibnizian Essentialism, Transworld Identity, and Counterparts’ (Cover and Hawthorne 1992).

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208.  To Peter Menzies and Philip Pettit, 6 May 1994

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208.  To Peter Menzies and Philip Pettit, 6 May 1994 [Princeton, NJ] Dear Philip and Peter, I’m puzzled by your paper in defence of modal fictionalism.1 I agree that it’s peculiar that fictionalism should be shot down by a mere technical bug. The issue ought to be whether the ideological extravagance of primitive truth in fiction is better or worse than the ontological extravagance of the many worlds. I also agree that the best hope for a rescue is to try some fancier scheme of fictionalist translation. --But I don’t understand how your rescue works. The problem was that by the fictionalist’s lights, (6) Necessarily, there are several worlds is false; whereas Gideon’s original fictionalist translation of it, (5) According to PW, for all worlds w, at w there are several worlds is true. No good. The fictionalist translation of (6) ought to be a falsehood by the fictionalist’s lights, anyway. You produce truths (5*) and (5**),2 and you say that they are not correct fictionalist translations of (6) – OK so far. (Almost OK, but see below.) But now show me the falsehood that is your fictionalist translation of (6). Is there any? Maybe not – maybe what you’re saying at the end is that fictionalism simply shouldn’t offer a translation of (6). If not, I need to know better why not. Further comments. Whether it rescues fictionalism or not, your (5*) bothers me because the phrase ‘those worlds’ should have a plural antecedent, but all it has is a singular antecedent. (Or rather, it might as well have had. ‘All worlds’ is gram­mat­ ical­ly plural, to be sure; but since you could just as well have written ‘for any possible world w’, that doesn’t help.) I suggest some Boolos-style plural quantification within the prefix, to replace (5*) by (5#) According to PW, there are many possible worlds such that for any one of them, w, at w there are several of them. The underlined part3 is a standard beginning that could head any translation. Think of it this way. First I, the modal realist, am required for some reason to put   ‘In Defence of Fictionalism About Possible Worlds’ (Menzies and Pettit 1994).   ‘(5*) According to PW, for all possible worlds w, at w there are several of those worlds’ (Menzies and Pettit 1994, 30, their italics). ‘(5**) According to PW, for all PW-worlds w, at w there are several PW-worlds’ (Menzies and Pettit 1994, 31). 3   That is, the italicized part of (5#). 1 2

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my translations of modal sentences into standard form, always beginning with ‘there are many possible worlds such that . . .’; and then the fictionalist applies his prefix to that. Your (5**) also bothers me a bit, because I’m supposed to understand what a fictionalised quantifier is. But I don’t. I understand what a fictionalised sentence is, so I understand what a fictionalised quantified sentence is. And I understand what an ordinary quantifier over fictional entities would be if the fictionalist believed in such entities, which he doesn’t. But what you’re giving me appears to be neither of these things that I understand. --You say later that I translate (8) Necessarily it is possible that blue swans exist by a sentence (9) in which the at-modifier is ambiguous.4 I agree that the at-modifier in (9) is ambiguous. But I disown your ‘at2’-modifier, and I don’t agree that (9) is my official translation of (8). Assume first that (8) is rewritten in quantified modal logic as: (8.1) Nec Pos Some x (Blue x & Swan x). Then follow my translation rules in ‘Counterpart Theory and Quantified Modal Logic’, step by step. By T1, the translation is (8.2) [Nec Pos Some x (Blue x & Swan x)]@. By T2i, taking the case with no variables free in Φ, this is (8.3) All w, if World w, then [Pos Some x (Blue x & Swan x)]w. By T2j, again taking the case with no variables free, this is (8.4) All w, if World w, then Some v, World v & [Some x (Blue x & Swan x)]V. By T2h, this is (8.5) All w, if World w, then Some v, World v & Some x (In x,v & [Blue x & Swan x]V). By T2c, this is (8.6) All w, if World w, then Some v, World v & Some x (In x,v & [Blue x]V & [Swan x]V).

4   ‘(9) For all worlds w, at w there is a world wʹ at which blue swans exist’ (Menzies and Pettit 1994, 32, their italics).

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208.  To Peter Menzies and Philip Pettit, 6 May 1994

407

By T2a, this is (8.7) All w, if World w, then Some v, World v & Some x (In x,v & Blue x & Swan x). That completes my official translation. But by ordinary predicate logic we can drop the vacuous quantifier, and its restricting clause, to obtain a simpler logical equivalent of (8.7), (8.8) Some v, World v & Some x (In x,v & Blue x & Swan x). In plainer language: some world has blue swans in it. Your second ‘at’ in (9) is indeed an ‘at1’. It does indeed give way to a restriction to things in world v. But the first ‘at’ was not ‘understood in a relational way’ in my translation. Rather, it vanishes altogether, by reason of the vacuity of the first quantifier. --Now when it comes to (6), of course I don’t stand by this official translation scheme; because I take (6) to be true, and I don’t think several worlds are ever in one world. But I claim that restriction of quantifiers is a contextual affair, and restrictions go away when they’d make hash of what is said. So my translation of (6) involves not a relational ‘at2’, but rather a vacuous initial quantifier All v (if world v, then (Exist several w (World w))). That quantifier, and its restricting clause, can be dropped to give Exist several w (World w). That’s (equivalent to) my realist translation of (6). That’s false by your fictionalist lights; you think it’s just part of my fiction. So that’s what I hand over to you fictionalists, challenging you to translate it into something you deem false. Yours, David Lewis c: Brock, Rosen

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209.  To Robert C. Stalnaker, 26 April 1995 [Princeton, NJ] Dear Bob, The point you were arguing at dinner has expanded; and the more it expands, the more it convinces. Here’s how I’ve written it up for inclusion in some later draft of ‘Elusive Knowledge’.1 [. . .]2 --I liked ‘What Possible Worlds Could Not Be’ very much.3 It helped me a lot to understand how you – and many more – see the matter. But thereby it also helped me to understand better how I disagree. I’m afraid I am inclined to think that you, along with Carnap, are trying to occupy a middle ground that is not really there. Couldn’t have put it better myself! I do call you and Carnap quasi-realists; and I don’t accept the reply that you’re willing to say all that a realist would say. Yes, you are. But the trouble is that you’re willing to say more than the realist does. Your positive statements are all that a realist could wish; except that they stop too soon, and not out of professed ignorance. But there are also your rejections of questions and your disclaimers, and it is these that seem to me to render your realism quasi. Sometimes your liberal Platonist sounds like a lot like a structuralist. A math­ em­at­ic­al structuralist, as I conceive of him, thinks that there exist ever so many good candidates – indeed, isomorphic candidates – to play the role of the number system, or the hierarchy of sets, or whatever. He sees nothing to be gained by making his official arbitrary choice among the many candidates; and he takes to heart the supervaluationist principle that what’s true on all ways of making the unmade arbitrary choice is just plain true. He rejects questions, and he falls silent, about matters – matters not of mathematics but of metaphysics – which would require making the choice. But such a structuralist is a realist about something, though it may be something a lot less structured than the alleged uniquely correct candidate for the role would have been. He is committed to the existence of all the many candidates. Or he is committed to the inaccessibly infinite supply of modelling clay out of which each of the many candidates is to be built. That’s now my own position about math; see the appendix to Parts of Classes and, for the final step that came too late for the book,   (Lewis 1996).   Concerning the Rule of Actuality. See ‘Elusive Knowledge’ (Lewis 1996, 554–5). 3   (Stalnaker 1996b). 1 2

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210.  To Hud Hudson, 8 May 1995

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‘Mathematics is Megethology’, Philosophia Mathematica (1993). Presumably there could be a structuralist modal realism; but I’d still want to know, in the modal case as much as in the mathematical, just what is this abundant modelling clay, commitment to which makes structuralism work. Yours,

210.  To Hud Hudson, 8 May 1995 Princeton University Princeton, NJ Dear Prof. Hudson, Thank you for your paper.1 I agree: where Kants is the whole of a certain transworld cat-fusion, ‘Necessarily Kants doesn’t exist’ is true; whereas ‘Kants exists’ is also true, at least on one good disambiguation. Likewise, ‘There are many worlds’ is true on at least one good disambiguation; whereas ‘Possibly there are many worlds’ is false. I may be a little less tied than you think to an official fixed choice of disambiguations; when it comes to tacit restrictions of quantifiers, I think the right disambiguation in any given context is, within limits, the one that makes the message make sense. The oddity you raise turns out to be of extreme importance to the project of ‘modal fictionalism’: the idea that modal realism is a fiction, but modal realist ana­ lyses should be taken as tacitly prefixed by ‘according to the fiction of many worlds’. Thus a fictionalist analysis of ‘There might have been blue swans’ would come out: ‘According to the fiction of many worlds, there is a world with blue swans in it’. See Gideon Rosen, ‘Modal Fictionalism’, Mind 1990, 327–254; Rosen, ‘A Problem for Fictionalism About Possible Worlds’, Analysis 1993, 71–81; Harold Noonan, ‘In Defence of the Letter of Fictionalism’, Analysis 1994, 133–139; Rosen, ‘Modal Fictionalism Fixed’, Analysis 1995, 67–73. (Best read in that order.) Sincerely, David Lewis c: Rosen

  ‘Brute Facts’ (Hudson 1997).

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211.  To Allen P. Hazen and David Kaplan, 4 October 1995 Princeton University Princeton, NJ Dear Allen and David, I’m trying, on behalf of John Burgess and Gideon Rosen, to get clear about the early history of two gadgets related to actuality operators in modal logic. (Or ‘now’ operators in tense logic – I won’t much bother to distinguish the tense-logical case from the modal.) My impression is that they were known to me years before any appearance in print we’ve been able to find; that I may well have got them from one or both of you, and maybe one or both of you should be credited with their invention; that they’re anyway so close to areas of your interest that you’re very likely to know where they came from. The first is the idea that we might have modal or actuality operators that, so to speak, modify not a sentence but rather one place of a two-place predicate. The examples I know involve modalized or tensed comparatives. Suppose for simplicity that I used to be so opinionated that I had only one belief world. And suppose I used to think that your yacht was longer than it was – in the sensible, not the silly, sense. We all know how to formulate this if we’re willing to quantify over lengths, or over some sort of entities that serve as surrogates for lengths. (Surrogates could for instance be numbers understood as measuring length in inches; or they could be this- or other-worldly exemplars of various lengths; or . . . .) Then we say: for some L, L is the length of your yacht, but I used to think that: for some Lʹ greater than L, Lʹ was the length of your yacht. OK; but what if some sort of nominalist and actualist comes along? He doesn’t believe in lengths, or in any of the serviceable surrogates for lengths that might be offered. Well, you might offer him the logical form: Your yacht [as-I-used-to-thinkit-was is longer than as-it-actually-is] your yacht. The whole affair in brackets is a complex predicate; it’s made by applying two predicate modifiers – the two hyphenated phrases – to the simple predicate ‘is longer than’. We could have similar constructions where neither of the two modifiers is an actuality modifier. Suppose I used to think your yacht was longer than I would have thought it was if I’d listened to Fred. That comes out: Your yacht [as-I-used-to-thinkit-was is longer than as-I-would-have-thought-it-was-if-I’d-listened-to-Fred] your yacht. Some, and I for one, would say that this trick doesn’t really serve the cause of nominalism and actualism (or presentism) because any fool can see that the quantifications over repudiated objects are still there implicitly, and will be made explicit

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211.  To Allen P. Hazen and David Kaplan, 4 October 1995

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when we give the semantic analysis of the predicate modifiers. A stubborn opponent will claim to have a primitive understanding of the modifiers. Standoff! I trace this idea back to pages 13–14 of my On the Plurality of Worlds (1986), and before that to footnote 10, page 349, of my ‘New Work for a Theory of Universals’ (Australasian JΦ, 1983). In both places, the example is ‘A red thing can resemble an orange thing more closely than a red thing can resemble a blue thing’. But I expect it goes much further back, maybe in connection with the yacht example. The second is the idea of a backspace operator. (It reminds me of the tricks in Quine, ‘Variables Explained Away’,1 or in the combinatory logic he was there presenting in simplified form.) Let’s illustrate it for tense. For simplicity I’ll mostly stick to tense operators that reset the value of a time-index, but that don’t quantify: ‘today’, ‘last Melbourne Cup day’, ‘the previous day’, . . . . We could have a carriage-return operator, pronounced ‘now’ or ‘today’: wherever it occurs, no matter how deeply embedded, it resets the time-index to the day of utterance. We could have Frank Vlach’s pair of a tab and tab-set operator; tab resets the time-index to wherever it was set at the immediately previous occurrence of tab-set (and when there’s no previous occurrence of tab-set, it acts like carriage-return and resets the index to the day of utterance). Tab is pronounced ‘then’; Vlach didn’t offer any pronunciation for tab-set, but I think that at least sometimes you can pronounce it ‘once’. That pro­nun­ci­ation works best in quantified cases: ‘Someday it will be the case that: it was once the case that: forever after: what happened then would be remembered’. Or in more idiomatic word-order: ‘Someday it will once have been the case that what happened then would be remembered forever after’. Presentists refuse to quantify over times. That costs them a loss of expressive power. Use of tab and tab-set restores some of the missing expressive power. I say that the unwanted quantification isn’t gone, but rather it’s hidden in the semantics for tab and tab-set; some will claim to have a primitive understanding; I say that if you can believe that, I’d like to know if also you think ‘Variables Explained Away’ gets you out of ontic commitments wholesale! . . . But tab and tab-set don’t restore all the missing power. (What you get is like the expressive power you’d have if you could bind two time variables at once but never three.) What’s to do, short of giving away presentism and quantifying over times fair and square? Suppose you have a backspace: it resets the time-index to the setting given by the last-but-one operator that we’re still inside the scope of. Thus: ‘Last Cup day: last Cup day: the previous day: (it was sweltering but backspace: it was cool)’ means that on the day before the last-but-one Cup day it was sweltering, but on the last-but-one   (Quine 1960b), reprinted: (Quine 1966).   

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Cup day it was cool. You can iterate backspaces to reset to the last setting but two, last but three, or whatever you like; presumably this regains all the expressive power you’d get by quantifying over days. I say the unwanted quantification isn’t gone but rather hidden; some will say they have a primitive understanding; . . . Nowadays, the standard source for backspace seems to be Harold Hodes, ‘On Modal Logics Which Enrich First Order S5’, JΦL 1984. But I’m pretty confident that I heard of it long before. My best guess, but not a very confident guess at all, is that David mentioned it (invented it?) in the course of the UCLA oral exam at which Frank Vlach was advanced to doctoral candidacy, in 1970 or thereabouts. Thanks very much for any light either of you can throw on the history of these two gadgets! Yours, David c: Burgess, Rosen

212.  To Daniel Nolan, 16 January 1996 [Princeton, NJ] Dear Daniel Nolan, I’ve been looking at your paper ‘Recombination Unbound’.1 But mostly at the beginning of it: because by the time I’m through the initial discussion of the ForrestArmstrong argument,2 enough unfinished business has piled up that it might be best to try to clear that up before going further. I’m now inclined to think that you’ve indeed found a problem with the F-A argument as I’ve hitherto understood it; but that the argument can be patched to survive the problem; and hence that my need for a ‘size and shape permitting’ proviso (if I don’t want to be committed to the possibility of proper-class-sized worlds) does not go away. Two simplifications. I’m going to confine my attention to possible worlds which consist at least partly of atoms arranged in some sort of spacetime. I don’t say what sort of ‘atoms’ these are: maybe point-particles of matter, maybe tropes, maybe multi­ply located simple universals, maybe . . . . (But I anyway don’t mean ordinary chemical ‘atoms’ of hydrogen, boron, or whatnot – those aren’t real atoms, they’re composites of several atoms each.) I also don’t say much about what the structure of   (Nolan 1996).    See ‘An Argument Against David Lewis’ Theory of Possible Worlds’ (Forrest and Armstrong 1984).

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212.  To Daniel Nolan, 16 January 1996

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the ‘some sort of spacetime’ may be; maybe in general it should just be an arbitrary metric space. I’m also going to disregard any intrinsic qualitative difference there may be between atoms, whether in the same or different worlds. That’s a fair move, since it makes things harder for me, not easier. And I’m also going to confine my attention to those things which are mereological sums of atoms, disregarding whatever bits of atomless gunk may coexist with the atoms. A version of the argument as I’ve hitherto understood it. Let the whole of the actual world (except for the atomless parts, if any, that we’ve agreed to disregard) consist of K atoms, for some positive number K.  (Maybe finite, maybe infinite.) Then, since whenever we have some of those atoms, we have their mereological sum, the number of mereological sums of atoms is 2K-1. (The ‘-1’ is needed because there’s no such thing as a sum of zero atoms. However when K is infinite it won’t matter: 2K-1 will then equal 2K.) For instance if there are 2 atoms there are 3 sums; if there are 3 atoms there are 7 sums; . . .; if there are a countable infinity of atoms there are an uncountable infinity of sums; if there are beth-alpha atoms, for any ordinal alpha, there are beth-(alpha+1) sums. In every case, the number of sums is greater than the number of atoms. By recombination, if it were not bound by my proviso, we’d have a big world where there coexist nonoverlapping duplicates of all those sums. Since any duplicate of something containing an atom will itself contain an atom, each one of these duplicates contains at least one atom; so the big world contains more atoms than the actual world does. But it didn’t matter that we started with the actual world; start with any world you please, you get a bigger world (where ‘bigger’ means ‘more atoms’). For instance, start with the big world just mentioned; you get a bigger world still. And so on. Suppose for reductio that we start with the biggest world of all – no, there’s a bigger world than that. And it didn’t matter that you started with things all in the same world. Suppose for reductio that there are K atoms in all the worlds together. Now we have a big world where there coexist nonoverlapping duplicates of all those K atoms – so this big world has (at least) K atoms. Now as before there’s another world with 2K-1 atoms, and that’s more than K; which contradicts our supposition that there were only K atoms in all the worlds together. The problem I think you’ve found. The argument as I just stated it is no good; because it supposes that if we have N different things to be duplicated, then we need N different things to provide duplicates for all of them. But what if two of those N things were duplicates of each other? – Then a single thing could serve as duplicate of both. Indeed, what if all those N things were already duplicates of each other? Then a single thing could serve as duplicate of all N of them.

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How to repair the argument. Let’s say that some things are diverse iff no two of them are duplicates. And let’s say that a sum of atoms is diverse iff its non-atomic parts are diverse: in other words, iff it never happens that A and B are two different parts of it, and each of them consists of more than a single atom, and they are duplicates. If a world contains K atoms, and if the sum of its atoms is diverse, then that sum has 2KK-1 diverse nonatomic parts; and if we also throw in some one of the atomic parts (some single atom) – which, because it is an atom, is not a duplicate of any of the nonatomic parts – then we get 2K-K diverse parts; whence by recombination we have a bigger world with at least 2K-K atoms. (2K-K does indeed exceed K whenever K exceeds 1. We do need to assume that it’s possible to have two atoms. Safe bet?) So if we start with a diverse world (containing more than one atom), we do indeed get a bigger world. The pursuit of diversity. As any politically correct university official will tell you, diversity is the solution to our problems. But how do we insure diversity? Insuring diversity of the sum of all atoms in our starting world might be a tall order; but that’s more than we need. If there are K atoms in all the worlds together, then what we need is a big world – Giganto – containing a diverse sum of K atoms. The atoms in the diverse sum needn’t be all the atoms in Giganto. Then we’d have a world Humungo that contained coexisting nonoverlapping duplicates of all the diverse nonatomic parts of that diverse sum; and Humungo would contain more than K atoms; so Humungo alone would contain more atoms than all the worlds together – which is absurd. Now I don’t have a general proof to offer you that if there’s a world containing K atoms, then there’s a world containing a diverse sum of K atoms. But I can offer you the argument for a special case, and I suggest to you that my argument should generalize. That is, it should generalize if you take a sufficiently liberal view – as you do, though I do not – regarding the possible shapes and sizes of spacetime. Maybe this view would do the job: for an arbitrary metric space, spacetime could have the metric structure and the cardinality of that metric space. Suppose we have a metric space, and some atoms located at some of its points. (At most one atom per point.) Call that sum scalene iff no pair of two different atoms is at the same distance apart as any other pair of two atoms. That means that there are no four different atoms w, x, y, z such that the w-x distance equals the y-z distance; and also that there are no three different atoms x, y, z such that the x-y distance equals the y-z distance. If two different nonatomic parts of the atom-sum were duplicates, all their pair-distances would have to match; so if the sum is scalene then its nonatomic parts are diverse. I’m going to suppose that there are no limits on how to locate point-sized things within a spacetime, except perhaps for the rule that no two of them can ever go at the very same point. (And even if that rule isn’t imposed, I may still obey it. And

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212.  To Daniel Nolan, 16 January 1996

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I shall.) This supposition isn’t Recombination, but I reckon it comes from the same intuitions that Recombination comes from. Now here’s my special case: suppose we want to locate countably many atoms in Euclidean 2-dimensional space in such a way that their sum is scalene, and hence diverse. I say it can be done. Take the atoms in arbitrary order. Put the first one anywhere. Put the second one anywhere else. Scalene so far. Now we can put the third one anywhere except on the bisector of the line between the first two, or on the circle that’s centered on the first and passes through the second, or on the circle that’s centered on the second and passes through the first – no worries, two circles and a line don’t fill up the plane, we still have places left over to put that third atom. Still scalene. And we can put the fourth one anywhere except on a certain three lines and six circles. And we can put the fifth . . . . And we can put the nth anywhere except on a certain finitely many lines and circles – no worries, finitely many lines and circles still don’t fill up the plane. And when we’re done, we will have a scalene, hence diverse, sum of countably many atoms arranged in the plane. Quod erat demonstrandum. Now: generalize that! Unfortunately, I only really know how to go a little way further – to Euclidean (or curved) spaces of higher dimensionality. But what I conjecture, and what I’d like to have a proof of, is this: for any cardinal number of atoms, there exists a scalene sum of that many atoms in some metric space. For large enough numbers of atoms, the metric will have to take values in a nonstandard continuum rather than in the standard real numbers – if there were only con­tinuummany different distances available, there wouldn’t be enough different distances to permit a scalene sum of more-than-continuum-many atoms. And maybe the metric space will have to be of higher cardinality than the number of atoms. But – by your lights, speaking ad hominem – these suppositions should not reach beyond ­possibility. [. . .] Yours, David Lewis c: Gideon Rosen, D.M. Armstrong, Peter Forrest

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213.  To Robert C. Stalnaker, 28 February 1996 Princeton University Princeton, NJ Dear Bob, Thank you for the two papers.1 I look forward to reading the one about supervenience; but I started by reading the dialogue about impossibilities, and I wanted to write to you about that right away while it was fresh in my mind. Two preliminary questions. First: may I share it with students in my possible worlds seminar? May I allow them to make copies? Second: did you, by any chance, send a copy to Bill Lycan with a note to say that you hoped he’d find one of the characters a kindred spirit? If you did, let me send him a copy of this letter. I do of course find Louis a kindred spirit, and for the most part I like the paper very much. But I have one reservation: I think Will could have given his side of the question a better run for the money than he did. And he would have done, if he’d kept closer to some of his real-life counterparts, especially Graham Priest [In Contradiction, Nijhoff 1987].2 Will needlessly lets Louis score points off him. Mind you, I don’t believe a word of what Priest says! But I think his position is well worked out, it isn’t vulnerable to any fair arguments, it achieves stalemate. All I have against it is an incredulous stare – and that’s enough, I reckon. Reading Priest is a lesson in the value of dogmatism. I’ll go through the dialogue saying where I think Will would have done better to take a line closer to Priest’s. 4, bottom. Will might better have said that impossible worlds are worlds about which some contradiction is true. For he may later want to say that some contradiction is true simpliciter – as it might be, that the set of non-self-members both is and isn’t a self-member, or that it is true in W that P and it is not true in W that P – without saying that this world is on that account an impossible world. He’ll be OK if he can deny that this world is part of the subject matter of the true contradiction in question. 5, near top. Same point continued. When asked to grant that the actual world is not an impossible world, Will should grant it at most in the sense just considered. That is, he should not concede that there are no true contradictions; but, at most,

1   ‘Impossibilities’ (Stalnaker 1996a); ‘Varieties of Supervenience’ (Stalnaker 1996c). Both reprinted in (Stalnaker 2003). Lewis’s suggestions in this letter are incorporated into the expanded version of ‘Impossibilities’ in (Stalnaker 2003). 2   (Priest 1987).

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that there are no true contradictions about what goes on in the actual world. (And maybe he shouldn’t concede even that much; maybe he should be agnostic about which sort of world this is; maybe, even, he should think there are phenomena best explained by the hypothesis that this is an impossible world.) 6. Will should say, as he does, that Louis begs the question against him by supposing that even when we take impossible worlds into account, the set of -P worlds is still the complement of the set of P worlds. But Will should not deny that the truthtable rules apply. Rather, he should use those very rules to infer that when P and -P are true together in a world, then at that world P is false as well as true; because -P is true only if P is false. He should say that an impossible world has not only true contra­ dic­tions but also ‘truth-value gluts’; and that Louis’s question-begging may be redescribed by saying that Louis ignores worlds with gluts. 7. Will should protest that he uses the tilde exactly as Louis does, and so does not owe an explanation of his allegedly idiosyncratic meaning. Will agrees with Louis that tilde is a reverser of truth values: -P is true iff P is false, false iff P is true. (So if P is both true and false at w, so likewise is -P; and conversely.) Will should also protest that he uses ‘contradiction’ exactly as Louis does: P and -P together, for some P. 8. What is the status of the claim that the actual world is possible? Will should say it’s an empirical question. He might say, as Priest does, that contradictions are not to be multiplied beyond necessity. Given that methodological rule, Will might have any of various opinions about how the balance of evidence stands. 10. Will should claim to distinguish two cases. (A) It is true, and not also false, that the cupola is round; it is false, and not also true, that it is not round. It is true, and not also false, that it is square; it is false, and not also true, that it is not square. Nor are any contradictions about anything else true. A world of this sort, if there is one, is possible – though maybe it’s unimaginable. (B) It is true and also false that the cupola is round; true and also false that it is not round; true and also false that it is square; true and also false that it is not square. A world of this sort is impossible. Yours, David

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214.  To Richard B. Miller, 12 March 1996 [Princeton, NJ] Dear Richard Miller, Thank you for your ‘Island Universes’ paper.1 One thing to add to what you say is that the ‘what if the wormholes hadn’t been there?’ problem still hits us even if we say that worlds can be unified otherwise than in a straightforward spatiotemporal way. Suppose it’s easy to get rid of the wormholes. We don’t want to say

(1) If we’d done so, there would have been an n+1st dimension of spacetime.

But no more do we want to say

(2) If we’d done so, there would have been some extra relation, alien to actuality, but analogous to the spatiotemporal relations. (3) If we’d done so, there would have been some extra external relations, alien to actuality, though maybe they wouldn’t in any sense, even an analogical sense, have been spatiotemporal relations.



Your amendment of (1) seems to me to make a much worse problem than we had before. Doesn’t it seem possible that there might be a world of things entirely causally independent of one another, worldmates entirely causally unrelated? I sympathize with your dislike of letting philosophy dictate to physics – and isn’t it a physical question to what extent things that coexist are causally related? Something I don’t much mind is having it turn out that the demarcation of worlds is conventional, and up for grabs in solving a problem. Modal realism is realism about possibilia – how they’re grouped into worlds is a side-issue, though one that often matters to the applications of modal realism in semantics or philosophy of science. You may be right that no one has any very clear and convincing idea of what revisions quantum mechanics may require. I’m not sure: as far as I know, GRW and Everett don’t lack clarity; though obviously they’re not altogether convincing, because not all who’ve heard of them have come away convinced, but note that it’s not even gospel that ‘the cat’s wave function does not collapse . . . until it is observed’. For Everett, there’s no collapse at all; for GRW, observation is an interaction of a kind that makes collapse more probable – but observation is not the only interaction of that kind, collapse doesn’t absolutely require the kind of interaction that makes collapse probable, and interaction of that kind doesn’t make collapse entirely certain. Yours,   ‘Actuality, Island Universes, and Schrödinger’s Cat’ (unpublished). But see (Miller 2001, 7–8).

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215.  To Daniel Nolan, 13 December 1996

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215.  To Daniel Nolan, 13 December 1996 [Princeton, NJ] Dear Daniel, I’ve recently had occasion to look more closely at ‘Recombination Unbound’, which you sent me some while ago. On the previous reading, I took what you said about what I said on trust, but this time I checked it; and I regret to say that I found a problem. It comes when you discuss the ‘recast’ version of the Forrest-Armstrong argument that appears in On the Plurality of Worlds (for short: PoW). I said: ‘Suppose the big world has K electrons in it . . . For each [nonempty subset of these electrons] there is a world . . . in which just those electrons remain and the rest have been deleted. (I take this to be a subsidiary appeal to recombination.)’ You said, correctly, that my conclusion does not follow from the following principle (henceforth P): ‘for any objects in any worlds, there exists a world that contains any number of duplicates of all those objects’. That’s correct. You said that P was ‘the principle appealed to’ in my argument. That’s not correct. What I said was: ‘a subsidiary appeal to recombination’. You proceed as if P was a capsule summary of the principle of recombination, but it isn’t. P is your paraphrase of Q (PoW, p. 89): ‘Not only two possible individuals, but any number, should admit of combination by means of coexisting duplicates’. P is fine as a paraphrase of Q, but where did you get the idea that Q was meant to capture the full force of re­com­ bin­ation? – Not from anything I can find in PoW! What I said on the previous page had two parts, in two consecutive sentences. R1: ‘Roughly, the principle is that anything can coexist with anything . . .’. R2: ‘Likewise, anything can fail to coexist with anything’. The dragon-and-unicorn example then illustrated R1; the talking-head example illustrated R2. Further discussion, leading before long to Q, was a further development of R1; there was no point trying the reader’s patience by going through a parallel development of R2. But R2 was never revoked! And it’s R2, suitably developed, that applies. Take any fusion of some but not all of the electrons in the big world, together with all the electron-free parts of the big world. It could ‘fail to exist with anything’, just as the talking head could. In particular, it could fail to coexist with any further electrons. More precisely, it could have an otherworldly duplicate that failed to coexist, in its own world, with any further electrons. There’s my appeal not to P, not to Q, not to any development of R1; but rather to R2 developed in terms of duplicates. That will do the job if, but only if, the big world is devoid of certain kinds of symmetries. Trouble will arise if, for some two different fusions of some but not all the electrons of the big world (plus all the electron-free parts), the fusions are

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duplicates of one another; then a single little world will be a duplicate of both. A sufficient condition to avoid this trouble would be that the electrons in the big world are scalene: arranged in such a way that no two pairs of them are at the same distance. Does yet another subsidiary appeal to recombination deliver a scalene arrangement? Not if it’s an appeal to improved descendants of R1 and R2 which, after all, don’t say anything about the arrangements of the coexisting things. Rather, it would have to be the sort of appeal to recombination that you get on page 90 of PoW in the discussion of Quinean ersatz worlds. (And, incidentally, in the dragon-and-unicorn example, which says there could be a dragon and a unicorn side by side.) It’s plain to see that you wanted there to be a single sentence somewhere that encapsulated all of recombination. I deliberately didn’t provide one. The reason why was (1) that I couldn’t say how far recombination would go without giving away my neutrality between rival treatments of properties, and (2) that there was anyway no hope for a formulation that would put an upper limit on the plenitude of worlds, so nothing was lost by stopping with several separate cases. (For both points, see p. 92.) --------------------------------------------------------------------------------------------------------Apart from that . . . I really like the paper. The idea that there are proper-classmany worlds, and big worlds with proper-class-many distinct parts now seems to me much more of a live option than it did when I wrote PoW. (1) Simplifying re­com­bin­ ation would be nice, as I thought all along. (2) Given that plural quantification, even over all the proper classes, is OK and ontologically innocent, having proper-classmany worlds is not nearly as technically crippling as I thought, though it will still be somewhat of a nuisance. (How can the semantic value of an ad-sentence be a function from propositions to propositions? How can the semantic value of an ad-adsentence be a function from and to functions from propositions to propositions? How . . .) (3) Since it turns out, thanks to the Burgess-Hazen tricks, that we can have structuralist mathematics if we have any proper-class-many distinct things, we needn’t look any further for the whereabouts of an adequate ontology for standard mathematics. So am I persuaded? No; I now think of the conjecture that there are properclass-many worlds as an attractive but daring speculation, and I’m glad I have the option of suspending judgement about it! [. . .] Yours, David Lewis

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216.  To Bradley Monton, 28 May 1998

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216.  To Bradley Monton, 28 May 1998 [Princeton, NJ] Dear Brad, Now that the semester is over, one thing I’m doing is going through the forbidding heap of papers people have given me to read. (Selectively, I assure you!) One paper I came to is yours on recombination. I regret to say that I found it was dated last September. Sorry! Anyway, I’ve read it. I pretty much agree with your dislike of the ‘size-and-shape permitting’ proviso. It’s hard to see how any break could at once avoid objectionable arbitrariness and avoid any risk of cramping the style of physics. (I don’t think, though, that the physical theories you mention would bump their heads on a size limit. A ten-dimensional string-theoretic world, even an infinite-dimensional Hilbert space, would just be continuum-sized, wouldn’t they? We already thought our world was probably continuum-sized.) Maybe the passage you were trying to remember was my passage about how presumptuous it would be to try to correct mathematics on philosophical grounds. If so, that’s Parts of Classes, section 2.8. (George Boolos calls this passage ‘science worship’. OK by me, I reckon there are worse things to worship! But George says something else that matters more to me: that working mathematics can fit into something weaker than full ZFC, something that doesn’t give you the humungously large infinities. See his ‘Must We Believe in Set Theory?’ in his collection Logic, Logic, and Logic.)1 As you say, Daniel Nolan gets into trouble by seizing on a sentence and taking it to be my official formulation of Recombination. But it seems to me that this doesn’t wreck his point (or anyway, doesn’t wreck one of his points). Let’s take it in slow motion. We have a big world such that, for every world W there is, some part of the big world is a duplicate of W. Suppose there are K electrons in the big world. Suppose K is an infinite cardinal – in other words, suppose there are less than proper class many electrons in the big world. Then there are 2K-1 different nonempty subsets of these electrons. For each subset, there is a variant world obtained by keeping the electrons in the subset and deleting the rest. (So far, so good.) So there are 2K-1 variants. Daniel says this step is suspect, and I agree. Imagine that the electrons in the big world are arranged in a line like the positive and negative integers. Take a subset that omits one of the electrons. Take another subset that includes that electron and omits a different one. Two different subsets. But   (Boolos 1998).

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only one variant world, since the spatiotemporal arrangement of electrons is the same either way. So there may not be as many variant worlds as there are subsets. (That assumes – as I’m happy to assume – that worlds are individuated not haecceitistically but by isomorphism. But if worlds are individuated haecceitistically, a different version of Daniel’s point still applies. In that case, we do indeed have a different variant for each subset, so we have 2K-1 variants. And each of these variants has a duplicate in the big world. So within the big world we have 2K-1 duplicates of variants. No – because now we’re allowing there to be isomorphic variants, so that means that one single proper part of the big world can be a duplicate of two different variant worlds. That said, let’s return to the assumption that we can individuate worlds by isomorphism.) It’s not as easy as Nolan says in the passage you quote at the bottom of your page 5. There won’t be just one three-electron world, say, because different threeelectron worlds will differ in the spatiotemporal (or whatever) arrangement of the three electrons. How many three-electron worlds there will be isn’t clear. But anyway I was wrong to think there had to be as many as there are three-membered subsets of the set of electrons in the big world. I’m rather inclined to think we will after all get enough different variants that we can restore the argument, but it’s not as easy as I used to think. If so, we’re back to a choice between imposing a size limit, and hoping it can somehow be not arbitrary, or else rejecting the assumption that we have a set of electrons in the big world, with a cardinality, as opposed to a proper class. But are these different? One way to describe Nolan’s position is that he does accept a size limit; but his size limit isn’t any infinite cardinal, rather it’s the size of the proper classes. In that case, what stops growth when you hit the size limit isn’t some arbitrary-looking stipulation; it’s just the familiar fact that you can’t treat proper classes as if they were sets. And if ever there was a size limit high enough that it didn’t threaten to cramp the style of physics, proper-class-many should be it! Yours,

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217.  To Robert Black, 28 January 1999

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217.  To Robert Black, 28 January 1999 [Princeton, NJ] Dear Robert, I’ve now read your paper ‘Against Quidditism’.1 I liked it very much. Here are some comments. It would be nice, I think, if the question of quidditism could be made independent of the choice between ‘abstract’ and ‘concrete’ modal realism. ‘Abstract’ quidditism is easy, I think, provided your ersatz worlds don’t have to be purely mathematical. Let fundamental properties themselves be constituents of your abstract constructions: we could have, roughly, a function that maps co­ord­in­ ate ’tuples – ersatz spacetime points – onto sets of fundamental properties. (Take equivalence classes to see to it that you don’t get allegedly different worlds that differ just by transformations of coordinates.) If you believe in the existence of actually uninstantiated fundamental properties, this will give you a thoroughgoing quidditism; whereas if you believe only in instantiated ones, you can put numbers or whatnot in place of the uninstantiated properties, take equivalence classes under permutation of these code numbers, and thus have quidditism with respect to the instantiated but not the uninstantiated properties. ‘Concrete’ anti-quidditism is harder. Let’s work up to it in stages. First, consider this relational theory of charge: Contrary to our usual view, there are no such fundamental monadic properties as unit positive and negative charge. Instead there are a pair of fundamental external relations: L, like-chargedness, and O, oppositechargedness. They obey certain contingent laws of nature: not both aLb and aOb; if aLbLc, or if aObOc, then aLc; if aLbOc, then aOc; if aLb, then bLa; if aOb, then bOa. Positive charge is just being like-charged to the nuclear particles of atoms hereabouts, negative charge is being like-charged to the peripheral particles. Myself, I think it’s a contingent question whether this relational theory is true or whether our usual property theory of charge is true. Both are possible. Some worlds work one way, some the other. Some worlds are mixed: they have the two monadic properties and they have the two relations as well. Others will think – influenced, I fear, by verificationism – that the two theories are equivalent. Still others will think, a priori, that if one or the other theory is true, then it must be the relational theory, not the property theory, that’s true. These last, if in addition they’re modal realists, are anti-quidditists about the properties of positive and negative charge. They say there’s no such thing as an antimatter world just like our world   (Black 2000).

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except with all the charges reversed: since the structure of the L-relation and the O-relation would be just as in actuality, this allegedly different world is indiscernible from ours. (And if they also believe in identity of indiscernible worlds, it just is ours.) Second stage: we can likewise trade in other families of monadic fundamental properties for families of relations. If we somehow had an a priori preference for the relational theories of quark colour, flavour, etc., we could be anti-quidditists about those families of properties as well. Third stage: similar, except that now we treat all the fundamental monadic properties as if they were one big family. That way, we could be concrete antiquidditists not just within the families but even across family boundaries. Fourth stage: we could similarly trade in the fundamental external relations on new relations, and end up as anti-quidditists about relations as well as properties. But we’d have to call a halt somewhere, else we replace the very relations that we’ve just introduced, L and O for instance, and the thing eats its own tail. Here’s a completely different way to be a ‘concrete’ antiquidditist. First, be a trope theorist. (I think this has some independent advantages: see my ‘Against Structural Universals’, AJP 1986.) Then you’ll no longer say that properties occur repeatedly, either within this world or across worlds. Rather, some tropes match other tropes, for instance all unit-negative-charge tropes in this world match one another. Then deny that there’s any cross-world matching of tropes. The only mo­tiv­ ation I can see for this denial is that it gives you anti-quidditism, if that’s what you want. Properties are maximal world-bound classes of matching tropes. They are not identical across worlds. At best, otherworldly properties are sometimes counterparts of thisworldly properties, for instance in virtue of similar nomological roles. This is meant to imitate my anti-haecceitism; it works because under trope theory, the tropes and their classes are unrepeated particulars. (This is something like the move you mention near the end of the paper of insisting that no fundamental property is found in more than one world. But I think it goes better if we first adopt trope theory; else we have to answer the embarrassing question ‘why is repeated occurrence between worlds any worse than repeated occurrence within one world?’) So as a ‘concrete’ modal realist I don’t absolutely have to be a quidditist, though I still think it’s the most straightforward thing for me to be. Why might I want to be an anti-quidditist? One reason is that as a quidditist, I must acknowledge differences between worlds that we have no way even to express in thought or language; and hence questions that we not only have no way to answer, but no way even to ask. Consider our world and another world, different according to the quidditist where positive and negative charge are everywhere swapped. Which of these two worlds is ours? There’s

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217.  To Robert Black, 28 January 1999

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a right answer and a wrong answer, a true proposition and a false proposition; but not only can’t we tell which is which, we can’t even express them unambiguously. (‘Let “positive” rigidly denote the charge on nuclear particles hereabouts. Now, ours is the world where nuclear particles hereabouts are positively charged.’ – Useless! You might as well say that the meter bar is a meter long.) Well, I grant that there are indeed these ineffable, unanswerable questions – but who ever promised me there couldn’t be such questions? The worst part of being a quidditist, I guess, is that I’m in danger of agreeing with Kant about something (Kant as told by Rae Langton, anyway) and I’d never want that to happen! Your reason is that quidditism drives up the number of different possibilities. As an ad hominem, this no longer works against me (though it would have once). As you mention, I’m increasingly happy with the idea that there are proper-class-many worlds, and also single worlds with proper-class-many parts. One reason is that this gets around arbitrary-seeming restrictions on the principle of recombination. Another is that it gives me enough stuff to afford an ontology for structuralist mathematics, without putting it off in platonic heaven, outside the worlds altogether. The first reason is argued in Daniel Nolan, ‘Recombination Unbound’, Philosophical Studies 1996; the second is in Nolan’s doctoral dissertation.2 I’ve changed my mind quite a lot about proper classes. I used to think that the fact that we can, without restriction, collect many into one was a reason why we couldn’t believe in proper classes; now I think it’s a reason why we must believe in proper classes. (That’s cryptic. Hint: it’s a different sort of collecting.) I used to think plural quantification was a substitute for believing in proper classes; now I think we need to be able to quantify plurally over proper classes themselves. I used to have little use for the idea that some classes are too big to be sets; now I think that limitation of size, more than the iterative conception, is the guiding idea of set theory. All this is in my book Parts of Classes or, with slight improvements, ‘Mathematics is Megethology’ in my Papers in Philosophical Logic. My final comment concerns the first line of your paper. Why ‘closet’? The modal realism in ‘Anselm and Actuality’ seems pretty overt to me! Yours, David Lewis Copy of this to Cian Dorr, a Princeton graduate student who’s interested in, and ­favourably inclined toward, anti-quidditism.

  Topics in the Philosophy of Possible Worlds (Nolan 2002).

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218.  To Tyler Doggett, 18 May 1999 [Princeton, NJ] Dear Tyler, [. . .] Did you know a Princeton graduate student named Hwan Sunwoo? He’s running a line he calls ‘modal quasi-realism’.1 The idea is that there’s a primitive modal quantifier ‘there might have been’ which ranges over unactualized possible worlds and things. The possibilia are not ersatz; they’re ‘concrete’. The primitive modal quantifier is not translated into an ordinary one-world quantifier preceded by a modal operator; it’s just a quantifier over a big domain, our least restricted quantifier. When I heard Sunwoo give a talk on this, I thought I couldn’t tell the difference between his view and mine. He and I agree that the least restricted quantifier ranges over ‘concrete’ possibilia; quantifiers over this-worldly things are restrictions of that least restricted quantifier. He says you can pronounce the least restricted quantifier as ‘there might have been’. I say so too. He says you cannot pronounce the least restricted quantifier as ‘there are’; I disagree. But that’s just a disagreement over English usage. There’s no disagreement whatever over logic or ontology! Yet it all sounds so much more comfortable the way Sunwoo wants to say it! Nobody minds saying ‘There might have been a talking donkey – indeed there might have been infinitely many of them’. So it seems that what evokes the incredulous stare is just a matter of pronunciation. So far as lack of parsimony, spatiotemporal discontinuity, etc. go, Sunwoo’s position is exactly the same as mine and folks don’t seem to mind it at all. Sunwoo says other modal notions are reducible to this primitive unrestricted quantifier. I say so too. He says the quantifier is ‘modal’, so modality is irreducible; I say that the least restricted quantifier is just a quantifier, so modality is reducible to quantification. But what’s in a name? [. . .] Yours, David Lewis

  Modality and Quantification: The Modal Quasi-Realist Approach (Sunwoo 2000).

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219.  To Graham Priest, 9 January 2001

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219.  To Graham Priest, 9 January 2001 Princeton University Princeton, NJ Dear Graham, Thank you for your review of the Cambridge collections of my papers.1 I much enjoyed it. As for suggested changes, most are trivia; only two are at all substantive, and those are minor. First the trivia. Page references are to your 16 December draft. [. . .] The first substantive point is on page 4, line 17-up. I do of course reject much of Quine’s skepticism about modality. But there’s one part I accept, and that’s his skepticism about essentialism. Howzat? Don’t I have my way of making sense of essentialism – your essential properties are those you share with all your counterparts? Yes, but. Mine is a half-hearted and flexible essentialism, since I think the appropriate choice of a counterpart relation is both vague and context-dependent. When Quine says (‘Worlds Away’, 1976)2 that the trouble with essentialism (besides the trouble with modality generally) is that there’s no determinate counterpart relation, I think he’s exactly right. Accordingly I have no patience with the thousands who think there’s a debatable issue, and a right answer, about whether, for instance, you essentially have the origins you actually have. I say more about this in a forthcoming paper called ‘Things qua Truthmakers’.3 I’ve sent you a copy. The other substantive point is on page 5, line 17. I certainly want to say that mathematical objects exist. (Perhaps this is merely a verbal disagreement with the Meinongian, though there’s certainly a more-than-verbal disagreement once he denies that our disagreement over ‘exists’ is merely verbal!) But I’m not committed to saying that mathematical objects, for instance pure sets, are parts of worlds. (They might still be ‘in’ worlds in the sense that they’re members of the domains we restrict ourselves to when talking about particular worlds, but that only goes to show that the domain associated with a world might consist of more than the parts of that world. I’ve sometimes spoken of existing ‘from the standpoint of’ a world.) I’d certainly like to be able to say that the mathematical objects were parts of the pluriverse. (That’s not to say they’re parts of single worlds. Some parts of the pluriverse are mereological fusions of parts of several worlds.) But until recently I’ve thought this was out of the question because the pluriverse wasn’t big enough. I used to think that the number of parts of the pluriverse was one of the smaller uncountable cardinals. Daniel Nolan has now persuaded me that there’s a better case than I thought for thinking there are proper class many parts  (Priest 2002).   2 (Quine 1976b).   3  (Lewis 2003).

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of the pluriverse, and, as he points out, that plus the set-theoretical structuralism I endorse in ‘Mathematics is Megethology’4 reopens the question whether there’s room enough for all the mathematical objects within the pluriverse. I applaud your paragraph ‘. . . it would be wrong to think of Lewis as a systematic philosopher’. I really don’t want people thinking they have to agree with everything I say in order to agree with anything I say! (You’ll be familiar with the problem.) I also find it more than a little off-putting when industrious Germans write systematic expositions of the Lewisian system. I’m willing to present views premised on my other views if I have to, though I (increasingly) try to avoid this, and to tell the reader when it’s so and when it’s not (like a mathematician telling his readers whether a proof depends on the axiom of choice). For instance I have a pair of papers, ‘Things qua Truthmakers’ which says what I can say about truthmaking if I do help myself to counterpart theory, and ‘Truthmaking and Difference-Making’5 (available in the Melbourne Uni preprints) about what I can say if I don’t. Paraconsistency.6 I’m increasingly convinced that I can and do reason about impossible situations. (‘Sylvan’s Box’7 played a big part in persuading me.) But I don’t really understand how that works. Paraconsistent logic as developed by you and your allies is clear enough, but I find it a bit off the topic. For it allows (a limited amount of) reasoning about blatantly impossible situations. Whereas what I find myself doing is reasoning about subtly impossible situations, and rejecting suppositions that lead fairly directly to blatant impossibilities. In other words, I understand what it would be to do without rejection by reductio ad contradictionem altogether, but I don’t understand what it is to be selective, using reductio sometimes and sometimes not. But it’s the latter, not the former, that I feel a need to do. A (draft?) paper by Daniel8 seems promising, but maybe it just repackages my problem as a problem about what’s the right similarity metric on possibilities together with impossibilities. Hard-line paraconsistency. It still seems to me that we have a complete stalemate, just as I said in the passage you quote, about whether our world might, so far as we know, be contradictory. (By the way, I keep forgetting whether you’d rather say that contradictions are possible, or that for all we know we live in an impossible world. Do you have a uniform policy?) That doesn’t stop me from sometimes making believe that impossibilities are possible, subtle ones at least. I agree with you about the many uses to which we could put make-believedly possible im­pos­si­bil­ities, if we were willing to use them. The trouble is that all these uses seem to require a distinction between the subtle ones and the blatant ones (very likely context-dependent, very likely a matter of degree), and that’s just what I don’t understand.  (Lewis 1993c).   5  (Lewis 2001b).   The next two paragraphs have been published as Letter 2 of ‘Letters to Beall and Priest’ (Lewis 2004c). 7  (Priest 1997).   8  ‘Impossible Worlds: A Modest Approach’ (Nolan 1997). 4 6

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220.  To Hud Hudson, 3 April 2001

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Controvertibility. I think a philosopher who plays for stalemate at all costs can (almost?) always succeed. Plantinga, for one, has demonstrated that abundantly. I think we need to get used to that, since when it takes us by surprise it can cause unfortunate failures of nerve. I shouldn’t, for instance, let Plantinga persuade me to become less confident in my atheism. Leftovers. The books are indeed collections of leftovers, Vol. 2 less so than the others. That’s what CUP wanted, and I thought they knew better than I did what people might find useful. Rational dilemmas. I’m afraid I’m unconvinced that the decision-theoretic disputes are the same sort of thing as dilemmas in law or morality. In the former case, those on one side of the dispute seem to have no inclination whatever to admit that those on the other side are doing something more than simply making a mistake. They reject – not just accept the negation of – what their opponents say. Whereas in the moral or legal cases, I think all parties have at least some initial inclination to say that the victim indeed does have two conflicting obligations – whether or not they’re willing to say so in the end, and whether or not they’re willing to draw the further conclusion that the victim has an obligation to make true a contradiction. Greetings from Steffi. If all goes well, we’ll be in Melbourne for about ten days in either June or July. See you then. Yours,

220.  To Hud Hudson, 3 April 2001 Princeton University Princeton, NJ Dear Hud, I much enjoyed the ‘Dust and Ashes’ paper,1 and I agree with it almost completely. There’s one point I would question, but I’m not at all sure whether I’m dis­ agree­ing with you, or only with a concession you make to the opposition (e.g. Dean and Peter). You speak a couple of times of there being ‘no objectionable causal intermediary . . . to interfere with the immanent-causal connections’. I take it that you are contrasting your solution with one on which the psychology-preserving causal chain passes through the mind of God. (And maybe also partially body-structurepreserving, so that you’re resurrected looking like you rather than, say, a luminous   A Materialist Metaphysics of the Human Person (Hudson 2001, ch. 7).

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golden sphere.) I know it’s widely thought that such external intermediaries are indeed objectionable – not to mince words, they make the difference between survival and death – but I don’t agree. A good way to test whether some sort of connection is really essential to survival is to imagine how you’d respond to the news that in all the years you’ve seemingly survived, this connection has often been broken. In some cases such a discovery really would be deeply distressing, in other cases not. It would merely be an interesting scientific advance. Some people seem to think, for instance, that exact spatiotemporal continuity is essential. Well, imagine it turns out that we live in a movie-world: whenever we move, we go in tiny jumps, say at the rate of sixteen jumps per second. Now are you scared to go for a walk? – Not likely! Imagine you discover that your office is on a distant planet, hooked up to Earth by a Star-Trek-style transporter (the kind that transmits just structural information, not also matter or energy). When it seems to you that you’re walking through your office door, what really happens is that you are instantaneously scanned and disassembled down to atoms, whereupon the structural information is transmitted superluminally to a receiver disguised as the other side of the door, whereupon you – if it really is you – get reassembled out of a supply of local atoms. (The whole business is so reliable that it’s safer than walking through a real door – after all, you just might stumble and bash your head.) The transmitted information is an external causal intermediary. You’re in your office when you find this out. Now are you deathly afraid to leave? Myself, I’d find this discovery nothing more than an interesting surprise, except that I’d very much wish that a second transporter-door could be installed through which I could get to Melbourne without the long plane flight. Or imagine discovering that (deep) sleep doesn’t work the way we thought it did. The human brain needs frequent repairs that terribly garble the information stored in it: memories and personality. What happens is that a backup of the information is taken and put in inactive storage somewhere, the repairs take place, the garbled information is erased, and then the backup is reloaded. You could imagine – I don’t think it matters – that the storage site is inside the body, say a small organ near the stomach, hitherto ill-understood; or that it is aboard one of the flying saucers of the benevolent extraterrestrials who look after us; or that it is the mind of God. Now you’re getting sleepy. Are you afraid to doze off? --I was wondering how essential the materialism is to your view. Suppose there were immaterial souls. Case 1. They’re featureless ‘pellets’, all alike. Then it seems to me utterly implausible that keeping the same one has anything to do with my survival. For all I know or care, they could get replaced every Thursday, with my preowned one going to somebody else. Case 2. They’re not featureless: they’re repositories of some or all of the psychology wrongly thought to reside in the brain.

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220.  To Hud Hudson, 3 April 2001

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Suppose there were an ‘eater of souls’, as is sometimes imagined in horror stories. Couldn’t God manage to resurrect a victim of the eater in much the same way He’d resurrect a merely material person? --I mostly agree with your responses to Al, but I think there’s more to be said. On the costs and benefits of modal realism: I think the main benefit is that we can do without any form of primitive modality, unlike any of the ersatzist or fictionalist alternatives. Thousands agree with me about what the choice is that we face, disagree with me about which choice is on balance better. Fair enough, and I don’t see that there’s more to say. (Except that I’m a bit taken aback by those who seem to think that primitive modality is no cost at all!) Anyway, it doesn’t matter. As Al admits, given primitive modality, we can have counterpart theory within an ersatzist or fictionalist treatment of possible worlds. On contingent identity. Your ‘wimpy way out’ seems to me to be the essential thing to say. None of your counterparts is non-self-identical, therefore being nonself-identical is not a possibility for you. I’m afraid Al has simply misrepresented what counterpart theory says. What does counterpart theory say about contingent identity? In the first place, of course it says what everyone says about de dicto contingent identity involving non-rigid designators: the oldest man is the wisest man, but it might have been otherwise. In the second place, we have cases like the statue and the lump, or me and my body, where one thing has two different counterparts under two different counterpart relations evoked by two different ways of referring to that thing. This flexi­bil­ity seems to me to be one of the main benefits of counterpart theory. In the third place, and this I suppose is what Al had in mind, though (1) ‘For some x, possibly x ≠ x’ is never true, (2) ‘For some x, for some y, x = y and possibly x ≠ y’ does come out true. (2) does not wear its meaning on its face: to understand it, you have to look at the translation scheme from the modal language to the counterpart-theoretic language. It turns out to be true because a value of the two variables x and y has double counterparts. If for some reason you’re uncomfortable with (2) even after you understand what it means, you can get rid of it, and without prohibiting double counterparts or otherwise monkeying with the metaphysics of counterpart theory. Just monkey with the translation scheme instead. (That’s been suggested, I  forget by whom. Hazen, maybe.) It makes no real difference, but it might diminish sales resistance. One way to say it in something more like plain English, bypassing the scheme for translation from quantified modal logic, is this: nothing could have been nonself-identical; however an identity-pair (the pair of a thing with itself) sometimes could have been a non-identity pair. The potentialities of the pair cannot be read off from the potentialities of its terms. Something like this, only with bigger structures than pairs, is due to Hazen. And here’s a challenge for Al: how can he say, what’s

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obviously true, that he might have been twins? (He might have been one of a pair of twins? – True, but not what I meant to say. He might have been the fusion of the pair? Definitely not what I meant to say! (But maybe it’s true – I’m not sure just how far the flexibility of the counterpart relation can be pushed.)) I don’t agree with you, still less with Al, that ‘the relativity of modal properties seems like a genuine cost’, to be balanced against successful puzzle-solving. I think it’s a genuine benefit. I agree with my younger self, who proposed counterpart theory while a student of Quine’s, that judgements of essence and potentiality are a fishy business, not governed by adequate standards of what’s right and what’s wrong. Could I have had different origins? Could I have been brought by a stork? – Say what you like! A lot of present-day confident consensus about matters of essence seems to me illusory. People think they hold opinions about genuine questions when really they’re just playing follow-the-leader. A striking example is the very sudden eruption, circa 1970, of a wave of alleged ‘intuitions’ in favour of essentialism of origins. I don’t remember ever seeing an argument in its favour. I think that what people noticed, rightly, that it was OK to think that origins were essential, and they jumped to the hasty conclusion that it was not OK not to think so. Yours,

221.  To Phillip Rutherford, 20 April 2001 Princeton University Princeton, NJ Dear Phillip Rutherford, Thank you for your letter. You’re quite right about what I thought, and I still think almost all of it. I looked at the ‘How Can we Know?’ section of Plurality and found that I still agree almost entirely with it.1 But there have been two later developments. One is that I now think the prospects for a ‘structuralist’ interpretation of math – one that does not amount to a wholesale reform of existing mathematics – have improved. Three references. (1) My Parts of Classes (Blackwell, 1991), section 2.6, on set-theoretical structuralism. (2) The appendix to Parts of Classes, written jointly with John Burgess and Allen Hazen, which explains the technical trickery required to make set-theoretical structuralism work. (3) ‘Mathematics is Megethology’, reprinted in my Papers in Philosophical Logic   Section 2.4 of On the Plurality of Worlds (Lewis 1986c).

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221.  To Phillip Rutherford, 20 April 2001

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(Cambridge University Press, 1998) which is a somewhat better presentation (I hope), and a much less hesitant endorsement, of the same idea that’s covered in (1) and (2). Maybe the technical trickery needed to simulate quantification over relations is not your dish of tea – it isn’t altogether mine – in which case you might just take it on faith that it works. But, mind you, structuralist math is no cure-all. It is not epistemologically innocent. The problem about how we can know the fundamental math­em­ at­ic­al (set-theoretical) axioms turns into a problem about how we can know the corresponding principles of the framework of ‘megethology’ (monadic secondorder mereology), but it’s the same problem either way. Structuralist math is also not ontologically innocent. You dump the commitment to special ‘platonic’ objects; so you dump all the hard questions about the intrinsic natures of these alleged objects, their essences, their whereabouts, etc. So far, so good! But you’re still committed to the existence of a very great deal (much more than any of the usual infinite cardinal numbers!) of something. Now there are two ways to go. You could point out that this commitment to a humongously infinite amount of something is needed for standard axiomatic set theory (on its intended interpretation) but is not needed for the rest of standard working math – topology, differential geometry, functions of a complex variable, and so on, and so forth. Still less is it needed for physically applicable math, which is what Hartry really cares about. Maybe a much smaller infinity would suffice. Maybe – I’d like to know whether this is so – physically applicable math, and the overwhelming majority of abstract math, could get by, un­altered, with only continuum many atoms, which might be the points of the spacetime continuum we already believe in. You could be a fictionalist about parts of axiomatic set theory – mainly the unrestricted power set axiom – and a structuralist realist about all the rest of the math department’s curriculum. Despite my piety toward established mathematics (Parts of Classes section 2.8) – what George Boolos called ‘science worship’ – that would be OK with me. For scepticism about the outer reaches of set theory, plus thoroughgoing realism about working math, see Boolos, ‘Must we Believe in Set Theory?’ in his Logic, Logic, and Logic (Harvard University Press, 1998). Or else you could say that the ontology of modality, if done properly – that is, if freed from an arbitrary-seeming restriction I imposed on the principle of re­com­ bin­ation – also demands the same humongously infinite amounts of something, namely of possibilia (whether these are ‘abstract’ or ‘concrete’). Far from innocent! But you get an ontology for structuralist mathematics at no extra cost. See Daniel Nolan, ‘Recombination Unbound’, Philosophical Studies 84 (1996): 239–62; ‘Individuals Enough for Classes’, forthcoming somewhere – sorry, I don’t know where – possibly under a changed title.2 2  Unpublished. Available at: https://sites.google.com/site/professordanielnolan/home/files/IEFC.pdf. The material from this paper is set out in (Nolan 2002, ch. 7).

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The second later development since ‘How Can we Know?’ is that the prospects for making sense of counterfactuals about impossible situations, and for distinguishing true counter-possibles from false ones, are much better than I used to think. Again this is something I owe to Daniel Nolan. See his ‘Impossible Worlds: A Modest Approach’, Notre Dame Journal of Formal Logic 38 (1997): 535–72. Whether Daniel’s ‘modest approach’ could deliver what Hartry thinks we’d need in order to be math­ em­at­ic­al realists, namely counterfactuals to the effect that if the mathematical facts were different our opinions about them would be correspondingly different, I don’t know. But at least it’s no longer instantaneously ruled out by the supposed trivial truth of all counterfactuals with impossible antecedents. Maybe, after all, it is nontrivially true that if 17 weren’t prime we wouldn’t think it was. But if so, mind you, that would not mean that our opinions were caused by mathematical facts! Jaegwon Kim showed long ago that not all counterfactual dependence is causal (‘Causes and Counterfactuals’, Journal of Philosophy 70 (1973): 570–2),3 and this would be just another example of his point. Next I want to say something about ‘Causal Explanation’. I said, and I still say, that explaining why an event occurred consists of giving some information about how it was caused. But note that information about how it was caused need not consist of specifying some of its causes. One way to give (partial) explanatory information about how some mathematical opinion was caused is to say that its causes, though they are not themselves mathematical objects, fall into some sort of math­em­ at­ic­al­ly specifiable pattern. (‘Causal Explanation’ pp. 219–20, from the paragraph that begins ‘An explainer might well . . .’ through the sentence of the next paragraph that ends ‘. . . or a resonance phenomenon’.) This gives you a sort of sense in which you can have mathematical explanations of mathematical opinions, which are at the same time causal explanations. Whether this sense would satisfy Hartry I do not know. Finally I want to raise an issue about Hartry’s ‘A Motivation . . .’ that’s unconnected to the questions raised in your letter.4 I said we’re reliably right about math because we got certain axioms right, and then our deductions from those axioms preserved truth. Hartry wants an explanation of a general faculty for getting axioms right (p. 238).5 Why? The axioms on a very short list are all that matter. Explanations always end in unexplained explainers. Maybe we got those few axioms right by sheer good luck. (Or maybe not.) That would explain why we’re right about the rest of math, just as explanations which go back to unexplained initial conditions at the   (Kim 1973).  ‘Section 2: A Motivation for Mathematical Anti-Realism’, chapter  7: ‘Realism, Mathematics and Modality’, Realism, Mathematics and Modality (Field 1989). 5   (Field 1989, 238). 3 4

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222.  To Michael C. Rea, 24 August 2001

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time of the big bang explain the subsequent evolution of the universe. That’s ex­plan­ ation enough. Best regards, David Lewis c: Hartry Field

222.  To Michael C. Rea, 24 August 2001 Princeton University Princeton, NJ Dear Professor Rea, Your main question, if I understand you, is this.1 Should we take the counterpart relation to be a three-place relation that relates, as it might be, Socrates, one of his otherworldly counterparts who collects taxes, and the mind of the speaker who is saying (or the thinker who is thinking) that Socrates might have been a tax collector? Or should we instead take counterpart relations to be two-place relations, relating, as it might be, Socrates to his counterpart, but add that there are many of these relations, and that different speakers in different contexts might mean (or different thinkers might have in mind) different ones of these relations? The second, as you thought. I’m not sure why you were in any doubt about it: the passage you quote, not to mention many other passages in Plurality, and also the formalization in ‘Counterpart Theory and Quantified Modal Logic’ should be enough to settle the matter decisively, and I don’t see what more you need. So far, so good. I’m afraid there are some problems elsewhere, though. First paragraph: ‘The truth of [Lewis’s] brand of counterpart theory is not supposed to be a purely conceptual matter’. Why not? I can’t tell whether what you say is right or wrong, because I’m not clear what you mean by it. I’d have said, and I still say, that what I was doing was conceptual analysis. Maybe the problem is that we disagree about what conceptual analysis is. Third paragraph: ‘The property of being similar in this or that respect to other objects in other worlds is intrinsic’. Sometimes, but often not. It depends on the respect. The property of being similar in shape to so-and-so objects never differs between intrinsic duplicates, so that is indeed an intrinsic property. But the property

 See World Without Design: The Ontological Consequences of Naturalism (Rea 2002, 90–4).

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of being similar in origins to so-and-so objects can differ between intrinsic duplicates, since intrinsic duplicates may differ in their origins. If you were conceived in the ordinary way, and your duplicate was created ex nihilo as an embryo, no third thing is similar in origins to both of you. But a property that can differ between duplicates is extrinsic. Likewise, the property of having so-and-so otherworldly counterparts (under some fixed counterpart relation) will be an extrinsic property whenever the counterpart relation is one that gives some weight to similarities in extrinsic respects. For the same reason, many similarity relations, and many counterpart relations, are not intrinsic to their pairs. Fourth paragraph: ‘. . . there are counterpart relations according to which you do have rock-counterparts, electron-counterparts, horse-counterparts, and the like’. I’m not committed to that, and I’m strongly inclined to reject it (except maybe for the horse-counterparts). What seems to have happened goes like this – Any two things share some property; . . . OK, in a sufficiently inclusive sense of the word ‘property’. so any two things are similar in some respect or other; . . . Maybe. But I rather doubt that just any property-sharing (inclusive sense) ought to be called a respect of similarity. Does it really contribute at all to similarity if two things share the property of not coexisting with a unicorn? so any two things (in different worlds) stand in some counterpart relation or other. No! It’s one thing to say that every counterpart relation is a similarity relation, another thing to say that every similarity relation is a counterpart relation. I’m certainly committed to the multiplicity of counterpart relations, but I also think there are limits to that multiplicity. I have no firm view about what those limits are, but I certainly think there are some property-sharings (inclusive sense) that lie beyond them. Sixth paragraph: ‘. . . on the question whether modal properties are relational’. Distinguo. You were previously discussing the question whether modal properties are extrinsic. But, if we think of properties (as we legitimately may) as having a quasisyntactic constituent structure, then a property may be relational in the sense that it has a relation as a constituent, and yet intrinsic in the sense that it can never differ between intrinsic duplicates. The (structured) property of having a square duplicate is relational – it has the relation of duplication as a constituent – and yet intrinsic. (Here I assume that duplication is reflexive.) The property of having a square counterpart, that is of being possibly square, would likewise be relational but intrinsic, under the (unlikely) supposition that we’ve selected a counterpart relation that gives weight only to intrinsic respects of similarity. Admittedly, the terminology is a mess,

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223.  To Michael C. Rea, 7 September 2001

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and some authors do use ‘extrinsic’ and ‘relational’ interchangeably; but it’s worth distinguishing. See Lloyd Humberstone, ‘Intrinsic/Extrinsic’, Synthese 1996.2 Seventh paragraph: ‘Lewis’s view . . . is committed to the claim that there are many different kinds of metaphysical possibility . . .’. I trust I’m not committed to the view that there is any kind of ‘metaphysical possibility’ whatsoever. I regard the notion of ‘metaphysical possibility’ as a misguided one, carrying a false presupposition. Sincerely, David Lewis

223.  To Michael C. Rea, 7 September 2001 Princeton University Princeton, NJ Dear Professor Rea, Conceptual analysis versus inference to the best explanation. In all but the simplest cases, conceptual analysis does work by inference to the best explanation. We find ourselves disposed to make a priori judgements about what’s possible, how various possible cases must or may be described, etc.; and we try to systematize these judgements as best we can. In part, it’s a job of thinking up hypotheses, including ontological hypotheses as well as analyses; in part it’s a job of looking for evidence – a priori judgements – that we might at first have overlooked; and in part it’s a job of seeking a reflective equilibrium between our a priori judgements and theoretical desiderata such as parsimony, avoidance of arbitrariness, etc. Since our a priori judgements are often to some extent hesitant or indeterminate, there’s plenty of room for trading off. It’s very like the attempt to systematize empirical evidence, except that the evidence isn’t empirical. As in the empirical case, conceptual investigation is a fallible business and shouldn’t be expected to lead to certainty. What you thought I thought about how analytic metaphysics works is fine except at one place: ‘. . . justified on the grounds that it coheres well with an overall theory of the world’. If ‘the world’ meant ‘reality’, OK; but if it meant ‘this world’, no. Could I have been a poached egg? In some moods, I can take seriously the sup­pos­ ition that I might have had different origins but more or less the same later life; or that I might have had the same origins but a very different later life; or that I might have been a horse (or anyway a horse-like animal with a human mental life); or a

  (Humberstone 1996).

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disembodied spirit; . . . But not that I might have been a poached egg, or an electron, or a rock! Right: it would be nicer not to have arbitrary and unknown limits on what sort of similarity relation can govern judgements of de re modality, but I think the cost in defying fairly confident a priori judgements is on balance excessive. That could be reversed if we discovered new evidence: contexts which made it seem not so bad to say that I might have been a poached egg. Metaphysical possibility. Once upon a time, ca. 1970, we were of two minds about whether water could have had a different chemical structure, whether cats could have been Martian spy-robots, whether tigers could have been reptiles, whether heat could have been a fluid, whether Hesperus and Phosphorous could have been different, . . . . We wanted to say: in a sense yes, in a sense no. So far, so good. But then we made a big mistake. We decided to distinguish two kinds of possibility: epistemic and meta­phys­ ic­al. E.g. it is (or once was) epistemically but not metaphysically possible that water is XYZ. The term ‘metaphysical possibility’ was meant to be one half of the distinction used to handle these cases, and hence to contrast with ‘epistemic possibility’. So it carries a presupposition that the two-kinds-of-possibility view was the right way to go. That presupposition is false. Instead of two kinds of possibility, there’s one kind of possibility. Each of these cases is associated with a possibility, sure enough; but what’s ‘in a sense yes, in a sense no’ is whether the possibilities in question are rightly described the way I did. What there are two of isn’t kinds of possibility, it’s ways to describe a possibility. To pile confusion on confusion, there’s an unrelated way in which im­pos­si­bil­ ities can allegedly be ‘epistemically possible’: the way arising from ignorance of a priori matters, e.g. logic. (Duntz, a C student in intro logic, reckons that for all he knows, maybe it’s true that [cats purr iff (dogs bray iff [(cows moo iff fish don’t swim) iff pigs fly])]; but in fact this alleged possibility is ruled out by what Duntz knows about cats, dogs, cows, fish, and pigs.) There are possibilities simpliciter; and there are restrictions to possibilities compatible with the actual laws, or with someone’s knowledge, or with actual history up to now, or with moral perfection, or . . . . It’s OK to say ‘epistemic possibilities’ and mean those possibilities that are not known not to obtain; but in that case they’re a restricted case of possibilities simpliciter. So you can’t say that ‘metaphysical pos­si­bil­ ities’ just means possibilities simpliciter and also say that some epistemic possibilities (other than the a priori ignorance sort) are not metaphysical possibilities. I don’t think there’s anything ‘metaphysical possibility’ can mean, given its history of usage, that won’t presuppose the two-kinds-of-possibility mistake. So let’s abandon the term along with the mistake. Sincerely, David Lewis

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PART 3 Ontology

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224.  To J.J.C. Smart, 31 July 1969 UCLA Los Angeles, CA Dear Jack, I am thinking, rather tentatively, that I should change the planned topic of my GDY lectures.1 I take it that it’s a long time before they need to be settled; but I’d like to make up my mind sooner. Among other reasons, I want to apply for fellowships on the premise that I’ll work on the lectures during my year in Oxford; so I’ll need a topic to put on fellowship forms. New topic: the paradoxes of time travel. The idea would be to defend at length the consistency of some – of course not all – time travel stories; for instance, those by Heinlein. A time-traveler is simply a person whose world-line is abnormally shaped – broken, zig-zag, looped, or what-not. Cf. Hilary’s defense of time travel in ‘It Ain’t Necessarily So’;2 but this would be a much more lengthy performance. It’s sort of a jazzy topic, at least students have found it so, and it makes for nice digressions into the topics of time, T-terms, personal identity, memory, causation, alternative worlds, fatalism. Sort of a sugar-coated first course in metaphysical problems. It would really be public lectures; no part of it would be news to philosophers, though the way of assembling the parts might be news to some. The other topic – counterfactuals, causal explanation, and D-N explanation – is more risky. I don’t now have a theory, only the hope of figuring one out. And if I did, it might be hard to present without either presupposing a lot that outsiders would find hard to buy or mixing new stuff of my own with canned elementary lectures, e.g. on Hempel, truth-functional vs. strict conditionals, and so on. A catch: I want to bum money from the NSF, among others. For this, my topic must be in history or philosophy of science. Causal explanation is about as paradigmatically Φ of science as you can get. Not so time-travel – especially since I don’t want to talk about the Gödel universe with closed time-like paths or about positrons being time-reversed electrons. Besides, someone who wants to philosophize about science fiction should be prima facie a crackpot in the eyes of a reasonable referee, so I’d have to depend heavily on letters of reference to correct that impression. The time-travel routine I already have sort of worked out; I’ve done it as a long evening informal lecture to a bunch of undergraduates, and as tutorials with some of

1   Gavin David Young Lectures, delivered by Lewis in July 1971 at the University of Adelaide. For these lectures, see (Janssen-Lauret and MacBride forthcoming). 2   (Putnam 1962).

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our graduate students. (They hear about it from each other, and come around and ask me to do it again for a new audience – much as if I knew a good dirty song to sing them.) Thus if I were officially working on that at Oxford, I’d be fairly free to do whatever I wanted to do at the time. The other project would be a bigger deal, and might not at all coincide with the ideas I was having. Another consideration: what did Davidson do for his G.D.Y.? If he did his stuff about events, adverbs, and causation, then my original topic might have been too close to his. (Incidentally, I’d very much like to see a set of notes of Davidson’s lectures, if you have one that can be copied.) Thank you very much for the note about N.S.W. and the ravings of Sellars. On Sellars, though, I think Hilary said enough: ‘Life is short’. There’s just arrived a big manuscript from Brian Ellis on probability logic; I’ll maybe read it in September, when I get a month off between two terms of moderately heavy teaching. Or maybe I won’t read anything, but try to finish writing some things. I tried to get Steffi for her birthday an Australian bird book. My bookstore ordered What Bird is That?,3 but I think it must be coming from Australia in a bottle. Maybe it will yet arrive before we leave for Australia! Yours, David and Steffi (but not now here to sign)

225.  To W.V. Quine, 18 August 1969 UCLA Los Angeles, CA Dear Van, Enclosed are a toy1 and a task. I hope the toy will compensate for the task, though to play with the toy is itself a task. The toy: I invented some ways to counterfeit some set-theoretic constructions using only calculus of individuals and a nextness-predicate. The counterfeit isn’t good enough for mathematics, but is good enough to replace set theory in some philosophical applications. It would, for instance, give you alternative methods to do   (Cayley 1966).

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  ‘Nominalistic Set Theory’ (Lewis 1970d).

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many of the things in Steps; I believe it would also give you a – somewhat mangled – model theory to accompany the syntax. I’m not yet tempted to give up sets, though, and I trust you won’t be either. (Yet if forced to choose between useful entia marginally gratis, I’d far sooner give up sets than possibilia!) It’s mostly just for fun. The task: I’ve given you as a reference for several fellowships. Jack Smart has arranged for me to give the G.D.Y. lectures in the summer of 1971. (Excuse me: by ‘summer’ I mean the cool time starting in June, not the hot time starting in December.) I’m thinking to take the whole year 1970–71 off, go to Oxford, write the lectures, and think about whatever else I may happen to get interested in. The main purpose of going to Oxford is to let Steffi study philosophy of law with Ronald Dworkin and perhaps Hart; I could work almost as well in any pleasant place. I enclose reference forms for a travel-only Fulbright to Australia for summer 1971 and for several alternative fellowships to Oxford for 1970–71; there will be more of the latter later. I trust one letter will do for the lot, with only minor stylistic changes. Warnings: the A.C.L.S. uses some primitive copying device such that their form mustn’t be folded. I enclose copies of my statements of plans so you can see what I’m up to. I apologize for giving you paperwork, and thank you very much for doing it. Yours, David

226.  To Charles Chastain, 8 March 1970 UCLA Los Angeles, CA Dear Charles, I like trans-world nominalism. (Really inter-world – consider that TWA doesn’t yet fly spaceships.) My working ontology is actual and possible concreta, together with any sums or sets over these; but if I had to choose between giving up the sets or giving up the possibles I’d give up the sets. I question two details, though: why don’t you let propositions be sums of worlds (with some adjustments to allow you not to have an impossible proposition)? Is it because you want propositions to be structured? Alternatively, why not let them be semantic representations in some suitable Universal Markerese – thus inscriptions, or sums of inscriptions? I don’t like your properties; the property rabbithood comes out the same as the property undetachedrabbit-part-hood, doesn’t it? That’s just like the Quine example you said you’d got around, but I don’t think you can in general get around the objection Quine was

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making. However, there are some gimmicks you can use to take a sum and encode information about which division of it into parts you are interested in; I’ll send you a paper ‘Nominalistic Set Theory’ about this.1 (Not to go further, because known to contain mistakes.) We sail 25 June. Hope to leave here early June, depending on the extent to which I can give my 31 final from a distance. Will you be in Ithaca in mid-June? Congratulations on Toronto. Tell us more. Howard’s doing? One year or more? Yours, David PS Enclosed are correction pages for ‘General Semantics’, end of the section on intensions for basic categories.2 I haven’t the strength of character to write in naïve set theory!

227.  To J.J.C. Smart, 1 May 1970 UCLA Los Angeles, CA Dear Jack, You’ll find little or nothing about properties in Convention1 when you recover it from Gasking; you’ll find a little bit in the ‘How to Define . . .’ paper,2 near the end of the section called ‘The Interpretation of T-terms’. The key sentences are (1) ‘I take it that a property is identified when, and only when, we have specified exactly which things have it in every possible world’. (2) ‘A property in turn may be represented by a function P which assigns to any world w the set Pw of things which, in the world w, we have the property’. I was being non-committal in (2), but what I really think is that the property is the representing function. The property of being a pig, for instance, is that function from worlds to sets whose value, for any world w, is the set of all pigs in w. Properties are functions; functions are sets of ordered pairs; ordered pairs are sets of sets; so properties are sets of sets of sets, and therefore ought not to bother you. If possible worlds and possible things bother you, I suggest you regard them also as set-theoretic constructs, in the manner of Quine, ‘Propositional Objects’,  (Lewis 1970d).   2  (Lewis 1970b).

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 (Lewis 1969).   2  ‘How to Define Theoretical Terms’ (Lewis 1970c).

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Ontological Relativity, pp. 147–52.3 (You will, however, want to modify Quine’s construction so that it’s based on true rather than false physics; but it’s easy to see how that can be done.) I myself would rather leave possible worlds and things unreduced, because I hold the bizarre view that there’s no intrinsic difference between the actual world and other possible worlds – ‘actual’ is a token-reflexive analogous to ‘present’, except that it refers to the world of utterance rather than the time of utterance – and if I held that along with the view that possibles are set-theoretic constructs of Quine’s sort, I would have to conclude that I myself am an entity of pure set-theory! If nothing exists in more than one world, and if furthermore nothing has any property in worlds where it does not exist, then a simpler theory of properties is possible: a property is the set of its possible instances. The property of being a pig is the set of pigs – but not only of the actual pigs, rather of all the pigs in all possible worlds. It wasn’t I who used Ramsey clauses to explicate interanimation; I dimly remember Bohnert4 saying such a thing. Do you know Neil Wilson’s ‘Substances without Substrata’, Review of Metaphysics 1959?5 He there suggests that proper names are Ramsey-variables, just like Bohnert’s T-terms, and that sentences involving proper names are detached clauses. (No mention of Ramsey or Bohnert – but it’s nevertheless the same idea.) Wilson’s paper is best known as the source of the Principle of Charity, but there’s much else there of interest. We’re waiting to hear the war news from Cambodia and Yale, and looking forward more and more to a vacation from this deplorable country. (UCLA also is due for a march through the administration building later today, but I expect it to fizzle.) We’ll be in Oxford before you, I see. Our plan is to stay close to Oxford in July and August, when there will be lots of tourists elsewhere, and travel for most of September, ending up in Munich where we’ll pick up a new car. (BMW 1600 – some improvement over a VW bug with 125,000 miles.) Steffi has been working hard learning French; she’ll take her language exam tomorrow. After that things will slack off for a couple of weeks; we’ll be able to go to San Francisco for a while. Then comes packing; then train trip east by short stages, with stops in New Mexico to see my brother, Oberlin to see my father and sister, Ithaca to see our friends the Chastains, New York to see Steffi’s family, and Princeton to see my future colleagues and maybe settle some arrangements. Steffi regrets that she can’t send regards in her present condition, but only des amitiés. Yours, David   (Quine 1969).   Herbert G. Bohnert. See for instance ‘In Defense of Ramsey’s Elimination Method’ (Bohnert 1968). 5   (Wilson 1959). 3 4

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228.  To T.G. Gardiner, 1 October 1970 Headington Hill Oxford, England Dear Mr. Gardiner, We consulted Argle and Bargle about your letter, and it turns out that they agree that if matter were everywhere absent and nowhere present, there wouldn’t be any holes. They also agree that if any one uniform sort of matter were everywhere present and nowhere absent, there wouldn’t be any holes. So, they think, holes result from both the presence and the absence of matter – more precisely, from its presence in one region combined with its absence in another. But you must remember that Argle and Bargle are mere philosophers, and don’t know very much about the speculation of physicists. If they looked at John Wheeler’s paper ‘Curved Empty Space-Time as the Building Material of the Physical World: An Assessment’ in Nagel, Suppes, and Tarski, Logic, Methodology and Philosophy of Science, they might become less certain that there couldn’t be holes without matter.1 Bargle wouldn’t mind that, but Argle would find it most distressing. Thank you for your letter. Sincerely yours, David and Stephanie Lewis PS Give our greetings to the Cresswells if you have a chance.

229.  To Donald C. Williams, 12 May 19711 Headington Hill Oxford, England Dear Donald, We were sorry to hear of your hospitalization. We wish you to have had a quick and easy recovery! Oxford has become home, more than Los Angeles ever did. Los Angeles is too big to grasp, whereas Oxford is the right size: small enough to learn, but too big to learn perfectly. We’ve had a very good year here, and we regret that it will soon be time   (Wheeler 1966).

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to leave. Still, we’re looking forward to our continued travels. We fly to Australia at the end of June; I give my time travel lectures in Adelaide in July; and we go on to Princeton in mid-September. Ever since the prospect of moving to Princeton became a serious one, a year and a half ago, we have felt homeless; only when we have settled in Princeton will that be ended, and we look forward very much to living some place again, rather than passing through. Travel is fine, but we have been gypsies a little too long! I know well why Yost didn’t want to admit to teaching philosophy at UCLA. We also try not to tell casual acquaintances that we come from the UCLA philosophy department. If we do, it usually happens that a friendly conversation ends, and it is demanded that we either defend or attack Angela.2 I’m unwilling to attack (not out of any loyalty to Angela herself, but to my friends in the department), and quite unable to defend! Steffi can sometimes manage to divert the conversation into a discussion of the points of law at issue – the best solution, when it works. Thank you for your comments on my paper about Tim the time traveler.3 My Adelaide lectures will be similar, but much longer: five or six one-hour lectures. I’ll say much more about the question of personal continuity, and about apparent changing of the past in a branching spacetime. (Apparent only, because both the changed and the original version of the past are there all along, in different branches.) You ask why Tim can’t talk to his earlier or later selves face-to-face, not only on the telephone? Why can’t they hug and kiss, if so inclined? They can, of course; I didn’t mean to suggest that the telephone was required. (It might be less disconcerting to use the telephone, however!) I disagree with you when you say ‘the way in which numbers can’t change is very different from that in which past (or future) events can’t’. What can change are things made up of temporal parts, because change is dissimilarity between different temporal parts of something. Numbers and the events of a given instant are alike in not being made up of temporal parts – therefore alike in the respect that make it impossible that they change – however unlike they are in other ways. However, I am speaking here of instantaneous events – not prolonged events like battles or lives. The latter are made up of stages; the stages can be dissimilar; and so the prolonged events can and do change – they are not perfectly monotonous. I admit both sorts of events: the instantaneous and the prolonged. A prolonged event has infinitely many instantaneous events as parts, just as a line-segment consists of infinitely many points. I think, though, that it is unfortunate that I speak of both the instantaneous and the prolonged events as ‘events’ or ‘stages’ in (say) Tim’s life. It would be well to use distinct terms, but I’m not sure what terms these should be.   Angela Davis.   ‘Could a Time Traveler Change the Past?’, 26 November 1970 (read to the Jowett Society, University of Oxford, November 1970). 2 3

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I don’t say ‘that a thing doesn’t change when it acquires new relations’; in some cases it does, in some cases it doesn’t. 47 doesn’t change when it acquires new relations – for instance, when it temporarily becomes the object of my attention – because it is not the case that there are different temporal parts of 47 that differ in the relations they bear to things. But your man in Vietnam to whom a son is born in St. Louis does change, as you say. For not only does the whole (83-year-long) man acquire new relations, but also there is a difference in relations between his later and his earlier temporal parts. (I’m concerned here with changes in relations only. Let us imagine that the man is frozen in suspended animation at the time his son is born, so that his inherent qualities and his relations to very nearby things are not changing at that time.) You say I ‘oughtn’t to suggest a mere miss, since history seems to record that no one then shot at Grandfather, as reliably as it does that he wasn’t killed’. But I had in mind a miss that went unnoticed and unrecorded. The gun was well silenced; and if Grandfather heard the bullet, he did not recognize the sound for what it was. On personal identity: I would make it a matter of continuity in kind, together with causal continuity, that the scattered segments of Tim (taken in the proper order) combine to make a single person. That is: if you trace through them in the proper order, then all properties at most points, and most properties at all points, vary gradually; and further, each stage is the way it is because the preceding stages were the way they were. (‘Preceding’ in personal time – not necessarily in external time.) But of course this causal continuity involves reversed causation, and I must therefore give an analysis of causation compatible with that. It may be that if Tim’s time trav­el­ ing were inexplicable, then the causal (including reversed causal) continuity needed to unite the segments of Tim into a single person would be absent; I’m not sure of this. I am sure that if there were an explanation of the wrong sort – activity of a demon attempting to simulate time travel by means of suitable miraculous creations and destructions, for instance – then causal continuity would fail and we wouldn’t have a case of time travel after all because we wouldn’t have a single person. You say ‘the man who “can” but doesn’t run a mile in four minutes jolly well can’t run a mile in those four minutes’; and, in general, failure to do something is de­cisive reason to conclude that ability was lacking. I recognize a concept of ability on which this is so; but I don’t think it’s our usual notion. Abilities are not such fleeting things. I have the ability to type; I retain it when not typing and even when asleep. Nevertheless, I very occasionally hit the wrong key. We might say that my ability has momentarily deserted me; but I think it is more accurate to say that even one who has the ability may occasionally fail. After all, my ability is an ability to type – not an ability to type infallibly. I would suppose that Tim’s failure is explicable; and ex­plic­ able not just by appeal to the fact that Grandfather lived on, but explicable in some

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commonplace way, just like Tom’s parallel failure. But I would not infer from this that Tim lacked the ability to succeed. Similarly, if I hit the wrong key, I presume my failure to type correctly is explicable, but I don’t think it follows that whatever prevented me from typing correctly did so by momentarily depriving me of my ability to type. It takes more than will and ability to succeed – it takes also a modicum of luck. But if you have the ability, you shouldn’t need much luck. Of course, we could lump together luck and (what I call) ability; nothing wrong with this, but I don’t think it’s quite what we most commonly express by ‘can’. Is the record so plain that no time travelers have ever turned up? I think it’s full of holes. If you want to find past events that could be interpreted as the activities of visitors from the future, it shouldn’t be hard. Heinlein (Door into Summer)4 suggests interpreting the career of Leonardo da Vinci as a case of time travel, and that seems plausible enough. I don’t (for no good reason) really believe that there have been time travelers, but I think it’s consistent with what we know of the past that there have been. Of course, they would have to have been relatively cautious ones – ones who didn’t try to make themselves too conspicuous. I don’t agree that ‘an irruption from a future time is pretty sure to have been dramatic and hence to have become famous’. Indeed, the life of a visitor from the future, if he were well-informed, would be quite an extraordinary life, because of his foreknowledge of what he would and would not succeed in doing; I grant this, but do not take it as an argument that a visit from the future would not be possible. Our very best wishes to you both. Yours, David

230.  To Derek Parfit, 13 May 1971 Headington Hill Oxford, England Dear Parfit, I owe you an expansion of my cryptic remarks yesterday; and it seems best to expound my line in a letter, rather than throw it at you in some future class. To start with: I buy your main point that what matters is psychological connectedness which need not – does only de facto in the present state of technology –   (Heinlein 1957).

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have the properties of identity. Or rather: in cool moments I think that what matters is psychological connectedness; in uncool moments I think that what matters is some mixture of psychological and bodily connectedness – but still connectedness of more-or-less momentary stages rather than identity. But although it’s connectedness that matters morally and emotionally, I don’t want to forget about identity; it’s a side-issue, but one I retain an interest in. So what follows is intended to be compatible with your views, not an attack on them. A person is a continuant consisting of mutually connected stages. For what follows it does not matter whether the stages are altogether instantaneous or of very short duration; and it does not matter whether the connectedness is purely psychological or a psychological-and-bodily mixture. Some definitions: 0) A person0 is an ordered set of person-stages that is logically connected – that is, any two stages that are sufficiently close together are strongly connected (but it is not required that distant stages be at all connected). 1) A person1 is a person0 that is connected throughout; that is, any two of its stages, however distant, are at least somewhat connected. 2) A person2 is a person0 that is not part of any larger person0. (Thus a person0 that is not a person2 might better be called a mere segment, not the whole, of a person.) 3) A person3 is a person1 that is not part of any larger person1 (thus a person1 that is not a person3 might better be called a mere segment, not the whole, of a person). What is a (continuant) person? Either a person2 or a person3; we have not had to decide because, de facto, almost all and only persons2 are persons3. Life is short; almost every person2 dies before the connectedness between his youngest and oldest stages fades out entirely, and therefore is also a person3. But consider now, as in your ΦR paper,1 a person2 who lives a very long time – so long that there is no connectedness at all between his oldest and his youngest stages. To be more precise: let us suppose he lives 999 years, and let us suppose that stages s1 and s2 are somewhat connected if and only if they are no more than 100 years apart. Here we have a person2 who is not a person3 because he is connected locally but not connected throughout. Call him Methuselah. Methuselah as a whole is a person2 but not a person3. However, according to the definitions I gave, 100-year segments of Methuselah are persons3. They are locally connected and connected throughout (since they are not too long) and thus they are persons1; further, they are the longest segments of Methuselah that are persons1 and therefore they are persons3.   ‘Personal Identity’ (Parfit 1971).

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I take it that the question of personal identity is the question: are this stage and that stage two stages of a single person? Now if s1 and s2 are any two stages of Methuselah and I ask if they are stages of a single person2, the answer is that they are. If I ask whether they are stages of a single person3, the answer is that they are if and only if they are no more than 100 years apart; in other words, that they are if and only if they are at least somewhat connected. Good: if we decide that persons are to be understood as persons3 rather than persons2, then connectedness – what really matters – and personal identity (being stages of a single person) coincide, and that’s nice. But the decision to take persons as persons3 rather than persons2 leads to trouble. Methuselah consists of an indefinite number of overlapping and non-overlapping persons3. There are more than one at a time. If Methuselah lives from the year 0 to the year 969 (on a suitable Methuselan calendar) then there is a person3 who lives from 100 to 200; one who lives from 101 to 201, . . . and one who lives from 199 to 299. (Of course there are many more than these in the period I’m considering: a person3 doesn’t have to begin exactly on Methuselah’s birthday in a given year!) These persons3 are not strictly identical, obviously. If they were strictly identical, then (strict identity obeys Leibniz’s Law) they would have the same dates of beginning and ending, which they don’t. So all these 100 non-identical persons3 (and infinitely many more) are alive at a time t late in the year 199. That makes for crowding: Methuselah is alone in his room at time t. How many persons in the room? It ought to be that there is only one. But we’ve decided to take persons as persons3 rather than persons2; and we know of 100 (and more) different persons3 that are all in that room at t. Tensed identity to the rescue. A and B (continuants) are identical-at-t if and only if the stage of A located at t and the stage of B located at t are identical simpliciter. All of our 100 different persons3, though not identical simpliciter to one another, are identical-at-t to one another. If we take persons as persons3, but also decide to count by tensed identity rather than by identity simpliciter, then we shall say that after all we have one and only one person in Methuselah’s room at t. That is: there is a person in Methuselah’s room at t, and it is not the case that there are a person A and a person B in Methuselah’s room at t that are not identical-at-t. In other words: there is a person in Methuselah’s room at t such that all and only persons in Methuselah’s room at t are identical-at-t to him. Thus if I can persuade you that tensed identity is the kind of identity that you count continuants by, then I can answer the obvious objection to the view that persons are persons3 rather than persons2: to wit, the objection that if so, then there are too many persons in Methuselah’s room at t. Now I think you oughtn’t to mind being so persuaded. The cases where it gives different results to count by tensed identity and to count by identity simpliciter are

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mostly fantastic hypothetical cases. For instance, if a person2 dies soon enough so that he is a person3 as well (and also does not fission or fuse), then if he is alone in his room at t, both ways of counting will agree that there is exactly one person in the room at t. But if the cases where the two ways of counting diverge are fantastic cases, it’s to be expected that ordinary language will be unsettled about how to describe them; so you shouldn’t mind coming to whichever conclusion best serves the purpose of making judgements of personal identity coincide, so far as possible, with judgements of connectedness. As for Wiggins’s dividing person, I said in class how to apply tensed identity to that; there are two persons all along. Both lived identical early lives, but they came apart at the operation. One will die in Australia, the other in Iceland. Call them A and B. When I say that they are two persons all along (with initial overlap) I am speaking in terms of tenseless identity, identity simpliciter. Speaking in terms of tensed identity, I rather say: if t is any time before the operation, A and B are identical-at-t; if t is any time after the operation, A and B are not identical-at-t. The main drawback of the two-persons-all-along solution seems to be that it’s absurd to say that two people, rather than one, sit in the waiting room waiting for the doctor to split their brain. Still worse: let them undergo the operation at age 29 – were there two babies rather than one in the pram 28½ years before? But these objections are met if you can be persuaded to count by tensed identity rather than identity simpliciter. If t is a time a few hours before the operation, there is a person in the waiting room who is identical-att with everyone else in the waiting room (A is in the waiting room and so is B; although they are not identical, they are identical-at-t, and that’s enough to say that there is one person in the waiting room). Likewise, the pram contains A and B but does not therefore contain two babies: for A and B are identical-at-the time in question, though not identical simpliciter. Identity-at-t does not obey Leibniz’s Law with respect to tensed predicates. Since it is something other than identity there’s no reason it should. It is true at t of A that he will die in Australia; A and B are identical-at-t (taking t earlier than the op­er­ ation); it does not follow, and is false, that it is true at t of B that he will die in Australia. I said even more cryptically that I could make personal identity a matter of degree – just as connectedness is a matter of degree – not because identity is a matter of degree but because personhood is a matter of degree. Returning to the case of Methuselah and the persons3 that are segments of him, let me explain what I meant by that. Further definitions: 1+) A person1+ is a person0 that is connected throughout to a certain fairly high degree d+; that is, any two of its stages, however distant, are connected to at least that degree.

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1-) A person1- is a person0 that is connected throughout to a certain rather low degree d-, d- being a much lower degree of connectedness than d+. That is, any two of its stages, however distant, are connected to at least degree d-. 3+) A person3+ is a person1+ that is not part of any larger person1+. 3-) A person3- is a person1- that is not part of any larger person1-. Personhood, I said, is a matter of degree: a person3+ is more a person than a person3who is not a person3+, since the former is better connected. For simplicity I consider only two degrees of connectedness – really there should be a continuum of degrees of connectedness and hence a continuum of degrees of personhood. Let’s suppose that the degrees d+ and d- have been chosen so that an ordinary short-lived person2 qualifies as a person3+, and hence also as a person3-. Not so Methuselah, however. Let us say that the connectedness of his stages fades out at such a rate that his stages s1 and s2 are connected to degree d+ if and only if they are no more than 90 years apart, and connected to degree d- if and only if they are no more than 110 years apart. Every segment of Methuselah that is exactly 90 years long is a person3+ and every segment of Methuselah that is exactly 110 years long is a person3-. A 90-year segment is more a person, because better connected throughout, than a 110-year segment. (An 80-year segment is still more a person; a 120-year segment is still less a person; and so on.) The question of personal identity, I said, is the question: are this stage and that stage two stages of a single person? And I say that the answer is now a matter of degree. Let s1 and s2 be stages of Methuselah 100 years apart; let s3 and s4 be stages of Methuselah 80 years apart. Then s1 and s2 are stages of a single person3- but they are not stages of any single person3+. On the other hand, s3 and s4 are stages of a single person3+ (as well as stages of a single person3-). Therefore s3 and s4 are stages of a single person to a greater degree than s1 and s2 are, because the person3+ (or rather persons3+) of which s3 and s4 both are stages is a person to a greater degree than is any of the persons3- of which s1 and s2 are both stages. In this way, personal identity – just like connectedness – holds to a greater degree between s3 and s4 than between s1 and s2. We could say that s3 and s4 are linked by personal3+ identity whereas s1 and s2 are linked by personal3- identity only. Enough! Yours, David Lewis PS Not enough. I shall also make you a xerox of a xerox of ‘Can the Self Divide?’ by John Perry.2 Perry rejects the two-persons-all-along solution that I presently f­avor;   (Perry 1972).

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I think it’s fair to say that his solution amounts to forgetting about continuant persons and understanding sentences about persons (giving their truth conditions) explicitly in terms of stages and connectedness thereof. Identity will be understood as identity simpliciter – but of stages, not of whole continuants.

231.  To Jonathan Harrison, 20 July 1971 University of Adelaide Adelaide, Australia Dear Professor Harrison, I’ve just read with much pleasure and interest the copy of ‘Dr. Who . . .’1 that you sent J.J.C. Smart here. I’m presently visiting Adelaide to give six lectures on ‘The Paradoxes of Time Travel’, in which I argue that time travel, as imagined in science fiction, is logically possible. (Not that you can’t write an inconsistent time travel story – many SF writers have – but that you can write a non-trivial consistent one. Heinlein’s, for instance, are logically perfect. Wells’s is imperfect, but the blunders can be explained away.) I hope to make my Adelaide lectures into a book called The Paradoxes of Time Travel. The manuscript of that is not in presentable condition, but I am sending you (separately) a short paper that I extracted from it last fall for the Jowett Society at Oxford, called ‘Could a Time Traveler Change the Past?’ I’ve heard of three other papers about time travel that have not yet appeared. One by Geach (anti), one by Shoemaker (pro, but heavily qualified), and one by Bill Newton-Smith. So it can no longer be said that ours is a philosophical problem that has been entirely abandoned to the amateurs! Sincerely, David K. Lewis

  ‘Dr. Who and the Philosophers or Time-Travel for Beginners’ (Harrison 1971).

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232.  To George Boolos, 2 December 1971

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232.  To George Boolos, 2 December 1971 Princeton University Princeton, NJ Dear George, I’ve looked now at the Skolem paper.* It’s close to what Hodges and I do in ‘Finitude and Infinitude . . .’1 but not quite the same. Taking Skolem to be talking about the calculus of individuals – he calls it both ‘Klassenkalkul’ and ‘Gebietekalkul’, the latter meaning ‘Calculus of Regions’ – what Skolem shows is that every formula is effectively equivalent to a truth-functional compound of formulas of the form (1) At least n things are parts of X where X is a term built up from free variables of the original formula, constants for the universal and null individuals, and operations of union, intersection, and complementation. What we show is that given an axiom of atomicity – which Skolem doesn’t assume – every formula is effectively equivalent to a truth-functional compound of formulas of the form (2) At least m atoms overlap Y where Y has the form (x1 ∩ . . . ∩ ӯ1 ∩ . . .), the variables x1, . . ., y1, . . . being all and only the variables free in the original formula. (We don’t put it quite that way, but we might as well.) How big is the gap? Obviously, a formula of form (1) is equivalent to a formula of form (3) At least n things are part of Y1 ∪ . . . ∪ Yk where each Yi has the form specified for Y above. Given atomicity, we know that at least n things are parts of something iff at least m atoms are parts of it, and hence iff at least m atoms overlap it, where m is such that 2m-1 < n ≤ 2m; so given atomicity, a formula of form (1) is equivalent to one of form (4) At least m atoms overlap Y1 ∪ . . . ∪ Yk with the Yi’s as before. Since the Yi’s denote disjoint things, every possible way for (4) to come true is describable in the form (5) At least m1 atoms overlap Y1 & . . . & at least mk atoms overlap Yk *   Untersuchungen über die Axiome des Klassenkalküls und über Produktations- und Summations­ probleme, welch gewisse Klassen von Aussagen betreffen’ Skrifter Videnskabsakademiet i Kristiana No. 3 (1919), reprinted in Skolem, Selected Works in Logic, ed. Jens Erik Fenstad (Universitets forlaget, 1970). 1   ‘Finitude and Infinitude in the Atomic Calculus of Individuals’ (Hodges and Lewis 1968).

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where the mi’s sum to m; so (4) is equivalent to a disjunction of all formulas of the form (5), which is a disjunction of conjunctions of formulas of the form (2); so that’s how to get from Skolem’s result to ours. I note that Skolem’s paper is regarded as the source for decidability by quantifier elimination of monadic second-order logic. (Regard seeming first-order quantifications as second-order quantification over atoms; regard Px as meaning that x is an atomic part of y; so our calculus of individuals can be reconstrued as monadic second-order logic.) See Hilbert & Ackermann 3.12 and 4.1; Church, middle of page 293.2 Yours, David

233.  To Jack W. Meiland, 13 December 1972 Princeton University Princeton, NJ Dear Professor Meiland, Thank you for your paper on time travel in two-dimensional time.1 I rather think that a passage theory of time must be either a serious theory of twodimensional time, like yours, or no theory at all, nothing but mystification and a miscellany of fallacious refutations of the manifold theory. It’s pleasant to find someone who chooses the former! I don’t find your two-dimensional theory inconsistent or paradoxical. I only wonder why it’s needed, since I think a one-dimensional manifold theory is adequate to represent all ordinary facts about time, adequate to represent the possibility of time travel in which the past is unchanged and even adequate – if branching is permitted – to represent the possibility of something close to Wellsian time travel. But I also wonder whether your theory is really any different from mine. Your horizontal time dimension plainly corresponds to my external time; and your vertical time dimension seems very like what I call the personal time of a given time trav­ el­er (or of a normal person). Am I right to think, for instance, that you disallow travel in vertical time just as I would disallow travel in personal time, so that the only time 2   Principles of Mathematical Logic (Hilbert and Ackermann 1950); Introduction to Mathematical Logic (Church 1956).

  ‘A Two-Dimensional Passage Model of Time for Time Travel’ (Meiland 1974).

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233.  To Jack W. Meiland, 13 December 1972

457

travel in your model is change of horizontal time with respect to vertical time? You say, and I do not, that vertical or personal time is a second time dimension, but I wonder how much this disagreement amounts to. I can draw a two-dimensional graph that looks like yours, with personal time as the vertical dimension and external time as the horizontal dimension. A person (a time traveler or not, as the case may be) is represented by the locus of (v, h) points such that the stage v units in personal time after his birth – v units down the worldline – is located at external time h.

Here I’ve graphed a normal person A, and also a time traveler, born the year of A’s death, who visits the past and returns. For comparison, I’ve also represented A and B in the ordinary spacetime manifold with one time dimension, personal time being indicated by numbers. The first graph is two-dimensional, but it isn’t a map of two-dimensional time. Analogy: disregarding time, there could be a fourdimensional graph on which a certain railway line is represented by the locus of (r, x, y, z) points such that the place r miles down the line from the terminal is at spatial coordinates x, y, z in some reference frame. The four-dimensional graph is not a map of four-dimensional space because distance down the line is not a fourth spatial dimension.

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My two-dimensional graph might perhaps seem more like a map of twodimensional time if we plotted in locations of events. That can be done in several alternative ways. But first let me simplify: the vertical dimension will henceforth be the personal time of one specific person X, not (as on my diagram of A and B) personal time in general. That will avoid some problems about how to plot in the events. X may be a normal person, or a time traveler in a non-branching manifold or a time traveler in a branching manifold, like C below.

An event is located, in the first instance, in external time. We have its h-coordinate. To plot it, we must locate it also in X’s personal time, thus assigning it a v-coordinate. At least sometimes we must assign an event more than one location in X’s personal time, in which case that event will be plotted at more than one (v, h)-point on the graph; for instance, a conversation between X’s younger and older stages, if X is a time traveler in a non-branching manifold, will be plotted in at least twice over. Rule 1: Plot event e at (v, h) iff e occurs at external time h. Rule 2: Plot event e at (v, h) iff e occurs at external time h and some stage of X that is v units of personal time after X’s birth is also located at external time h (and thus is simultaneous with e in external time). Rule 3: Plot event e at (v, h) iff, for some branch b, e occurs at external time h in branch b, and some stage of X that is v units of personal time after X’s birth is located in branch b. Rule 4: Plot event e at (v, h) iff, for some branch b, e occurs at external time h in branch b, and some stage of X that is v units of personal time after X’s birth is also located at external time h in branch b (and thus is simultaneous with e in external time and also in the same branch as e). The alternative rules for plotting: events satisfy different desiderata. (1) It would be nice if the curve representing a person coincided with the set of points where events of his life are plotted. That is so on Rules 2 and 4; whereas on Rules 1 and 3 the events of X’s life will be plotted not only at points of the locus representing

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233.  To Jack W. Meiland, 13 December 1972

459

X but also elsewhere. (2) On the other hand, it would be nice if horizontal slices could be regarded as representing the past, present, and future from the standpoint of one of X’s stages. That is so on Rules 1 and 3; whereas on Rules 2 and 4 only present events are on the slice and the past and future are missing. (3) It would be nice if events e and f are never plotted at the same points unless they occur at the same external time and in the same branch; that is so on Rules 3 and 4, whereas Rules 1 and 2 superimpose the events of different branches just as they superimpose events at different places in space. None of the rules for plotting, however, gives us anything that we can properly regard as a map of events in two-dimensional time. (1) As noted, all four rules allow a single event to be plotted twice over in case X is a time traveler in a non-branching manifold. (2) Rules 2 and 4 leave most of the (v, h)-points unoccupied; in fact, all but those on a one-dimensional curve. In case X is normal, for instance, all events are plotted onto the v = h diagonal. The two-dimensionality of the graph is idle. (3) Rule 1 allows the two-dimensional map of events to be collapsed down to a one-dimensional map without loss. The events come out as vertical lines, and all the horizontal cross sections are alike. (They aren’t alike with respect to the locus of X; but the locus of X has been plotted not by plotting the events of X’s life using Rule 1 but rather by a method resembling Rule 2 or 4.) (4) Rule 3 also allows collapse, though perhaps not down to a single line. If X is normal, or a time traveler in a non-branching manifold, Rule 3 is the same as Rule 1; but if X is a traveler in a branching manifold, the plot will be something like this.

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The vertical lines are the events of the appropriate branch: the one the traveler is in at the personal time given by the v-coordinate. Thus they change at the personal times when the traveler enters a new branch; though the change is found only to the right of the branch point. The plot collapses not to a line but to a one-dimensional branching structure; still, this is one-dimensional. Rule 3, I think, is the one that comes close to matching your model; though I can’t tell for sure, since you concentrate on the locus of X himself rather than the surrounding events. Tell me: would my graph for one-dimensional but branching time using Rule 3 look like your graph for Wellsian time travel in two-dimensional time? If so, I think we have no genuine disagreement. There is only the verbal question of whether, given the possibilities of limited collapse, personal time deserves to be called a second dimension of time. But if the graphs would be different, then I don’t quite see yet how yours would go. I shall make a xerox of this letter for a student in my present course on time travel, Mr. Richard Mott, who wrote a paper arguing that I ought to regard personal time as a second dimension of time. Sincerely, David Lewis

234.  To Jack W. Meiland, 6 January 1973 Princeton University Princeton, NJ Dear Professor Meiland, Here you have the reading list for my course. It’s too short, as you see, but what else is there? It’s already filled out with papers not on time travel itself, but on such related topics as personal identity. My personal time is indeed meant to be the personal time of one definite person (or person-like animal, robot, deity, . . .) just as distance-down-the-track is distancedown-the-track on my personal railway line R.  No persons, no personal time, no railways, no distance-down-the-line. So I wouldn’t like to let the v-axis ‘represent personal time in general’. Here the point on the first page of the letter (the upper one of the two graphs)1 is a bit misleading; best think of it as two graphs plotted on the same page, one with the v-axis representing A’s personal time and one with the same   That is, the very first graph of the previous letter (p. 457).

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235.  To Charles Fillmore, 29 January 1974

461

v-axis representing B’s personal time instead. So if you think of the v-coordinate as something independent of particular persons, I think we may have a genuine difference after all. On branching: I think there are several ways to make a consistent branchingmanifold story, and it’s up to the author who wants to write such a story to choose. One way is to have the branches diverge in an extra spatial dimension. Another way is to have two non-interacting populations superimposed in the same spacetime. A third way is to have a complicated spacetime curvature* without embedding in a non-curved higher dimensional spacetime. A fourth way, perhaps, is to think of the two branches as two different possible worlds, but I’m not sure that this can be made consistent with travel from one branch to another. Sincerely, David Lewis *like so:

235.  To Charles Fillmore, 29 January 1974 [Princeton, NJ] Dear Chuck, The philosopher I mentioned to you as a believer in discrimination between crazy artificial properties and legitimate properties – more precisely, between predicates which do and do not express non-artificial properties, whether or not there exist artificial properties for other predicates to express – must have been David Armstrong (Sydney). Look at his paper ‘Materialism, Properties, and Predicates’, The

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Monist 56 (1972). He’s writing a much bigger piece on the subject, but I don’t know how far along he is.1 You might also look at the papers by Quine and Putnam in Nicholas Rescher et al., Essays in Honor of Carl G. Hempel (Reidel/Humanities Press, 1970).2 Everyone thinks there’s some distinction to be drawn here; and also that it’s an unimportant issue whether, once the distinction is somehow drawn, the word ‘property’ should be reserved for the non-artificial ones. What’s uncertain (and what most philosophers stay neutral about) is whether the distinction is merely a psychological one (perhaps admitting of degrees), or whether it goes deeper than that. Another possibility is that the genuine properties are the ones that appear centrally in the best of all true scientific theories, known or not; but maybe that’s psychological in the end also, via our standards of goodness for theories. I hope that’s some help. Yours, David

236.  To Allan Gibbard, 22 November 1974 Princeton University Princeton, NJ Dear Allan, Thank you very much for your paper on contingent identity.1 I’m sorry I took so long over it. But take it as a compliment: when confronted with a great backlog of work, I like to leave the fun parts till last. I’m mostly in agreement with what you say; and I like very much your way of arguing the case. Enclosed are a paper2 and some notes which represent my own efforts at dealing with these matters by means of multiple counterpart relations. I’ve worked them out much less thoroughly than you’ve done, since my primary interest was in defending against a threat to materialism and I built only as much theory as I needed for that application. Although you quantify over concepts hooked up by means of counterpart relations, while I quantify over individuals in particular worlds and use the   Universals and Scientific Realism (Armstrong 1978a, 1978b).   ‘Natural Kinds’ (Quine 1970); ‘On Properties’ (Putnam 1970).

1 2

  (Gibbard 1975).   ‘Counterparts of Persons and Their Bodies’ (Lewis 1971c).

1 2

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236.  To Allan Gibbard, 22 November 1974

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counterpart relations in interpreting the modalities, I think that’s no real difference. The real difference is that I’m everywhere more vague and evasive and wishy-washy, or (as I’d prefer to put it) more flexible and versatile. I’ve learned (mostly after I wrote the 1971 paper) to put a lot of weight on exact isomorphism of origins. I would put this by saying that we often, but not always, work with counterpart relations and similarity relations among worlds in which exact similarity throughout a spatiotemporal region weighs heavily vis-à-vis other kinds of similarity. But I wouldn’t go so far as you do in doing it all by isomorphic pasts plus conditions of persistence in later life. First, because isomorphic pasts are very well when you can have them, but you can’t always. I’m not prepared to reject all such de re modalities and counterfactuals as this: if a certain physical constant had been less, the sun would by now have become a white dwarf. I take it that for this we need a counterpart of the sun in a world where no regions are quite isomorphic to regions of our world. Second, because even when there are isomorphic pasts, I don’t think they’re invariably decisive. Sure I want to say that I could have lived a very different life after the age of two; the isomorphic past then outweighs all sorts of differences later in selecting my counterpart. But I also want to say (contra Kripke, Feldman, Plantinga, apparently you) that I could have had different origins – and more, that I could have had different origins while someone else had the origins that I actually had! Kripke says that such opinions come from confusing ignorance with possibility, but I don’t think so. So I think that we work with various counterpart relations, of which some work in the way you’ve described (more or less) and others don’t. Another bit of flexibility or, as the case may be, evasiveness. I think we have various understandings that permit us to select the appropriate counterpart relation (or at least to narrow down the candidates until the remaining ones agree for the purpose at hand). Sometimes, indeed, these understandings break down; then your qua-phrases are at hand for making the choice more determinate than it otherwise would be. But sometimes they don’t break down, and we can communicate very well without any need to provide qua-phrases. Your proposal to regard de re modalities or counterfactuals as meaningless unless a qua-phrase is provided seems to me to be a proposal for reform of language, not a plausible theory of the language we have. It seems to me exactly like a proposal that it is meaningless to call even Rescher bald unless you parenthetically say just what amount and distribution of hair you presently regard as the threshold. There too, we have our understandings, and – vague though they are – they serve pretty well most of the time. So I find your rejection of de re modal predication and counterfactuals, unless provided with qua-phrases, rather overdone. You might say, perhaps, that the qua-phrases are always needed but are sometimes provided tacitly rather than explicitly; that would almost, but not quite, be enough to grant the point I’m making.

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The remainder of the point is that qua-phrases don’t always suffice to select the proper counterpart relation and settle the indeterminacies of de re modality. Consider a certain restaurant, the Peking Express. Is it so that this very restaurant could have moved yesterday to a different location? That’s quite unclear; and it’s no clearer when I say that it’s to be answered taking the Peking Express qua restaurant. To repeat the point of the previous paragraph: since it so saliently is a restaurant, you knew already without benefit of the qua-phrase that the restaurant-counterpart relation was the appropriate one to use. But what’s that? Let’s grant to you completely what I do grant to a considerable extent, and say that we get the restaurant-counterpart relation from isomorphism of origins plus the conditions of persistence associated with ‘restaurant’, or with the names of particular restaurants such as the name ‘Peking Express’. Big help! There are some continuant entities we call restaurants that can’t survive relocation and can survive simultaneous change of name, owner, chef, menu and ambience. (The Peking Express used to be a crummy cheap-breakfast place for commuters.) There are other entities we call restaurants that can survive relocation and can’t survive simultaneous change of name, owner, chef, menu and ambience. I don’t mean that there’s a neat two-way ambiguity, in which case you could solve the problem by saying: ‘qua restaurant2’. Rather, we have a continuum of ways of resolving the indeterminacy of persistence conditions associated with ‘restaurant’, and I’ve pointed to two fairly extreme regions on that continuum. Maybe you should reply that not every classification is a sortal, and ‘restaurant’ isn’t; to which I reply (1) that I bet I could make similar problems for descriptions you do think are sortals, and (2) that then you’ve got no way to deal with the unproblematic de re modal predications and counterfactuals about restaurants, as that the Peking Express might have been less enthusiastically received, and indeed would have been (in our case) if the sour pork ribs hadn’t been so good. (I’ve said that there are some restaurants that have one sort of persistenceconditions, others that have others. Of course, I don’t mean to say that these classes are disjoint: something that from beginning to end suffers none of the changes I’ve mentioned is at once a restaurant of both of the two sorts I distinguished, and of many other sorts too that come from intermediate resolutions of the indeterminacy.) I’m glad to find someone else who seems to be prepared to split up Kripke’s package deal about proper names: a name gets its sense via a chain of transmission, and that sense is a rigid concept. The second part needs the first (since a rigid sense couldn’t be determined by our present cluster of descriptions, and what else is there but chains of transmission and clusters of description?) but the first part is fine without the second. Why shouldn’t a word have a non-rigid sense for us now because it was introduced with that non-rigid sense, it was picked up from the introducer in such a way that it retained its sense, and so on throughout a long chain of picking up,

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236.  To Allan Gibbard, 22 November 1974

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until finally we picked it up in a sense-preserving way from our teachers? (This without the inheritance of any cluster of descriptions adequate to determine the sense; and even, if you like, with an ever-increasing inheritance of errors.) Of course we both need something like this if we want to adapt Kripke’s theories by replacing rigidity in many cases by quasi-rigidity relative to various counterpart relations. (But Kripke might say: so much the worse for counterpart relations instead of rigidity.) I think, though, there are cases where we have a sense that isn’t even quasi-rigid, and we have it by chains of transmission without benefit of any adequate cluster of descriptions. I think it’s so for theoretical terms when used by the uneducated; but I think it’s so most clearly for literary pseudonyms. I want to insist that Twain might have not been Clemens; he who was actually Twain might not have been, in just the same way that he who was actually the inventor of bifocals might not have been. (I understood that this metaphysical contingency isn’t required to explain our residual epistemic contingency; but I believe in the metaphysical contingency anyway.) So my sense of ‘Twain’ isn’t rigid, or even quasi-rigid under the counterpart relation for persons. Then do I have an adequate cluster of descriptions to determine what this sense is? Maybe; I know the titles of some of the major works, and I even more or less remember the plots and style. But I think it’s not so that everyone who can use ‘Twain’ with its usual sense has an adequate cluster of descriptions; take a student who has learned that he’ll read the works of Twain next semester, and doesn’t know what he has to look forward to. He says, and I think he means by ‘Twain’ what anyone else does when he says it, that he wonders whether Twain is going to be a bore. He doesn’t know the titles; he doesn’t even know that ‘Twain’ is a pseudonym. (Actually, if you’ll grant that I mean by ‘Twain’ what the first users meant by it, even I don’t have an adequate cluster of descriptions. For the first users had only the first work written under the pseudonym; the non-rigid sense would then have to be, for them then, the concept of the author of that first work. The later works don’t come into it. But I don’t know which work was first.) [. . .] Yours, David

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237.  To W.H. Newton-Smith, 12 November 1975 [Princeton, NJ] Dear Bill, I’ve sent a copy of ‘Survival and Identity’,1 via Watertown – I hope that method works. Many thanks for your letter about the time travel paper2 (and again, many thanks for your help in 1970–71). Let me comment on the three objections you raise. 1) In the case of Icabod and Jason, I wonder how the Devil in 1900 knows what state Icabod will be in, if the Devil doesn’t interfere, in 2045. 1a) Does the Devil know this by means of a reversed causal process? Then I agree that Jason’s initial stages depend causally on Icabod’s final ones, but then I find it plausible that (with the Devil’s aid) Jason and Icabod comprise a single time-traveling person. 1b) Does the Devil not really know at all, but only guess and happen to guess right? Then there’s no case at all for saying that the first stages of Jason depend counterfactually or causally on the final stages of Icabod. 1c) Does the Devil do a Laplacean prediction, working forward from an earlier state of affairs which (unless interfered with) will cause Icabod’s life to follow a certain course? Call that state S, the Devil’s prediction P, the condition of Icabod’s final stages I, and the condition of Jason’s initial stages J. Then the case is like this, where the arrows represent causal dependence? I (Earlier)

S

(Later) P

J

None of the causal dependence is reversed. I expect this is the case you intend. You say that there’s counterfactual dependence of J on I, and hence causal dependence. I reply, with great confidence: there’s no causal dependence of J on I; some ana­ lyses of causation might say there is, but so much the worse for those analyses! So much for the threat that Jason might be the same person as Icabod. I also say, but without quite so much confidence: there’s no counterfactual dependence of J on I; or at least not under the resolution of the vagueness of counterfactuals according to which counterfactuals are relevant to causation. So much the worse for any analysis of counterfactuals which supports your statement that ‘if the last stages of Icabod had been different, the first stages of Jason would have been different’. I think my  (Lewis 1976c).   2  (Lewis 1976a).

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237.  To W.H. Newton-Smith, 12 November 1975

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stuff on counterfactuals explains how you aren’t forced to accept such ‘backtracking’ counterfactuals. The closest world where Icabod’s final stages are different isn’t one where the Devil’s prediction is different but rather one where the Devil’s prediction is mistaken. 2) You say that it would not be of much interest to show that the hypothesis of time travel was free of incoherence if it could be shown that in any circumstances some other hypothesis would be methodologically preferable. Why not? I’m interested in the range of possibilities for its own sake, not only as a menu from which we are to choose the hypotheses to which we give credence. If it were possible for there to be time travel, but impossible for anyone to have good reason to think so, that would indeed interest me! However, I don’t see that the issue actually arises, at least not in the way you (or your hypothetical ‘someone’) thinks it does. Other things being equal, I grant that we prefer hypotheses that don’t involve adding another inex­ plic­able, but I don’t see why other things would have to be near enough to equal so that the hypothesis of an inexplicable causal loop mightn’t be best on balance. I agree that we might, in a sense, have an explanation for the whole loop: but I think we’d find such explanations somewhat unsatisfactory (and so would retain our preference against hypotheses that require them) for two reasons. First, as I understand it, the theorems you have in mind only say that under certain conditions there must be closed world-lines somewhere; which is not yet to explain why there’s one here. Second, such an explanation (unlike the explanation of each part of the loop from other parts of it) doesn’t seem to be a causal explanation. 3) There are two senses of ‘relevance’ involved in the treatment of ‘can’. Suppose that (in a certain context, and under a certain resolution of vagueness) we say that something can be the case iff its being the case is compossible with all facts of kind K; then the facts of kind K, and those alone, are the relevant facts in the sense in which I spoke of relevance. Track record may or may not be relevant in that sense; it doesn’t matter, because any outcome this time is compossible with any track record. But we can also say that a fact is relevant in a secondary sense if it provides evidence regarding the facts that are relevant in the primary sense – that is, the facts of kind K. Certainly track record is relevant in this secondary sense. Suppose Tom, and thousands of others like him, fail again and again. Then indeed it becomes implausible that he can succeed – that is, it becomes implausible that there is no fact of the primarily relevant kind that precludes his success. It might even be, though I rather doubt this, that in any such case in which the number of failures is large enough, the methodologically preferable hypothesis would be that time travelers are unable (in some straightforward way) to kill their grandfathers. Perhaps the most attractive hypothesis would be that there is, after all, some sort of chaperone. But I insist that, however large the number of failures may be, this most plausible hypothesis may yet

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be false – however much secondarily relevant evidence the track record provides, it may be misleading – and the truth may be that each failure is due to bad luck rather than inability, and that no fact of the primarily relevant kind precludes success. This is just the previous point over again: the possibility of a certain sort of time travel doesn’t imply the possibility of it being reasonable to believe that such time travel has taken place. Yours, David Lewis

238.  To Peter Unger, 29 July 1976 Wellington, New Zealand Dear Peter, Perhaps you thought I was convinced, and didn’t see the sense of writing letters to people who don’t exist! No; I’m travelling and your paper1 reached me only today. So I’m sorry I couldn’t reply quickly, as you asked me to. I think sorites arguments, Eubulides’ or yours, are valid. There’s no subtle fallacy, and no need for a revolutionary new logic. What’s wrong is that the argument depends on a false premise. I mean the generalization: (*) Removing one bean from a heap leaves a heap or whatever. Almost every instance of (*) is true, and thus (*) is close to the truth and seems acceptable; but the sorites argument always uses one false instance as well as the true ones. The false instance, of course, is the one where we cross the border from heap to non-heap. Of course you ask me which instance that one is, rightly expecting that I’ll refuse to say. I refuse because ‘heap’ is a vague word, and what’s true about heaps depends on how the vagueness is resolved. Every instance of (*) is true on almost every reso­ lution of the vagueness and hence seems true. Also, every resolution of the vagueness makes almost every instance of (*) true, and hence makes (*) seem near enough to true. But no resolution of the vagueness makes every instance of (*) true. It’s indeterminate (i.e. it differs from one resolution to another) where the border is, but determinate that there’s a border somewhere, and hence that there are exceptions to (*), and hence that the sorites has a false step somewhere.   ‘Why There Are No People’ (Unger 1979b).

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239.  To Peter Unger, 1 November 1976

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I don’t think this rejoinder is an invention of mine, though just now I can’t think who else has taken the same line. No doubt you’ve heard it before, and prepared an answer to it. But I can’t tell from the paper what your answer would be. See you in the fall; I’ll be back in September. I’m afraid I won’t have a fixed address between now and then, though. Yours, David

239.  To Peter Unger, 1 November 1976 [Princeton, NJ] Dear Peter, Your paper ‘There are no Ordinary Things’1 arrived when I was away last week, and I read it today. General reactions: clear, eloquent, but repetitious and overlong. I think that even if I didn’t have any ideas about a way out, I’d be unconvinced for Mooreian ­reasons; all you say against that is that it’s possible for common sense to mislead (I agree) and that a Mooreian response is ‘extremely dogmatic’ (why should I mind?). I think the crude stuff from Moore is better than the fancy stuff from Quine; it’s more certain that there are swizzlesticks than that there are no false steps in the sorites, but it’s not more certain that the fundamental principles of Quine’s epistemology are right than that there are no false steps in the sorites. I found it hard to see what the sorites of cutting and separating adds to what has gone before. Maybe I was just getting tired toward the end, or maybe (as I think) you’re less clear there than elsewhere. Have you changed your views about living or conscious things, say by becoming more favourably inclined toward some sort of vitalism or dualism, or is it just that you wanted to limit the size of the topic? If the latter, I think you create a misleading impression that it’s the former, though you don’t quite say so. I assume you especially want my comments on the part about degrees of truth, pages 18 ff. First, the point that it’s no help to have degrees if we still have the sharp line between degree 1 and everything else (call it what you will) seems to me absolutely right, and important. I think I’m not stuck with that sharp line, for the two reasons I’ve told you, but if I were it would be very bad. I don’t know whether Sanford   (Unger 1979a).

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is or not. That is, the passage from the middle of 19 to the middle of 20 looks good. The next passage, the one you especially marked for my attention, isn’t so good. (I don’t think it’s ‘unfair’, but I think it’s a bit off target.) Sure, someone might introduce the term ‘degrees of truth’ to mean something like ‘degrees of proximity to truth’; nothing wrong with that terminology, but if such a one were misguided by the ana­ logy with degrees of coolness and failed to notice that, strictly speaking, everything with less than the maximal degree of truth was just false, then that would be a mistake. (And this mistake is relevant to the good previous point: that such a one might still be stuck with a sharp line between plain truth, and the various non-maximal degrees of proximity to truth.) But I didn’t introduce the term that way at all; in fact, you quote my explanation of what I actually meant by it, so there’s no point in specu­ lat­ing, as on the middle of page 21, about how the term might have arisen. If something is true to an intermediate degree in the sense that it’s somewhere near the truth without quite being there, then indeed it’s just plain false. But if something is true to an intermediate degree in the sense that it’s true on one set of legitimate resolutions of vagueness but false on another set, both of substantial measure, then it’s by no means just plain false. In short: not all talk about ‘degrees of truth’ is the same. Some may be confused. But someone who speaks of degrees and truth in my way need not suffer from any confusion you mention; and likewise for someone who means degrees of proximity to truth, provided that he recognizes that what is in this sense true to an intermediate degree is also simply false. Thank you for the paper. Though not at all convinced, still I admire the project. Yours,

240.  To Jonathan Bennett, 29 March 1977 [Princeton, NJ] Dear Jonathan, Many thanks for the expanded version of your APA paper on time travel.1 I like it very much. I find very little to disagree with – only one point of any importance, but that point is the one on which all the rest depends. ‘If I fail every time I try . . . that 1   Lewis presented ‘The Paradoxes of Time Travel’ at the Pacific APA March 1976. Bennett gave comments on Lewis’s paper at the same APA session. Bennett later enlarged the paper and then sent it to Lewis. Much later Bennett read ‘Lewis on Time-Travel’ at the Central APA, 26 April 2002, in a symposium on David Lewis.

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240.  To Jonathan Bennett, 29 March 1977

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does prove lack of ability’. I don’t believe that, at least not if it’s taken in the way you need for the rest of the argument. I think it is possible that any amount of failure, and even any amount of failure unified by a pattern of frustration in trying to depart from the scenario, is explained by miscellaneous bad luck and nothing else. It is possible – it is true at some worlds – it is true in stories that represent such worlds. So a thorough story about time travel does not need to include something special, and unitary, as a defense against ‘paradoxes’. Of course a thorough story can include a special, unitary defense – what I called a ‘chaperone to protect the past’ – and this could work in one of the ways you consider. But I think the most interesting sort of thorough story is one in which the traveler’s repeated attempts to depart from the scenario are frustrated by nothing but miscellaneous bad luck. It’s possible that you don’t mean to disagree with what I’ve just said, but only mean to claim something I’m inclined to agree with. You don’t put your point in terms of possibility. You say ‘that does prove’, ‘the only rational conclusion’, ‘we should stop saying’, ‘we should instead say’. Perhaps what you mean is that, after a certain amount of patterned frustration, Henry ought to believe that his failures have a unified explanation that implies lack of ability, and that it would be irrational for Henry to believe that he’d been stopped by nothing but a run of bad luck. And perhaps you mean that if we heard of someone who suffered such failures (and heard of him not as a character in a story but as someone in real life), then we could not rationally ascribe his failures to miscellaneous bad luck, but ought instead to believe in a unified explanation. If so, I’m inclined to think you’re right. But what of it? It is possible for someone to have the misfortune that, although A is true, he has evidence that would make it utterly irrational for him to believe A. A victim of a Cartesian demon is in this position. So is someone who sees a long enough run of heads with a fair coin. So (I’m inclined to agree) is a time traveler who fails enough times to depart from the scenario although there is no unified explanation of his failure. A story representing such a possibility is a story of a character who cannot (rationally) have correct beliefs about what’s true of him. A thorough story-teller need not refrain from telling stories of this sort. To do so, though, the story-teller may have to be especially thorough. What’s thought to be true in actuality tends to carry over into truth in fiction unless it clashes with something explicit in the story. One thing thought to be true in actuality is that people’s rational beliefs about their abilities are more or less right. To keep that from carrying over, the author had better make it explicit that this story is a story of someone who has the ability to do the things that, for miscellaneous reasons, he fails to do. Else the readers would justifiably share the character’s reasonable belief that he lacks the ability.

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Part of your point, I think, is that everybody in the story who knows enough about Henry would rationally believe in his lack of ability. (It’s like the story of the coin; and unlike the story of the demon, in which presumably the demon isn’t deceived.) But that doesn’t change things. Just as it’s possible for one person to be in a position in which it’s irrational for him to believe what’s true, so it’s possible for everyone to be in this position. And if it’s possible, then it can be true in a story. A verificationist, indeed anyone ever so slightly tinged with verificationism, would presumably doubt that it’s really possible for everyone to be permanently, irremediably, rationally wrong. From verificationist premises there might indeed be an objection to the possibility of time travel without special and unitary defenses. I doubt that you meant to be arguing from verificationist premises, though. I think verificationism discredits itself by denying possibilities of error when error clearly is possible, for instance in the case of the victim of the Cartesian demon or the run of heads with the fair coin. In the case of time travel verificationism again denies a possibility of error, but it’s less clear in advance that the error is possible. So much for the main point. Small points: [. . .] Again, thanks very much. Yours,

241.  To D.H. Mellor, 2 December 1977 [Princeton, NJ] Dear Hugh Mellor, There’s no problem of overlap, redundancy, or competition. The project you heard of from Mynott1 is one that I considered for a few years but have now given up. At Adelaide in 1971 I gave six lectures called ‘The Paradoxes of Time Travel’. They were meant to serve two purposes: (1) to discuss the problem of time travel at a level that would interest philosophers, and (2) to talk about several central issues in metaphysics in a popular way, with time travel serving as a unifying theme. I thought that it would be nice to make the lectures into a semi-popular book to serve the same two purposes; and so it might have been, had I had the time and energy and nothing I wanted to do more! But I made up my mind two years ago that I was never going to do it, and therefore accepted an invitation to publish a shortened version of the   Jeremy Mynott, an editor for Cambridge University Press.

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242.  To G.H. Merrill, 11 October 1978

473

‘Paradoxes’ as an article.2 I’m sending you that article, together with a few others that between them cover everything of interest that would have gone into the book.3 I’ve become interested in a principle about subjective and objective probability that should be to your liking. I illustrate it. Q: Suppose you are certain that this coin flip will be a genuine chance process, with chance x of yielding heads. Suppose you are certain of ever so much other seemingly relevant information, not including information about the outcome (or information too closely related to the outcome); never mind whether it is evidence tending to lead you to expect heads or not. What should be your degree of belief that the outcome will be heads? Answer: x. It seems to me that the principle I have in mind captures all we think we know about single-case objective probabilities; that it’s intuitively compelling; and that it’s gone very nearly completely unmentioned! I suppose that’s partly because it’s a prin­ ciple that relates subjective and objective probability, hence useless to anyone who wants to answer the question: what is the one and only legitimate concept of probability? Anything you’ve written relevant to this (besides The Matter of Chance)4 would much interest me.5 Sincerely, David Lewis

242.  To G.H. Merrill, 11 October 1978 [Princeton, NJ] Dear Gary, I’ve written to Thompson for you – good luck! I like your reply to Putnam.1 I know what his comeback should be, but I find it none too convincing. He should say (1) that in some sense there are not only the genuine relations that you regard as included in the structure of the world, but also the non-genuine relations represented by any old sets of ’tuples from the domain; and (2) the line between genuine and non-genuine relations is as much up for grabs, as much unsettled by any constraints he believes in, as anything else. So your     4   5   2 3

(Lewis 1976a). Presumably, ‘Causation’ (Lewis 1973a) and ‘Survival and Identity’ (Lewis 1976c). (Mellor 1971). For letters on chance, probabilities, and decision theory, see Volume 2: Part 6: Epistemology.

  ‘The Model-Theoretic Argument Against Realism’ (Merrill 1980).

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requirement that the predicates be interpreted by genuine relations is a fragment of the bad old idea of ‘intended interpretation’ – of fixing the interpretation by some sort of magical mental act. But I think (1) is questionable, at the tolerable cost – especially tolerable to you, I think – of declining to reduce relations to set-theoretic constructions out of possibilia; and I also think that it might be OK to simply insist that you do have the distinction between genuine relations and others, and are entitled to use it in saying what an admissible interpretation is. I may see you next month: I’m giving a talk at Circle2 at 3pm, Monday 27 November, called ‘Attitudes de Dicto and de Se’.3 (sic: not a typo for ‘de Re’!) Yours,

243.  To D.H. Mellor, 19 March 1979 [Princeton, NJ] Dear Hugh, I’ve finally read your Thyssen paper on Cambridge change.1 I don’t think I have any disagreement with your view, but I have a good deal with the presentation. I would prefer to interpret the things the friends of Cambridge change say in a way that makes sense to us; ask them, if they find there interpretations not to their liking, to explain to us how we have misrepresented them; and expect them to fail. Thus I would be inclined to say that of course there is Cambridge change: for instance, the change that occurs when an event first has the property of futurity, then loses that property and instead has the property of presentness; then loses that and gains the property of pastness. There is no contradiction in one and the same event having three properties, provided it has them (as it does) at different times. But I would say that this only goes to show that relations are sometimes called ‘properties’; no harm in that, call them whatever you please. The sort of property that things don’t have or lack simpliciter, but have or lack at times, is the sort of property that can also be called a relation. When the Cambridge changer says that the event has three properties at three times – properties that would be contradictory if had at a single time – I take him to mean nothing more or less than we mean when we say that this event bears relations to three times, three relations that no event

  University of Illinois at Chicago Circle.   

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3

  (Lewis 1979a).

  ‘McTaggart, Fixity and Coming True’ (Mellor 1981).

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243.  To D.H. Mellor, 19 March 1979

475

could bear to a single time. And when he says that the event changes in that it loses some of these properties and gains others, I take him to mean simply that the event bears different relations to different times. I would say that the difference between real change and Cambridge change is the difference between (1) something with temporal parts bearing different relations to different times in virtue of the different properties of its different temporal parts, and (2) other ways of bearing different relations to different times. Here by ‘property’ I do mean the sort of property that things have or lack simpliciter. On this we apparently do disagree, in view of your unwillingness to apply alternative (II) to the person J.B. Alternative (I) will do so far as grammar is concerned; but so far as grammar is concerned we needn’t distinguish real change and Cambridge change at all. I don’t see how that distinction could be made without the aid of temporal parts. I don’t regard (I) and (II) as rivals: J.B. bears the ‘married’ relation to 1980 iff J.B.’s 1980 stage has a certain property. No harm calling this property also ‘married’ so long as we don’t confuse the relation of continuants to times with the corresponding property of stages. Likewise, I see no harm in the things Jeffrey and Mackie say. I suppose I took for granted that they were talking about relations of events, facts, or propositions to times. I do think Jeffrey’s language is confusingly unorthodox, but I persuaded myself that it was OK by figuring out (as much as you do) how it is intertranslatable with a language in which we speak of propositions as true or false simpliciter, and also speak of them as being about particular times. A proposition is Jeffrey-true at t iff it is true, and about a time no later than t; it is true iff it is Jeffrey-eventually-true; it is about a time no later than t iff it is Jeffrey-true at t or Jeffrey-false at t. Likewise for Mackie, I thought fixity was meant to be a relation of events to times. I think there is a relation for which ‘fixity’ would be a suitable name and which does have something to do with the direction of causation; how much this has to do with what Mackie had in mind isn’t clear to me. (I talk about this in my ‘Time’s Arrow’ paper which I think you have.)2 So far as Jeffrey’s ‘ineluctability’ goes, I agree that the whole thing could just as well be turned around, and doesn’t shed any light on the direction of causation and the direction of time. *** I’ve had a letter from the Board of the Faculties at Cambridge, and I’ve just answered it. Good luck! Yours,

  (Lewis 1979b).

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244.  To Toomas Karmo, 10 July 1980 Australian National University Canberra, Australia Dear Tom, Thank you for the ‘ “I” and ‘Here” ’,1 which I’ve just read and found quite interesting. I agree with you up to a point, but no further. In the fission case (or the body-swapping/mind-swapping case) I think one thing not to say is that it’s the end of you and the people afterward are new people; and another thing not to say is that the question who’s who is settled by some mys­ teri­ous extra facts, over and above the ones specified in presenting the example. In the swapping case, I’m really quite comfortable – despite Williams’ efforts – about saying the TK-mind person is you, and if it were to happen to me, I hope I’d have the sense to prefer beforehand that the delights were to go to the DL-mind person and the tortures to the DL-body person rather than the other way around. In the fission case (granting that both your continuers have a claim to be you, and their claims are equal) you conclude that ‘I’, said beforehand, can’t be a referring expression with definite associated conditions of persistence. I rather conclude that it can’t be a referring expression which (1) has determinate and non-trivial conditions of persistence, and also (2) is determinately singular rather than plural. That leaves four hypotheses. The first is yours: that it isn’t a referring expression, but somehow adverbial. I haven’t thought much about this; a first reaction is that maybe it could be superficially parsed as an adverb, but an adequate analysis of this seeming adverb would make it look like a referring expression in disguise. But perhaps your policy would be to deny that any analysis is needed. My second hypothesis is that ‘I’ is determinately singular; its associated conditions of persistence are determinate but trivial, in that its referent doesn’t persist no matter what; and hence that it refers to a momentary person-stage. There may be a dispute between us about whether there are any such things as stages – temporal parts – of persons; if so, probably it would be a deadlocked dispute since if you don’t accept the concept of stage you probably don’t accept any other in terms of which it could be explained, but that doesn’t lead me to doubt that I have the concept. Also, if ‘I’ refers to a stage, something a bit tricky needs to be done to get the right meaning of ‘I will Φ’ or ‘I once did Φ’. My third hypothesis is that ‘I’ is determinately singular; its associated conditions of persistence are non-trivial but indeterminate, and it partially denotes one   (Karmo 1980).

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244.  To Toomas Karmo, 10 July 1980

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and partially denotes the other – is indeterminate between denoting one and denoting the other – of the two continuing persons involved in the case. I think there are cases of indeterminate denotation that should be pretty uncontroversial, so this case could fall under semantic apparatus we’d need anyway. Take ‘the oldest bald man in the room’ where Ted and Fred are both arguably bald, nobody else in the room is at all bald, Fred is older than Ted, but Ted is a clear case of baldness and Fred is a borderline case. The description is indeterminate in its reference because the predicate is indeterminate in its extension. (I’m using ‘denotation’ and ‘reference’ inter­change­ ably here.) My fourth hypothesis is that ‘I’ is determinately associated with the ordinary, non-trivial conditions of persistence for persons – mental continuity in virtue of causal dependence, as I think – but indeterminate between singular and plural. Think of it as short for ‘I or we, as the case may be’. Whether it’s singular or plural is settled by future history, but not settled by anything at the time. (Unless the world is deterministic, and it’s already causally determined that there will be a fission.) On this hypothesis it’s OK to say that I will be both of the two; united we speak, as one individual (since so far we’re speaking through a shared stage), and we say, in unison as it were, that we will be both of the two separated people there will be tomorrow. One of us will be one, one the other. But please don’t ask of today which of us will be which. That’s a question we can’t answer in unison, and today we can only answer those questions that we can answer in unison! I’ll be in Melbourne the first week of August – precise dates not yet settled – and maybe we can talk then. No doubt I’ll be around Monash not only for the seminar I’m giving on Thursday 7th but other times too. Yours, PS Sorry: I never said which hypothesis I accepted. Not the first; probably not the second; and between the third and fourth I wouldn’t want to choose, thinking that probably people have never made their mind up between alternative meanings that don’t diverge in any ordinary case.

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245.  To D.M. Armstrong, 18 December 1980 Princeton University Princeton, NJ Dear David, This letter is to record my comment last Tuesday about the first argument of Universals & Scientific Realism §6.1,1 which concerns the sentence (1) Red resembles orange more than it resembles blue. As a realist, you can take the apparent references to universals at their face value. What can the nominalist offer as an analysis of (1)? A difference in color sets an upper limit on how well two particulars can resemble each other; but this upper limit is higher if the difference is only between red and orange, rather than the greater difference between red and blue. A red thing and an orange thing, if otherwise they resemble each other as well as they can, can resemble each other better than any red thing and any blue thing. The red-blue difference detracts from resemblance more than the red-orange difference does. So we might first try this: (1A) Some red thing resembles some orange thing more than any red thing resembles any blue thing. If we could be sure that some red thing and some orange thing resemble each other as well as any red and orange things could, and likewise that some red thing and some blue thing resemble each other as well as red things and blue things could, then (1A) would serve. But of course we can’t be sure of that. Suppose a red thing and a blue thing are perfect duplicates in shape, size, chemical composition (except for a tiny trace of powerful dye), . . .; but no red thing and orange thing are such good duplicates. Then perhaps (1A) is false despite the truth of (1). On the other hand, suppose some red thing and some orange thing are perfect duplicates (except for the trace of dye), but no red thing and blue thing are such good duplicates. Then (1A) might be true, but not in virtue of (1). Likewise if we replaced (1) by a falsehood of parallel form, and analyzed that falsehood as we did the truth (1), the analysis might come out true. The trouble is, of course, that among actual particulars, not all possibilities for close resemblance are realized. But among possible particulars, all possibilities are realized. Suppose we have an ontology of possibilia, and suppose that unactualized red particulars are, literally, red particulars (and likewise for orange and blue).   (Armstrong 1978a, 58–61).

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245.  To D.M. Armstrong, 18 December 1980

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Suppose also that any two possible particulars resemble one another to a de­ter­min­ ate degree – it’s not that they resemble one another to different degrees at different worlds – and that particulars can perfectly well resemble one another without being worldmates. Then (1A) seems to do the trick, on the understanding that ‘thing’ never is restricted to the actual things. So we have an exchange of entities for entities: the nominalist does without universals in the analysis of (1), thanks to his ample supply of particulars. (We can reach the same point by another route. The nominalist may be a class nominalist, in which case he takes the color names in (1) as names of classes of particulars. He may then ask: how do we compare the resemblances among classes? To that, more than one answer could be given; but suppose he decides that class A resembles class B as much as member a of A resembles member b of B, where a and b are chosen to make the resemblance as good as possible. (This is like taking the distance between the US and the USSR as the distance between the closest points of each, i.e. across the Bering Strait.) Then he gets (1A). He may go on for familiar independent reasons to include unactualized particulars in the classes that he takes to be properties.) Now consider a different kind of nominalist: one who does not believe in possibilia any more than you do, and cannot therefore trade entities for entities. Suppose, however, that he is willing to use modal primitives. As a nominalist and actualist, he cannot interpret modalities as quantifiers either over unactualized possibilia or over abstract representatives thereof, but he uses modalities anyway. It seems that he can trade entities for modality. (Cf. Putnam’s discussion of trading entities for modality in philosophy of mathematics, ‘Mathematics without Foundations’, JΦ 1967; also Bas van Fraassen’s allegation that the Medieval realism-nominalism debate was about the status of modality as well as about universals, ‘Essence and Existence’ in Studies in Ontology: APQ Monograph Series 12 (Blackwell, 1978).) He gives a modal analysis of (1): (1B) Some red thing might resemble some orange thing more than any red thing could resemble any blue thing. This too seems to me satisfactory as an analysis of (1), though I myself wouldn’t care to leave the modal construction unanalyzed. However, I don’t see that the proponent of (1B) as an analysis of (1) owes anybody an analysis of the modal construction – it does seem like a legitimate modal construction of ordinary language. That’s important, because the modal construction of (1) cannot, in any straightforward way, be expressed in standard modal logic without quantification over anything but particulars. The obvious candidate is (1C) Possibly there is some red thing x and there is some orange thing y such that (necessarily, for any red thing s and any blue thing t, (x resembles y more than s resembles t)).

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I’m not sure how I can explain why (1C) fails to a nominalist who resolutely refuses to quantify over possibilia; but among my allies, I could explain the failure thus. (1C) is equivalent to something like (1D) – I omit counterpart-theoretic refinements. (1D) For some world w, some red thing x in w, and some orange thing y in w (for any world v, any red thing s in v, and any blue thing t in v (x resembles y in v more than s resembles t in v)). But (1B) involves a cross-world comparison: the resemblance of x and y in their ori­ gin­al world w versus the resemblance of the rival pair s and t in their world v. That is, (1B) is equivalent not to (1D) but to something like (1E), which begins the same way and ends differently: (1E) . . . (x resembles y in w more than s resembles t in v)). You can’t express (1E) in standard modal logic; in effect, all the world-variables are governed by the innermost operator in whose scope they fall, so you have a problem with anything involving cross-world comparisons. This is a well-known weakness of modal logic, and hence an argument in favor of explicit quantification over possibilia. You can indeed add gimmicks to modal logic to solve such problems. The bestknown one is the ‘actually’ operator, which enables you to revert to talk about the actual world even in the scope of an operator that has led you to consider alternative worlds. (‘If he were wiser, Fred might love someone whom, actually, he hates’.) The present problem is tougher in two ways. First, we don’t want to get all the way back to actuality, only to the world w introduced by the outer operator. Second, we want not a sentential operator but a predicate modifier – and a peculiar one, one that as it were applies to two places of a four-place predicate. There are two problems for the nominalist I’ve imagined, assuming he’s not content with ordinary language. The first is to devise the needed gimmick. The second (and this he has even if he says the ordinary language construction already is the needed gimmick) is to defend the view that he hasn’t just disguised his quantifications over possibilia. The first task  would, I think, be unpleasant but probably not hard in principle. As for the ­second . . . well, I’m glad it’s not a job I have to take on! In your copious free time at Boston, it would be nice if you could meet Allen Hazen; a lot in the second half of this letter is based on some things of his. Yours, David cc: Hazen, Jackson, Adams

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246.  To Michael Devitt, 31 August 1981

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246.  To Michael Devitt, 31 August 1981 [flying over mainland US] Dear Michael, Thank you for the chapters of the realism draft.1 They caught up with me at the AAP, and I’ve just read them. (On the plane, on the last leg of our trip home.) I like them very much, and applaud the goal of undoing the linguistic turn that discussions of realism have lately taken. I have some minor philosophical comments, some editorial trivia, and a couple of more significant disagreements. One of these is the matter of the ex­plana­tory role vs. eliminability of semantics, on which as you know I disagree with you and Hartry. I won’t try to write anything about that now. The other concerns the title question of Chapter 4: what has truth to do with realism? Prima facie, more than you say. For there’s an obvious refutation of realism using premises about truth as follows. ( 1) Suppose for reductio that the world, much as we take it to be, exists objectively and mind-independently. (2) If so, this world is vast and our powers of investigating it are limited, so there will be many questions to which we cannot possibly find out the answers. Let Q v.s. ~Q be one of these. (Perhaps it concerns Cleopatra’s blood type.) Either Q or ~Q. (3) If Q, then ‘Q’ is true. (By the T-schema) (4) If ‘Q’ is true, then ‘Q’ is verifiable. (By an epistemic theory of truth) (5) If ~Q, then ‘~Q’ is verifiable. (Likewise) (6) So either ‘Q’ or ‘~Q’ is verifiable, contradicting choice of Q. ∴ We reject the supposition (1). I suppose it’s something like this argument that makes people think that realism is a semantic question. And indeed I think that there’s this much truth to their view: the argument is valid, and its only false premise is one of the semantic ones, namely the step from truth to verifiability. (Unless one waters down verifiability so much that (2) becomes the false step instead.) (The ep. theorist might instead give up schema T.) The defence of realism must involve enough semantic theory to rebut this sort of argument. (Similarly, if I could make up a refutation of realism using false premises out of philosophy of sport, the defence would have to take up questions in philosophy of sport, making realism in some sense an issue of phil. sport.) [. . .] Excuse the airplane handwriting! Yours, David   Realism and Truth (Devitt 1984).

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247.  To Michael Tooley, 21 October 1981 Princeton University Princeton, NJ Dear Michael, Thank you very much for the chapter and two papers, all of which I found quite interesting.1 On the spatial location of mental events, I’m with you up to the point at which you invoke the thesis that all external relations are either spatiotemporal or causal. Okay; I believe it; or, at any rate, I don’t know of any counter-example. But I don’t see that I have good reason for believing it ‘regardless of whether a materialist view of mind is correct’. It’s only because of my materialism that I refrain from putting forward the ‘ownership’ relation as another kind of external relation. Small point about p. 15 of the Causality chapter: your ‘grue’ isn’t Goodman’s. A grue marble, in Goodman’s sense, doesn’t change color at t0. If it’s something first examined before t0, it’s grue at all and only times when it’s green (whenever those times may be), otherwise it’s grue at all and only times when it’s blue. I’m not sure this matters to your discussion, but Goodman seems to think the difference between his original grue and the sort you mention is very important. Page 16: Rudolph f. I agree with the substance of your discussion of theoretical terms, but have some reservations about the presentation. I think it’s artificial to suppose that all the theoretical terms purport to name properties (or relations); at least if those are taken to be universals in the sense of your previous discussion. (1) Some T-terms, say ‘Vulcan’, purport to denote particulars. Eliminate it by paraphrase; now you have the predicate ‘Vulcanises’. Replace that by the name of a property: ‘Vulcanising’. Now proceed. – Why not just replace the original name by a quantified variable? And do you want your treatment to depend on commitment to haecceities, which is what the value of the variable that goes in for ‘Vulcanising’ would have to be to realise the formula? (2) Some T-terms may already be predicates, but not ones that correspond to maximally specific properties, hence not ones that correspond to what you’d accept as universals. ‘The property of neutrino-hood’ may be an example of this;

1   The chapter was an early draft of chapter 1 of Causation: A Realist Approach (Tooley 1987). One of the papers was ‘Causal Relations and the Spatial Location of Mental Events’, which is a descendant of ‘Laws and Causal Relations’ (Tooley 1984). (Tooley 1987, ch. 6) is a revised version of (Tooley 1984). The other paper was on the indexation of loans.

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neutrinos apparently come in several varieties, yet it’s not clear that this makes the original neutrino theory be unrealised. I’d say that the thing to do is to let the Ramsey variables be unrestricted, capable of taking as values planets, genuine universals, less-than-maximally-specific properties (whatever you take those to be) or what have you. Then if it is supposed to be part of the theory that neutrino-hood is supposed to be a genuine universal, or whatever, let the theory say so explicitly. After all, you’re allowing yourself O-vocabulary that isn’t observational. In effect, what you do is give yourself non-observational O-vocabulary to say ‘. . . is a universal’, but you rather hide this in the logical machinery. The result is that the discussion circa page 29 gets rather confusing. Theories that quantify over properties may or may not be first-order. You seem to run together three separate things. (1) Being second-order. (2) Quantifying over properties. (3) Having Ramsey sentences that are not purely observational. In fact, if you want to quantify over universals in your Ramsey sentences, the last thing you want is to make your quantified variables be second-order in any standard sense. The following is good second-order logic: Fred walks and Ted talks

\$F ( F ( Fred ) & F ( Ted ) )

where the value of the variable F that makes the conclusion true is something we might call the property of either walking or talking. Either you flatly disbelieve in such a property; or you believe in it without counting it as a universal, and without taking it to be the sort of property you quantify over in Ramsey sentences. (I enclose a short manifesto on the subject of properties and universals – a draft treaty on terminology, roughly to the effect that the word ‘property’ shall be given to the intensional logicians and the word ‘universal’ to the metaphysicians. I’ll also send you (by slower mail) the paper in which the manifesto appears.)2 [. . .] Yours, David PS I don’t understand what you say about the alleged theory which consists of the single statement (x)(Px ⊃ Ox). Why does Lewis’s method imply that P-hood exists only if it is identical with O-hood? Lewis’s method says: P-hood is the unique property (if such there be) that belongs only to O’s. If ‘property’ is taken liberally, as I would take it, then P will be undefined in all cases except that in which it is impossible for anything to be 2   Presumably, an early draft of the section titled ‘Universals and Properties’ of ‘New Work for a Theory of Universals’ (Lewis 1983c).

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an O (in which case, indeed, P-hood = O-hood = the impossible property). Perhaps that’s what you meant; but if so, why not say how special the case is? But if ‘property’ means ‘universal’, as with you, there are many other cases. (Though I’d say that if it was meant to be part of the theory that P-hood was a universal, not just a property in the liberal sense, that should have been written into the theory explicitly.) (1) O -hood is a universal; no other universal belongs only to O’s; then P-hood is O-hood. (2) O -hood is not a universal; there is a unique universal that belongs only to O’s; then P-hood is something other than O-hood. (3) O -hood is a universal; one or more other universals belong only to O’s; then P-hood is undefined. (4) O -hood is not a universal; two or more universals belong only to O’s; then P-hood is undefined. (5) No universal belongs only to O’s; then P-hood is undefined. In any case, the example isn’t a problem. Such a stupid theory ought to turn out to fail to define its terms.

248.  To Allen P. Hazen, 30 May 1982 [Princeton, NJ] Dear Allen, [. . .] I think I agree that the interesting kind of time travel is hard to verify (Interesting: no branching, no guardian angel). What’s especially peculiar is that the more experimentation there is, the less reasonable it may be to believe the truth of the matter. To others, especially Jonathan Bennett, who’ve pressed this point, I’ve said: so what? I’m not a verificationist. I offered to defend the possibility of interesting time travel, not the possibility of verifying same. But you’ve given the point a new and worrying twist. When the failures pile up, does that just make there be deceptive evidence for a guardian-angel law? Or does that make there be a guardian angel law? I can’t just brush that off, as you say, given the Ramseyan theory. I don’t automatically mind unverifiable laws – lawhood isn’t that closely tied to methodology. But for a regularity to be simple and powerful, as it is if it has enormously many instances, does give it some claim on entry into the best true system. What keeps it out? Failure to be integrated with the rest, or with the best

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249.  To Lloyd Humberstone, 12 August 1982

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candidate to be the rest, I suppose. But this is on only if the standards can be set very high. But we hope they can be. A wild regularity that doesn’t fit in has its work cut out for it if it’s to get into the class of Maxwell’s equations, et.al. What if, every time, the traveler fails although there was some chance (as of trying time) of success? Then a guardian-angel law would fall under the prohibition suggested in ‘Causal Explanation’1 against laws that have at some time a chance of not holding. Revive the problem with a methodological theory of chances – but I think, reluctantly, that such a theory isn’t going to work. Maybe this is a way out. But I don’t really know what’s going on when I try to mix my views on chance and time travel, since chance seems to have a built-in presupposition that time behaves in a normal way. I think I don’t buy what you say about counterparts of properties. My fear, briefly, is that if I knew how certain properties at other worlds were ‘distinguished’, I might thereby know something that would pre-empt what you’re doing. We need to talk about this, preferably after I’ve thought more about universals. I hope to have done so in a few weeks, having signed up to give a talk on the subject at Sydney in early July. Yes, it’s true. Steffi’s new career notwithstanding, we’re off to Aus once more. We’ll be there three days from now. But not, alas, for the whole winter. Steffi returns late June to take up a job with the Public Finance Department of Kidder-Peabody; I return mid-July. Yours,

249.  To Lloyd Humberstone, 12 August 1982 [Princeton, NJ] Dear Lloyd, Thank you very much for your letter commenting on duplication and supervenience. I’m glad you reminded me of Michael Slote’s definition of differential properties.1 At the time Michael did it, I thought it a piece of bootstrap-tugging;2 now, of course, I’d be much more sympathetic, though duplication wouldn’t be my choice of   (Lewis 1986d, 214–40).

1

  (Slote 1967, 1970, ch. 5, sec. 2).   Cf. Letter 644. To Michael A. Slote, 16 February 1966, Volume 2: Part 6: Epistemology.

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a primitive. (Of course you’re right that there’s no road back from duplication/intrinsicness to naturalness – the paper will make that clear.)3 But there’s a difference and it’s related to the Gallois distinction you mentioned.4 It’s also part of a standing disagreement between modal realists and Priorians. Taking some liberties with Slote’s terminology, we get (Lewis) P is intrinsic iff, for any two possible things x and y, not necessarily worldmates, if Px and not Py, then x and y are not duplicates. (Slote)  P is differential iff, necessarily, for any two things x and y, if Px and not Py, then x and y are not duplicates. Thus an intrinsic property can’t differ between duplicates even if the duplicates are different worlds; whereas a differential property can’t differ between duplicates in the same world. (I’m supposing that Slote’s quantification is ‘actualist’, i.e. worldrestricted, just because that’s the usual thing when you mix quantifiers and modality, or was when he wrote. But I don’t think he says.) Consider the property that belongs to spheres in worlds where there are pigs and to cubes in worlds where there are no pigs. It is not intrinsic: it belongs to a sphere in this world but not to a duplicate sphere in a pigless world. But it is differential. It never differs between duplicates in a single world, whether the world is pigged or pigless. Yours, cc: Slote

250.  To D.M. Armstrong, 26 November 1982 [Princeton, NJ] Dear David, Brian has accepted the ‘New Work . . .’.1 It’s apparently safe to cite it as Volume 61, 1983, though it’s unsettled which issue it will be.

  ‘New Work for a Theory of Universals’ (Lewis 1983c).   The distinction between intraworld and interworld supervenience. Humberstone says in his letter to Lewis and in a 2018 article that André Gallois suggested the distinction to him in conversation circa 1976–8 (Humberstone 2018, 92). 3 4

  ‘New Work for a Theory of Universals’ (Lewis 1983c).

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250.  To D.M. Armstrong, 26 November 1982

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I’ve been thinking further about taking set-quantifiers as equivalent to large (maybe infinite) strings of individual quantifiers. Unfortunately the technicalities are a bit beyond me, and I haven’t been able to interest the higher-powered people here. I’ll soon get a chance to talk to George Boolos, at MIT, and may get some mileage from him. Here’s the catch. Unless we presuppose not only that there are finitely many non-sets, but also that there are fewer than some specifiable finite number, the setfree equivalents of even very simple sentences that quantify over sets rapidly become very long. Their length is not just infinite, not just uncountably infinite, but soon exceeds e.g. my estimate of the number of all the space-time points in all the possible worlds. So these long sentences aren’t written in this world or any other; they aren’t even written across many worlds, partly in one and partly in another. So do these sentences to which set-theoretic sentences are allegedly equivalent even exist? – Yes; they exist as set-theoretic constructions. But that’s no good; the point was to disbelieve in sets except as a facon de parler. Or is it? I don’t deny the truth of existential statements concerning sets, e.g. those sets that might be taken as stand-ins for unwritten sentences; I just ask that they be rightly understood. So I don’t, I think, deny that there are infinitely long unwritten sentences. I don’t deny it; but I don’t really mean it, not at face value. Or do I? Maybe I want to say that even at face value a quantification over sets is a wholesale quantification over individuals. That sounds quite plausible in the simplest cases, at least. Yours, PS Mark Johnston has become an enthusiastic defender of the identity view of per­ sist­ence through time. He’s working as the assistant in my time travel course, and we’ve staged a sort of debate. I hope the students are learning as much as I am, but I fear not: they tend to be on my side for the wrong – i.e. verificationist – reasons. They haven’t a clue why anybody could possibly think the rotating and nonrotating spheres differ if there’s no visible difference in where matter is when!

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251.  To Jerry A. Fodor, 26 November 1982 [Princeton, NJ] Dear Jerry, As chairman I was in no position to comment on your paper,1 and the party was scarcely an opportunity to talk. Common ground: I take it to be right that smart things can respond selectively to a wider range of properties than dumb things can; and that this ability can be nicely explained by supposing that the smart things have mental representations; and that this is a good reason for believing that the smart things have representations, a reason not available in the case of the dumb things. This is so whether we analyze intentionality in terms of representation-having, or merely think that representation-having is a leading candidate (or maybe the only known candidate) for the mechanism whereby intentionality is realized. At least, I hope that much is common ground. What I’m less happy with is the way you draw the line between the properties that can and that can’t be selectively responded to by the dumb things. If laws are fundamental laws, I agree that only a few very special properties are involved in laws – mass, charge, flavor, . . . . But I think this is too narrow a class: it doesn’t include the shape of the key to which my door lock responds selectively. If laws include derived laws, on the other hand, anything goes: it’s a derived law that any crumpled shirt accelerates in proportion to the net force on it. (I think you think this is a cheat; I don’t understand why.) So maybe we want a middle ground – properties involved in some privileged class among the derived laws. Or maybe we want to try something a bit different. Your examples suggested something different, which on a bit of further thought still seems promising. Some properties are intrinsic, or internal, to the things that have them; others are extrinsic, or relational, or external. I enclose a note2 about difficulties in defining the intrinsic/ extrinsic distinction; but I think there’s no serious doubt that it’s a distinction we understand. Your paramecium, photocell, thermostat, zip-code reader, lock, or what have you, responds selectively to intrinsic properties of the environment. Your examples of ‘nonprojectible’ properties, on the other hand, are extrinsic, whatever else they may be. How would you expect something to detect extrinsic properties? The trouble is that something has its extrinsic properties in part by having intrinsic properties   ‘Why Paramecia Don’t Have Mental Representations’ (Fodor 1986).   ‘Extrinsic Properties’ (Lewis 1983a).

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252.  To Jerry A. Fodor, 3 January 1983

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(it’s furry), and in part by being related to other things (it coexists with them in a largish region of space and time) which have their own intrinsic properties (they’re not furry) as well as their own further extrinsic properties (people use them to keep bread in). You can’t get very far just by investigating the thing in front of you (J.J.).3 What else do you need? Either a powerful sense that will gather the requisite information about a large part of the surrounding world, or a repository of relevant information gathered in the past. Which of these is the more likely explanation of your success in discriminating things furrier than breadboxes? I don’t believe that only intrinsic, never extrinsic, properties figure in laws – not unless we cut down to the fundamental laws, Maxwell’s equations and the like, in which case too many of the intrinsics also are left out. But I do think that, in another way, intrinsics can and extrinsics can’t figure in causal explanation. I take ex­plan­ ation to be information about causal relations among events; and I question whether there can be an event which is essentially the having of an extrinsic property. Becoming a widow, as happened to Xanthippe, is extrinsic – it’s not just a matter of what goes on where Xanthippe then is, but also involves what happens at the prison, long ago at the wedding, from then to now in the history of non-divorce, even what happened when the marriage laws were enacted and when they stayed unrepealed. So I don’t think that there’s any event which is essentially a becoming-a-widow and which befalls Xanthippe. If no such event, then no such event ever causes anything. Sure, there’s a pattern of genuine events that make it true that Xanthippe became a widow; and these genuine events cause things. But that’s different. Yours, David Lewis

252.  To Jerry A. Fodor, 3 January 1983 [Princeton, NJ] Dear Jerry, Thank you for your 23 December letter. Let me not attempt to sort out the disagreement about laws – it’s probably tied to a lot else. But on the smaller point – The dumb scales all by itself cannot detect the extrinsic property weight. It measures a force, which is intrinsic not to the weight but to the weight-cum-scales.

  ‘J.J.’ is short for ‘Jerold J.’: Fodor’s Siamese cat.

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(Or if the scales is a balance, it measures an equality of forces which is intrinsic to the weight-cum-balance-cum-other-weight.) A smarter system which includes also the bloke using the scales detects weight by putting the information about force together with what it knows about context, e.g. that there’s no nongravitational force on the weight. (Of course he needn’t think it through to use his knowledge about context.) Yours, David

253.  To Hilary Putnam, 3 January 1983 [Princeton, NJ] Dear Hilary, I wonder if I might have a copy of the part of your APA talk1 that dealt with my ‘Putnam’s Paradox’,2 with a view to commenting on it. I expect to agree completely with your statement that I’ll need the natural properties for many other purposes than to secure determinacy (more or less) of reference; and of course I don’t see anything contrary to materialism about it. Indeed, I take it to be part of the business of physics to discover the natural properties. One request, if you should have occasion to speak again about the natural properties move in response to you. The idea is due to Gary Merrill; I took care to give him due acknowledgment, and I’d be much distressed if the idea gets associated with my name to the exclusion of his. I take the point that you may have thought to spare him the discredit for such medieval notions; but there he’s adequately protected by having put them forward as what realists ought to say, while denying that he himself was a realist. Yours,

1   Hilary Putnam. ‘Being Realistic: A Reply to Field and Harman’. Eastern APA, Baltimore, MD, 29 December 1982. 2   (Lewis 1984b).

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254.  To Paul Churchland, 2 February 1983

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254.  To Paul Churchland, 2 February 1983 [Princeton, NJ] Paul Many thanks for your ‘Laws, Conceptual . . .’ draft.1 As you can guess, I agree enthusiastically with many parts – not at all with others. I enclose a copy of correspondence with Jerry Fodor (arising out of the paper he read at the NJRΦA) which takes up some of the same issues.2 Request: could p. 19, lines 11-up, become ‘. . . David Lewis, who has the contrary expectation . . .’. I don’t mind being known as an optimist; but I don’t see how one could go about ‘defending’ optimism, at least not once it’s been noted what the successes and failures on the record are. Page 6, bottom. I thought phlogistic chemistry was an 18th century idea. Hence I question both the ‘16th century incarnation of Putnam’ and the suggestion that ‘phlogiston’ is a common-sense theoretical term. ìproperties are the ones the basic laws are about: mass, I think perfectly natural í îkinds charge, spatiotemporal distance, flavor, charm, spin, electromagnetic field strength, . . . . Indeed, a ‘very small and exclusive company’. And indeed ‘the taxonomy of these kinds and their embedding laws must emerge from inquiry together’ – though I see this as a point more about lawhood than about naturalness. But there are also the less-than-perfectly natural ones: H2O, Gold, Dumbbell, chair, soup, dog, . . . . These lesser nobility are a tiny minority among the really gruesome properties. Cats aren’t all alike the way muons are; but neither are they on a par with the members of {Pluto, Gilbert Ryle, the Sydney Opera House, my briefcase, your nose, yonder cloud, the scattered totality of the world’s cobalt, a certain cubic mile of interstellar gas, . . . ad (uncountably) infinitum}; and even that isn’t nearly as bad as they get. I think we’re not wrong to think that our practical kinds are somewhat natural; but less natural than we might have hoped. Page 17, line 2-up. Aleph-0 seems far too low a bound. Of course ‘at least aleph-0’ is safe; but odd, in the same way as if you’d said ‘at least 800’.

1   Final version: ‘Conceptual Progress and Word/World Relations: In Search of the Essence of Natural Kinds’ (Churchland 1985). 2   Letter 251. To Jerry A. Fodor, 26 November 1982 and Letter 252. To Jerry A. Fodor, 3 January 1983.

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255.  To Hilary Putnam, 8 February 1983 [Princeton, NJ] Dear Hilary, Many thanks for the copy of your Baltimore reply.1 In a nutshell, the issue between us is this. You think egalitarianism about properties is an essential part of physicalism; whereas I can’t so much as see how to state physicalism unless inegalitarianism about properties is presupposed! More about this in ‘New Work for a Theory of Universals’, which I think I gave you along with ‘Putnam’s Paradox’. Switching from physicalism to theology, I say that God could no more make gruesome properties be natural than He could make prime numbers be cubes, so I decline to say what would be the case if He did. Another favor to ask. I’d like to be told Why There Isn’t a Ready-Made World, though I don’t promise to believe what you tell me. But somebody has (literally) ripped off those pages of that issue.2 May I have an offprint, please? Or two – one for me; one for the library to replace the missing pages when they bind the volume. Again, many thanks. Yours, David Lewis

256.  To D.M. Armstrong, 17 February 1983 Princeton University Princeton, NJ Dear David, Being a light-second distant from an electron is a relational, external, extrinsic property; it is not an intrinsic property. So you don’t misunderstand how I use ‘intrinsic’. But I say that all perfectly natural properties are intrinsic. Right; I deny that being a light-second distant from an electron is perfectly natural. It’s quite high in the hierarchy; imperfectly natural, but higher up (closer in definition to the top) than metallic or green. 1   Hilary Putnam. ‘Being Realistic: A Reply to Field and Harman’. Eastern APA, Baltimore, MD, 29 December 1982. 2   ‘Why There Isn’t a Ready-Made World’ (Putnam 1982).

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256.  To D.M. Armstrong, 17 February 1983

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And that’s too bad; for I’d wanted to say that whether or not there are universals that mark out the perfectly natural properties, still I meant there to be perfectly natural properties exactly when you would think there are universals. Which isn’t so, I take it, since your verdict on relational properties (19.II)1 is that they are genuine universals, but analysable ones, and hence no addition to our ontology. In the case at hand, your position would be that we have a relational universal made out of electronhood and a distance, hence nothing over and above the two universals it’s made out of, but a genuine universal all the same. So it turns out, a little surprisingly, that at this point I want to be just a bit more élitist than you do. Your reason for admitting relational properties is that one of them ‘would seem to be something identical which an indefinite number of particulars could have, particulars at any place in time’. I don’t find that very convincing. Suppose (what I remain neutral about) that there’s genuine identity in Moorean cases of seeming to have something in common; then I grant you further that there’s genuine identity among the cases of something being a light-second distant from an electron. But why pick on the relational property as the identical element? There are electronhood and the distance relation, and those are already admitted as ones running through the many. Admittedly, those aren’t universals had by just the particulars that are one light-second distant from electrons. Electronhood is had by the electrons, not by their companions; the distance is had jointly by the electrons and their re­spect­ ive companions. But is it clear that the identical element is to be found in the companions, rather than elsewhere in the electron-cum-companion aggregates? Your view has unwelcome consequences, given 20.I.2 First, you are committed to some degree of resemblance between any two particulars that are each a lightsecond distant from an electron. I find that moderately implausible. Second, you are committed to denying the exact resemblance of two particulars, one of which is a light-second from an electron and the other of which isn’t. What’s more, seeing that a vast flock of relational properties should be genuine universals if the one under consideration is, it will be very hard for you to admit any case of exact resemblance anywhere, unless perhaps in a repeating universe. For instance, you shouldn’t agree with those who say that all electrons are exactly alike, since it’s unlikely that any two of them have exactly the same relational properties. I find that conclusion very unwelcome indeed. A new (or perhaps foreseen) reason for you to admit relational properties as genuine universals appears in 10.VI of the Law book.3 We want there to be laws to the effect that all F’s are G’s, hence you want there to be N(F, G)’s in which one or both of   Universals and Scientific Realism II: A Theory of Universals (Armstrong 1978b, 78–80).   (Armstrong 1978b, 96–8).    3  What Is a Law of Nature? (Armstrong 1983, 147–50).

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F and G are relational properties. As it might be: whenever a nuon [sic, passim] is a light-second distant from an electron, that nuon decays. I have two suggestions. (1) It has already been granted, thanks to Smith’s garden, that N can relate quasi-universals. A relational property is a quasi-universal. A relational property such as being a light-second distant from Smith’s garden is a quasi-universal built from a genuine (relational) universal and a particular; whereas a relational property such as being a light-second distant from an electron is a quasi-universal built entirely from universals. But either way, we have N’ing of quasi-universals. (2) A structural property isn’t a relational property; where the whole has a structural property, the parts have the appropriate relational properties. I’m not, for the present, suggesting that you shouldn’t take the structural properties as genuine universals. They are intrinsic – that is, intrinsic to the structure that has them taken as a whole. As an alternative to my first suggestion, you might take it that laws involving relational properties always are derived laws, derived from N’ings of structural properties. Thus the F in the example just considered would not be the partly relational property of being a nuon a light-second from an electron; rather it would be the structural property of being a nuon-cum-electron separated by a light-second. That would N the structural property of being a decaying-nuon-cum-electron. I wondered whether Universals 19.III,4 the defence of the possibility of Relational Realism, required you to admit relational properties as genuine universals. I think not. In passing, though, I note that in this section you don’t seem to admit relational properties as genuine universals! For on 82 you go from ‘These particulars . . . lack any (non-relational) properties’ to ‘They would simply fail to instantiate any monadic universals’.5 Shouldn’t it be ‘. . . any irreducible monadic universals’? What I really want, of course, is perfectly natural properties corresponding to your irreducible genuine universals; let the conjunctions and the structures in, along with the relational properties and the nicer disjunctions, not at the top but fairly high among the nobility. What stops me from saying that, of course, is the same thing that compels you to admit conjunctions and structures – the danger of infinite complexity, with no irreducibles at all. I feel that this is a gimmicky technical point, and oughtn’t to have as much impact as it does on the shapes of our respective views; but it’s no good just saying that without a way around the point! [. . .] Steffi is entitled to two weeks of summer vacation. She thinks two weeks in Australia would be enough to be worth the flight. I wouldn’t think that; but if we come, I will stay longer than Steffi, as we did last year. The catch is that urgent business arrives at Kidder unpredictably, and people are expected to change their v­ acation   (Armstrong 1978b, 80–4).   

4

  (Armstrong 1978b, 82).

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plans if need be. So entitlement to two weeks might not mean entitlement to two consecutive weeks, or to two weeks with enough notice to permit us to use excursion fares. So I’m afraid we can’t schedule the annual DL lecture just yet. [. . .] Love to Jenny, and from Steffi, Yours, David

257.  To Hartry Field, 29 March 1983 Princeton University Princeton, NJ Dear Hartry, [. . .] I’ve taken an interest in a kind of nominalism(in the Harvard sense)-cum-logicism that ought to be well-known but isn’t. It’s the idea of Adam Morton’s ‘Complex Individuals and Multigrade Relations’,1 only used against quantifiers over sets, rather than against quantifiers over mereological sums (why Quine the chairs and tables)? It can be pushed to higher types at least a bit, as is claimed briefly by Gödel in a place Adam cites. Briefly: apparent singular talk about classes is abbreviated plural talk, usually infinitary, about individuals; set-theoretic truths are infinitary analogues of ordinary first-order logical truths. What makes mathematics harder than logic epi­ stem­ic­al­ly is infinite versus finite complexity. I’m not the one who knows enough to develop this technically. Those I’ve approached who do know enough don’t seem interested. It would be beaut for it to be true! Yours, David

  (Morton 1975).

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258.  To D.M. Armstrong, 30 March 1983 Princeton University Princeton, NJ Dear David, I have to tell you that Donald Williams died in January, after several months of illness. Katherine1 asked me to let ‘Donald’s friends in Sydney’ know; I’m not sure whether any besides you had met him, but perhaps Keith and David2 knew him at least by correspondence. Could you hand this on to them, please, and others as you see fit? Many thanks. [. . .] Kidder more or less forced Steffi (she volunteered, but under pressure) to give up her spring vacation with me in England, and to give it up at the last minute. Probably this increases her bargaining power for the summer vacation. Steffi thinks the best way to use her very limited time is to have two long plane flights, days of jet lag, and a philosophy conference. No accounting for tastes – but if we come, as seems increasingly likely, I at least will stay long enough to make the flight worthwhile. So, can you tell me when is vacation and when is term in August and September? Will you and Jenny be at home? Apart from the conference and trips, presumably I’d divide my time between Sydney and Melbourne, much as last year. You say it doesn’t worry you to be committed to a degree of resemblance between any two particulars each a light-second from an electron. OK; but aren’t matters a little worse than that suggests? That was just one example; there are ever so many relational properties to share or not share. De facto, if not necessarily, the consequence of accepting relational properties as genuine universals will be that no two particulars ever fail to share infinitely many universals, and no two particulars ever succeed in sharing all their universals. (To make good the first part, I may need to accept matterless space-time points as genuine particulars – am I right that you wouldn’t oppose that?) You say that having R to an F seems to be a universal or nothing. You don’t want to call it a quasi-universal, reserving that term for things essentially involving particulars. OK; never mind the term. But I suggest that it would be worthwhile making room for a kind of entity – a composite entity, which is nothing over and above its constituent parts – which is made out of genuine universals, but is not itself a genu­ ine universal. Such things might be multiply instantiable, at least sometimes, but their multiple instantiations wouldn’t make for similarity.   Katherine Williams, Donald Williams’s wife.   

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  Keith Campbell and D.C. Stove.

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We’ve talked before about disjunctive properties or negative properties as candidates for such a status; as I recall, you weren’t opposed to admitting such entities so long as (1) they weren’t mistaken for the genuine universals, and (2) they weren’t supposed to be extra things, distinct from the genuine universals and particulars. Of course you’d say that for them, as opposed to the genuine universals, multiple instantiation doesn’t mean being wholly present in each instance, and doesn’t make for resemblance. I’m suggesting that relational properties could have the same status: constructions out of universals, instantiable in a derivative, analyzable sense. As to whether there could be N-ings of these constructions: I can’t see why it’s worse that there could be N-ing of something built out of universals than that there could be N-ing of something built partly out of universals and partly out of particulars. I see why it would be desirable, as part of the doctrine that lawful connection is a purely local affair, that when (N(F, G))(Fa, Ga), F and G should be wholly present in a. And that wouldn’t be so, for instance, if G were not a genuine universal but were one of my proposed constructions, say a disjunctive property that was instantiated in a by having only one of its disjuncts present there. But it also wouldn’t be so in the case you’ve already admitted. Let F be the quasi-universal, being a fruit in Smith’s garden (ignore the disjunctiveness of being a fruit) and let a be a certain apple. F is a composite entity built up, in part, from Smith’s garden. If F were wholly present in a (in a sense literal enough for me to keep my grip on it), as opposed to being instantiated by a in some derivative sense suited to quasi-universals, then every part of F also has to be wholly present in a. But no – surely in no way is the whole garden part of the one little apple! Same point arises if you have N-ings of relational properties even if they are genuine universals. Can having R to an F be wholly present in a? It’s composed of R and F; R is wholly present between a and something else, F is present in the something else, not in a at all. How can something wholly present in a be composed of parts not wholly present in a? (I think you may think I’m letting the part-whole talk run away with me; and I know that you’re more reserved about saying that in a case of genuine instantiation, the universal is part of the particular. But I think I have to lean on the part-whole talk, taken seriously and literally (by which I don’t mean spatiotemporally!), if I’m to continue to understand what the difference between immanent and transcendent realism is supposed to be.) Another candidate for constructions out of universals which wouldn’t be genu­ine universals: conjunctions of incompatible universals. They’re not universals, because not instantiable at all. Why can’t something be composed of two incompatible universals in the very same way that an instantiated conjunctive universal is composed out of its conjuncts? – Because such a thing couldn’t be a universal, yet

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there’s nothing else for it to be? I suggest you tollens this. Given that there’s no restriction on the making of composite objects – something plausible enough in other connections, e.g. mereological summing of particulars – there has to be something other than a universal for an uninstantiable composite to be. Yours, David

259.  To J.J.C. Smart, 31 March 1983 Princeton University Princeton, NJ Dear Jack, The ‘Drift . . .’1 and accompanying letter came yesterday. I’m sorry; I did get your 18 February letter, I even saw that part of it needed a quick answer, nevertheless it joined a backlog caused by the pressure of graduate admissions followed by a spring vacation trip to England. We expect to be here over New Year’s; one or both of us might go to the Eastern APA, but that should end by the 30th. It would be very nice to see you in Princeton. There’s one constraint: cat Bruce is a healthy carrier of a nasty cat virus, so anyone who stays with us shouldn’t stay in a house with another cat for two weeks or so thereafter. (You can well imagine how this quarantine interferes with our social life! It’s been going on ever since Bruce tested positive as a kitten.) So, stay with us if at all possible. Otherwise, let us put you up elsewhere in Princeton, and let’s visit outside the house. I don’t know how well you knew Donald Williams, but you must have met him at Harvard. He died in January, on his Southern California mountain where he went when he retired. Katherine asked me to pass on the news to Donald’s friends in Australia. Studying with him was one reason why I think there’s more to metaphysics than can be read in Word and Object – I hope you’ll agree that he was a good influence. My present views can be traced partly to his question how Leibniz knew that he himself was not an unactualized monad – I fear you’ll doubt whether that was a good influence, but I think it was. ‘Putnam’s Paradox’ has not been revised, and has not been submitted for publication. It has been presented twice more, besides the Melbourne semantics sem­ inar: once at the Dutch Logic Society, Amsterdam, and once at Tufts University. It has   ‘The Drift to Idealism’ (Smart 1989).

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also been shown to Hilary, who took the liberty of mentioning it to a large audience at the 1982 Eastern APA. So there’s no sense asking you to keep its existence a secret now! Several people have urged me to publish it; I’ve had various reservations at least about publishing it as it stands, perhaps about publishing it at all. (1) Hilary’s writings create real uncertainty about what he means, and I’m not sure he quite knows himself. The ‘. . . Paradox’ has enough about obscurities of interpretation and about textual evidence one way and another to get in the way of the philosophical points, yet not enough to be a thorough and fair job as an interpretative paper. ‘He’s still alive, so ask him!’ – I’m afraid I think that with Hilary as he now is, that would result not in clarification but in the kicking up of still more dust; which, if it came at my request, I’d then be obliged to discuss. This is the sort of predicament that some ­people would deal with by writing about the views of a fictitious philosopher named Schmutnam – I don’t think that’s a very good solution. However, Putnam saw the ‘. . . Paradox’ and didn’t complain of being misunderstood; so perhaps I’ve worried too much about this. (2) I’m ruder about Putnam than I normally am about an author whose work I consider to be worth writing about. I’m not sure whether the rudeness is deserved or is excessive; very likely it’s both. (3) To make the Merrill solution go, there needs to be a way for some properties to be moderately natural – natural enough to be eligible referents – in virtue of their definability in terms of the perfectly natural properties. This part is too programmatic. I don’t seriously doubt that a story could be told; but I haven’t told it. And the details are not what I most want to think about. (4) One section of ‘New Work for a Theory of Universals’, to appear in the AJP (61)(1983), covers the main points of ‘. . . Paradox’ to the extent of about five typed pages; given the overlap, is there a justification to publishing both? I’ve more or less decided, despite these worries, that I will submit ‘. . . Paradox’ in a not-very-revised form. But the worries have not been conducive to quick work. So what can you do? I suggest that you cite ‘Putnam’s Paradox’, by title, but as a lecture rather than as an unpublished paper; and also cite ‘New Work . . .’. By the time you get your galley proofs, ‘New Work . . .’ should be out, so you can have page numbers and all. All this leads me to wonder: did I ever send you ‘New Work . . .’? I certainly meant to. But perhaps I slipped; or perhaps I only sent you what I had when I left Melbourne last year, which was the beginning plus an outline of the rest. I’ll mail a copy today. And I enclose a copy of the pages that cover the same ground as ‘. . . Paradox’. I enclose a copy of what Putnam said about ‘. . . Paradox’ at the 1982 APA.2 He seems to concede that inegalitarianism about properties would provide the ­ne­ces­sary 2   Hilary Putnam. ‘Being Realistic: A Reply to Field and Harman’. Eastern APA, Baltimore, MD, 29 December 1982.

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constraint on reference, provided the discrimination among properties was not of our own making; but he finds inegalitarianism spooky, medieval, and contrary to physicalism. (Whereas I don’t know how even to say what physicalism is without presupposing inegalitarianism of properties – see ‘New Work . . .’ 28ff. Note that I use ‘physicalism’ and ‘materialism’ interchangeably.) In your 18 February letter, you consider the suggestion that what the natural kinds are depends on what the laws of nature are. I agree halfway that ‘to be a natural kind is to be the sort of thing about which there are laws of nature’; the part I disagree with is the direction of analysis. I’d rather start with the distinction between natural and unnatural kinds, and use it in trying to answer the question how laws differ from other regularities. Part of the answer is what I’ve said for a long time (it turns out to be in Mill as well as Ramsey): laws are regularities that fit into strong and simple systems. But I think that’s not enough by itself, and another part of the answer had better be that laws are regularities about natural kinds. The combined answer would look something like this: laws are regularities that fit into strong and simple systems; simple systems are those that have simple formulations when expressed in a language whose primitive predicates refer to natural kinds. There’s more about this in ‘New Work . . .’, pages 35ff. A cataract operation seems to be a more complicated affair than I’d thought. I thought they just cut the cataract out, rather than cutting it loose and leaving it to dissolve! Ugh. I do hope the chest virus has gone, and that the second round of scraping will do the trick. Very best wishes from us both! I’m just back from twelve days in England: trains, model trains, folk clubs, beer . . . . It was not a lecture tour. In fact, I didn’t meet a single pommy philosopher. I did meet no less than three from Melbourne: Tony Coady, Ed Khamara, and Peter Singer. I met them separately, without prearrangement, Tony and Ed on the street in Oxford and Peter in front of Paddington! Steffi was to have come with me, but had to cancel her vacation at the last moment because a very big bond issue was coming to a climax. I hope this gives her bargaining power for the summer, and improves her chance of getting two consecutive weeks, with enough advance notice to permit us to use Apex fares. She thinks that the very best way to spend her only two weeks of vacation in well over a year would be to have two very long plane flights, several days of jet lag, and a philosophy conference. I might not think that. Never mind; if we do get to Australia, I at least will stay long enough to make the flight worthwhile! I take it that if we’re there in August or early September we’ll miss you. All the more reason to look forward to December. (Later.) I’ve just read the ‘Drift . . .’. I like it very much, think it appropriate as a way of honouring Maxwell, and mostly agree. I note that I am someone who claims to know of the existence of totally unconnected space-time manifolds, far more than

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259.  To J.J.C. Smart, 31 March 1983

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two, from which I’m causally isolated! I think that causal acquaintance with (part of) the known subject matter is needed for knowledge of contingent truths – knowledge of where in logical space we are – but isn’t needed for knowledge of noncontingent truths, in particular knowledge of what there is in all of logical space. I will be lecturing and writing about the possible worlds and all that during 1983–4, when I’ll be on leave from Princeton, and I’ve been giving a seminar on modal realism here as a start. I like the connection between Putnam’s ‘just more theory’ move and knowing how versus knowing that. I hadn’t understood what you meant when you alluded to it in the note, but it’s clear in the paper. I don’t altogether agree with what you say about Putnam on brains in vats. I think you’re more right than he is, but he’s more right than you give him credit for. (1) Putnam does say that by ‘vat’ Jim refers to vats in the image; to which you reply, fairly given your rejection of possibilia, that there aren’t any vats in the image to be referred to. OK. But sometimes Putnam says a different and better thing. (Sorry, no page references – I’ve lent my copy of Reason, Truth & History to a colleague.)3 Sometimes he says that by ‘vat’ Jim refers to a certain part of the programmed computer that provides him with his deceptive stimulations; namely, to the part (if any) that’s especially responsible for his mental tokens of ‘vat’, and for his associated experiences and thoughts. He refers to the causal source of his ‘vat’-thoughts. And this, you’ll agree, is something that does exist to be referred to (at least, it does if there’s some special part of the computer that’s especially responsible for this one part of the job of keeping Jim deceived). A causal theorist of reference should find it plaus­ ible that Jim refers by ‘vat’ to the causal source of his ‘vat’-thoughts, whatever that might be. A causal description theorist needn’t agree, but might. It depends which parts of the description Jim associates with ‘vat’ are supposed to have decisive im­port­ance in determining Jim’s reference. For the part of the computer does fit part of Jim’s description: the part that says ‘causal source of my “vat”-thoughts’. It prob­ ably doesn’t fit other, less causal parts: for instance, the part that says ‘large receptacle full of liquid’. Hilary would say, I think that the part of the computer fits the whole of Jim’s ‘vat’-description, since we must remember that other parts of the description might not mean for Jim what they’d mean for us. But I don’t believe that he has even begun to show this. It’s true that Jim’s words might have different referents than ours, given Jim’s different relations of acquaintance to his surroundings; it’s at least unproven, and I think clearly false, that these differences would happen in a wholesale way that would make Jim mostly right, rather than wrong, in what he thinks. (2) I question your statement ‘Putnam objects to the fantasy that Jim might be a brain in a vat . . .’ (p. 5). I think Hilary is (for once) quite careful about what he is and isn’t   (Putnam 1981).

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objecting to. I think he’s objecting to ‘Perhaps I am a brain in a vat’ and to ‘Perhaps we are brains in vats’ without objecting to ‘I might have been a brain in a vat’ or ‘We might have been . . .’ or ‘Someone might be . . .’ or ‘Jim, here, is a brain in a vat’. ‘I am a brain in a vat’ is supposed to be like ‘It’s raining but I don’t believe it’ – something that can’t be truly thought or truly and sincerely asserted, but by no means an impossible situation. The story of Jim could come true. Jim would be a brain in a vat; we bystanders can truly say so; we can also truly say that the same misfortune might have befallen us. But Jim can’t truly think ‘I am a brain in a vat’; for allegedly, given that he’s a brain in a vat, he can’t mean by ‘I am a brain in a vat’ that he’s a brain in a vat, indeed can’t mean anything true by those words! So it’s not in the least impossible that Jim might be a brain in a vat. What’s allegedly impossible is that Jim, or anyone else, could be in a position to truly say, or think, ‘I am a brain in a vat’. So the fear that perhaps we ourselves are in a position to say that truly is a nonsensical feat. (But couldn’t I fear that I’m in a vat otherwise than by fearing that I’m in a position to say those words truly? – I think so, and so doubtless do you; Putnam clearly thinks not.) Here’s a parallel I find useful. Jim is now not a brain in a vat, but an ignorant and provincial Sydneysider making his first visit to England. Geordie, an equally ignorant and provincial Tynesider, says truly, ‘By “Newcastle”, Jim here refers not to Newcastle, but to some city down under’. And Geordie goes on to say, still truly, ‘If I had been brought up where Jim was, the same thing might have happened to me: I too might have referred by “Newcastle” not to Newcastle, but to some other city’. But if Geordie goes on to say ‘Maybe some such possibility actually happened: maybe by “Newcastle” I refer not to Newcastle but to some other city’, then he has fallen into nonsense. Whatever he may or may not be acquainted with, whatever he may be referring to, he remains in a position to say truly ‘By “Newcastle” I refer to Newcastle’. (Or at least: ‘By “Newcastle” I refer to Newcastle if anything’.) He cannot sensibly worry about whether he is in a position to say truly ‘By “Newcastle” I refer to Newcastle (if anything)’. He is. That doesn’t stop him from having other worries – he can worry about whether he refers by ‘Newcastle’ to the same city that others refer to by that name, or whether the referent for him of ‘Newcastle’ has at all the properties he thinks it does. But there is one sceptical worry that needn’t trouble him. Yours, David

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260.  To Paul Teller, 16 April 1983 [Princeton, NJ] Dear Paul, Thank you for your letter of 14 April. Concerning your suggestion about nat­ ural­ness as a constraint on reference: I’m not sure what you’re proposing. It might be this: (1) that imperfect naturalness of some properties is to be understood in terms of definability from perfectly natural properties; then for words to have imperfectly natural referents is the same as for them to be definable from words, if such there be, with perfectly natural referents. Or this: (2) the imperfectly natural referents needn’t enter the picture at all; the constraint is that certain designated words shall have perfectly natural referents, and that certain stipulative definitions shall be respected. (1) is fine with me; it makes explicit something I’ve supposed, but left out because I didn’t have details – a theory of simplicity of definitions – to offer. (2) sounds more like a proposal for remaking language than an account of how reference manages to be (sufficiently) determinate in actual languages of the present and past. I doubt that words intended to refer to perfectly natural properties, and successful in doing so, have been very abundantly available until recent times – if then! Congratulations on your NEH. I got one too, and will be off all next year, writing and lecturing about possible worlds. ‘Off’ means ‘on leave’ – not, for the most part, off to distant places. I hope Chantal’s B school isn’t too much struggle. Steffi’s was bad in places, but she’s now much enjoying her job: Public Finance Department, Kidder Peabody, designing bond issues. Princeton to Wall Street is a long, but pos­ sible, commute. Yours,

261.  To Hartry Field, 23 May 1983 Princeton University Princeton, NJ Dear Hartry, Thank you for your very interesting draft on mathematical knowledge.1 I have a few comments.   ‘Is Mathematical Knowledge Just Logical Knowledge?’ (Field 1984b).

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First, I’m attracted to the view that the existence of sets follows, at least in easy cases, from the existence of their members – and here I mean following analytically, by synonym-substitution in logical truths. But how can that be: that the existence of this follows from the existence of those other things? – Because what’s called the existence of this isn’t really the existence of some new thing at all. Thus from the premise that Alma and Bert are a happy couple, H(a, b), it follows that ∃x∃yH(x, y), and it also follows that ∃αH(α). So how do Alma and Bert generate this new thing, this couple, which is a kind of set? – They don’t; the only entities there are Alma and Bert; they are a couple; to say that something is a couple is equivalent, surface grammar to the contrary, to saying that something and something are a couple. ∃αH(α) is abbreviated notation for ∃x∃yH(x, y). Singular set-existence claims abbreviate plural individualexistence claims, so it takes no magic for the former to follow analytically from the latter. The poms have the advantage over us that they habitually use plural verbs with ‘collective’ singular subjects: ‘The cabinet are meeting . . .’. Call this view Pluralism. It’s like the treatment Adam gave to mereological sums; I reckon the sums don’t deserve it, the sets do. It requires multigrade predicates, which I hope you don’t mind, and infinitary sentences, which you clearly don’t mind. If all we had were sets of individuals, I’m sure pluralism would be the way to go. Of course, you don’t have much math with only those. Gödel says you can go up the cumulative types, but he doesn’t say how and I can’t figure it out myself (and he wasn’t infallible). References in footnote 9 of ‘New Work for a Theory of Universals’, which I should have sent you. Does a pluralist disbelieve in sets? It seems so, but it might be hard to make that stick. A pluralist thinks that plenty of existential quantifications over sets are true. For instance ∃αH(α), thanks to Alma and Bert. ‘But a pluralist gives the existential quantifier a special meaning when it’s a set quantification’ – This sounds too much like the cheap special pleading Quine has long warned us against; like someone who, without offering any real theory, says ‘Oh, in a sense there are numbers; but they don’t exist in the sense you and I and the trees do’. ‘A pluralist thinks sets are nothing over and above their members’ – Any believer in sets thinks that. ‘A pluralist thinks the so-called existence of sets follows analytically from the existence of their members’ – so does the mathematical realist you’re opposing. ‘The pluralist doesn’t really think of the couple {Alma, Bert} as something distinct from Alma and Bert’. – In a sense, the realist doesn’t either; he grants that the set is composed of its elements. In another sense, the pluralist does think the couple is something distinct; for he rejects the (seeming) identities {Alma, Bert} = Alma and {Alma, Bert} = Bert. For he thinks the first means that anything that’s Alma or Bert is Alma, and the second means that anything that’s Alma or Bert is Bert, and those are surely false.

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261.  To Hartry Field, 23 May 1983

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Second, I think the sort of treatment of logical possibility advocated in your appendix has been advocated from time to time in things I’ve seen (besides Carnap) but I mostly can’t remember where. With one exception Dana, in ‘On Engendering and Illusion of Understanding’, JΦ 1971, pp. 806–7. He misleadingly says ‘This is nothing more than . . . S4’, but I think ‘this’ refers to a list of less than all the interesting properties of the modality he has introduced. I’m sure I’ve seen other discussions, dating back many years, but I can’t find them. I think one reason such a treatment gets short shrift is that the subject is supposed to be modal logic. And you don’t get much of a logic. Modalities are effectively eliminable, in the sentential case. And it isn’t schematic in the way a logic (usually by definition) is supposed to be; that is, you don’t preserve validity if you substitute arbitrary formulas or sentences for atomic predicates or sentence-letters. ◇P is a theorem, ◇(Q & ¬Q) isn’t. Thus your system doesn’t capture the whole of what stays valid under reinterpretation of the non-logical vocabulary. (Or else, there’s no interpretation of atomic P to make it mean the same as molecular Q & ¬Q, given that the former is and the latter isn’t ‘logically’ possible.) Does that matter to you? I’m not sure that it should. Finally, a question about footnote 13. I follow your instructions, I imagine 2 (S) spelled out in the logic of identity; and part of what I have then imagined is that 10 there’s a string of symbols of length much greater than 1010 . For the shortest way I know to say in the logic of identity that there are at least n F’s is by a string of length 7n-1. (This uses a trick. The brute force way goes up like n2.) Do you think this matters? I can’t figure out whether a corresponding problem for pluralism matters. I say that set-theoretic sentences are finite notation to abbreviate infinitary sentences. Very soon they get very infinitary; so that some very commonplace bit of set theory abbreviates a string with more characters than there are (on my estimate) space-time points in all the possible worlds together. Thus the abbreviated string has no way to exist – save as a set-theoretic construction! Need I mind? Yours, David

10

 ‘(S) ◇(there are at least 1010 apples)’ (Field 1984b, 525).

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262.  To D.M. Armstrong, 8 June 1983 Princeton University Princeton, NJ Dear David, I’ve been a bit confused in my recent letters to you defending the thesis that relational universals are parts of particulars. Correct my confusion, and the thesis is better off than before; but my statement of it needs fixing. (For ease of writing, I’ll write as if I definitely believed in universals; but you’ll understand that I still suspend judgement, and I’m considering what version of Realism to accept if any.) We have two non-overlapping particulars a and b, with intrinsic natures A and B respectively, and we have an external relation R that holds between them. Let R be the entire rope, the conjunction of all external relations of a to b. Together, a and b comprise a bigger particular c. For instance a and b might be an electron and a proton, R might be a rather complicated spatiotemporal relation, and c might be an atom of hydrogen. A few days ago, I thought I was in the following predicament. I wanted to assert all of (1)–(6), which add up to a contradiction. (1) R is part of c. (2) R is not part of a, and not part of b. (3) Further, no part of R is part of a, and no part of R is part of b. (4) c is the mereological sum of a and b. (5) In general, x is the sum of y and z iff, for all w, w overlaps x iff x overlaps either y or z. (6) In general, u overlaps v iff either u = v, or u is part of v, or v is part of u, or something is part both of u and of v. (If you’re prepared to call something an ‘improper’ part of itself, then (6) can be simplified and (2) can be subsumed under (3).) What to do? I was thinking, with great lack of enthusiasm, that we needed a ‘nonstandard mereology’ without (5). But (5) looks like something that ought to be uncontroversial. Indeed, it’s often taken as the definition of ‘sum’; in effect, it’s def­in­ ition D2.047 in Structure of Appearance.1 I’m not one who thinks you can reject a seemingly analytic principle just because total theory looks nicer that way; it’s obligatory to have some story about why it isn’t right, and I had no such story to defend

  (Goodman 1951).

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262.  To D.M. Armstrong, 8 June 1983

507

rejection of (5). Now I have, in a manner of speaking; but we’ll come to it the long way round. Better we should keep (5) and reject (4). What’s true is not (4), but rather (4ʹ) c is the mereological sum of a and b and R. The atom isn’t the sum just of its electron and its proton, since that leaves out the relation-rope that is also part of the atom. (4) is all very well for Nominalists: they don’t believe there is any such thing as the rope. And for Platonists: they believe in the rope, but they think it’s separate from the atom. But Immanent Realists characteristically recognise more parts of things than Nominalists and Platonists do, so it’s no surprise that they should insist on (4ʹ) instead of (4). Indeed, there is such a thing as a + b, the mereological sum of a and b and nothing more. For there’s a mereological sum of anything and anything. But a + b is not the whole of c, because it leaves out R. The whole c is more than the sum of its parts a and b. Not because it’s more than the sum of all its parts – nothing is that – but because a and b aren’t all its parts. As for a + b, that is what you call an abstract particular. It’s c in abstraction from some but not all its universals, since R is left out but A and B remain. It’s less than thick c, more than the thin particularity of c. So at this point the suggested solution is to reject (4), keep (5). But, after this is said, I will also add that in a sense we could instead keep (4) and reject (5). Alternative solution? – No, same solution, alternative terminology. Let me distinguish the standard mereological sum from the augmented mereological sum.2 The standard sum is defined by (5). The augmented sum is defined in terms of a standard sum: In general, the augmented sum of x and y is the standard sum of x and y and whatever external relations obtain between them. Standard sum is a topic-neutral notion; appropriately part of mereology understood as a generalisation of the logic of identity. Augmented sum is a more theoretically loaded notion. According to Nominalism, there’s no real difference: with no such entities as external relations, the standard and the augmented sum will always be the same. According to Platonists, there’s a difference, but augmented sums are artificial en­tities deserving to be overlooked: the standard sum of our electron and proton will be an atom, the augmented sum will be the atom plus a little bit of abstract heaven. According to Immanent Realists, however, the distinction will be an important one: ordinary concrete particulars will often be augmented sums, but not standard sums,   Adopted from ‘Necessary Facts’ (Williams 1963, 605; 2018, 107).

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of smaller ones, as our atom is an augmented but not a standard sum of its electron and proton. The notion of a mereological sum comes to us, in large part, from people who were not Immanent Realists and didn’t make the distinctions that Immanent Realists need to make. (Goodman’s main system in Structure . . . is an Immanent Realism; but without relational universals, so my remark applies even to him.) They introduce the notion by theory and by examples. The examples are by our lights examples of augmented summation. But the theory is the theory of standard summation. ‘Sum’ is a term of art, so the only source of meaning for it is philosophical tradition. So who’s to say whether it should mean standard or augmented summation? If we read ‘sum’ as ‘standard sum’, then (5) is an uncontroversial truth, whereas (4) is false according to Immanent Realism. That’s the solution I gave above. If we read ‘sum’ as ‘augmented sum’, then (4) is the uncontroversial truth; and (5) is false according to Immanent Realism. But now we do have a story about why (5) isn’t right; on this reading, the augmentation brings extra parts into the ‘sum’ which weren’t included, wholly or piecemeal, in the parts we summed. So now I’ve returned, the long way round, to the ‘nonstandard mereology’ that rejects (5). Only it isn’t the mereology that’s nonstandard; it’s just the terminology. This is where we go if we are Immanent Realists, and if at the same time we want to save the examples rather than the theory whereby ‘sum’ was introduced. Now I see how to be more sympathetic toward something you said in your 19 April letter which I rejected in my 4 May letter.3 You said: ‘But what . . . about [external] relations? Are they to be parts of the mereological sum of their terms? Funny parts. They are not supervenient upon the mereological sum . . .’. To which I said: ‘. . . I don’t see why not. What’s true is that external relations aren’t supervenient upon the relata taken separately, but that doesn’t mean that they’re not supervenient upon the sum’. I might better have replied that if by sum you meant the standard sum, then indeed the external relations aren’t supervenient upon that; but the standard sum, on the view in question, is a mere abstract particular, and the relations are just what have been abstracted off. But the relations are supervenient on, and are part of, the thing we usually think of as the sum; for instance, the external relations of the electron to 3   The 4 May 1983 letter is not printed here, but the relevant passage from that letter is as follows: ‘I agree that it’s very much a metaphor to say that relational universals are “wholly present between” their relata; or to resurrect Abbot’s “universalia inter res”, which I was echoing. And it’s worse than metaphorical if it suggests that the universals are part of the intervening space, which certainly wasn’t my intention. I don’t see anything wrong with saying that a relational universal, dyadic or otherwise, is part of the mereological sum of the relata. You say the relations aren’t supervenient upon the sum (except for internal relations, which we may set aside) but I don’t see why not. What’s true is that external relations aren’t supervenient upon the relata taken separately, but that doesn’t mean they’re not supervenient upon the sum. (Cf. “New Work . . .”, footnote 16, 2nd paragraph.)’

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263.  To Hartry Field, 6 July 1983

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the proton are part of the atom; but this thing is an augmented rather than a standard sum. I was too much answering your question from a Nominalist standpoint, on which the atom was the only candidate around to be the sum. Not because I wanted to argue from Nominalist premises, but because I didn’t notice that it mattered. --I look forward to seeing your paper on a combinatorial treatment of modality. Is it for the AAP? If it is, it and my paper may be closely related. My guess is that a combinatorial treatment using the resources of your theory of universals would handle the nearby possibilities quite smoothly, compared e.g. to a more linguistic treatment; but has a worse problem with alien possibilities than its rivals do. I’ll hold this letter until I have an itinerary. I know already one thing to apologise for: the excessively early arrival on Monday 1 August. Let me at least take a taxi from the airport! Yours, David cc: Johnston

263.  To Hartry Field, 6 July 1983 Princeton University Princeton, NJ Dear Hartry, Many things to talk about in your 31 May letter, hence my delay in answering. But the time has come (the Walrus said) . . . Pluralism: which entities do you dispense with? You say: why sets or sums rather than sequences? I say: why do I have to choose? If, or to the extent that, the Gödel-Morton medicine works, it gives me a way of explaining away apparent quantification over sums of things I believe in, over sets of them, and over sequences of them – all three, if I like. Of course, I don’t have to accept the opportunity thus offered. I don’t, in the case of sums, because I do believe in arbitrary sums of things I believe in. I’d be glad to, in the case of sequences; except that I was already explaining away sequencequantifiers as a special kind of set quantifiers. So if Pluralism is a cure for sets, sequences are taken care of already; and if Pluralism isn’t a cure for sets, and I’m stuck with sets, then again sequences are taken care of already. No harm taking care of them twice over, though.

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I suppose I could be in a different position. I could have said that sets are sequences considered in abstraction from their order (and their repetitiveness or lack of it); including, of course, highly transfinite sequences and sequences that may have sequences as terms. Then I’d think: set quantifiers are sequence quantifiers of a special sort, viz. those governing matrices in which the order of the terms makes no difference; then if Pluralism is a cure for sequences, sets are taken care of already; and if Pluralism isn’t a cure for sequences, and I’m stuck with sequences, then again sets are taken care of already (as sequences with the order disregarded). That is: set- and sequence-quantifiers are interdefinable, so you take your choice; if Pluralism works directly against either, it works indirectly against the other too; if it works at all, I suppose it could work directly against both. By the way, I suppose I’ve been using the Pluralist medicine directly against sequences, in the unproblematic finite case, for years, without thinking of it as part of any fancy nominalist program. See ‘Psychophysical & Theoretical Identifications’,1 footnote 6, and compare the longwinded notation used in the corresponding part of ‘How to Define Theoretical Terms’.2 Pluralism: what if you accept uncountably many individuals? Then – or if you get your infinities by accepting countably many individuals and somehow iterating the trick – nice short set-theoretic sentences abbreviate uncountably infinitary sentences (which aren’t even strings, since a string is a countable sequence). Yes: finite abbreviations for infinitely long sentences, which abbreviate infinite strings of quantifiers over genu­ine entities (individuals) by single fake quantifiers over fictitious entities (sets; or sequences, if you’d rather). No intention of waffling between unwelcome assertions of set existence and unwelcome trafficking in (abbreviated) infinitary sentences; the idea is to go unequivocally for the latter. I don’t see the difference between this and substitutional quantification as you (and I) understand it. There also, we have finite abbreviations of infinitely long sentences of the primitive notation; and our finite abbreviations use things that look rather like quantifiers but that we claim really aren’t quantifiers; and we claim that the translation back into (infinitary) primitive notation shows why they really aren’t quantifiers. Iterability. Here’s the sort of thing I know how to do. I’m going to separate the problem of iteration from the problem of the size of the domain of individuals by taking the case where somehow we’ve got a size limit: there are at most 2 individuals. And I’m going to forget about the empty set. I use lower-case variables for individual variables; upper-case for type 1; script for type 2. I want to write the axiom of union applied to type-2 sets. It will be a logical truth, as it deserves to be. It starts out looking like this.   (Lewis 1972, 253, n. 6).   

1

  (Lewis 1970c, 430).

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263.  To Hartry Field, 6 July 1983 " $Y "z( z Î Y º $W( W Î

511

& z Î W ))

First I eliminate my type-2 variable, and I turn membership of a type-1 set in a type-2 set into a disjunction of type-1 identities. I take advantage of the fact that in my small domain there are only three type-1 sets, hence at most three members of any type-2 set. (Remember we’re forgetting empty.) If I had allowed that maybe there are a countable infinity of individuals, we’d get an uncountably long translation (hence a non-string) right here – I’d need continuum-many new type-1 variables instead of only three. "F "G "H $Y "z ( z Î Y º $W(( W = F Ú W = G Ú W = H )& z Î W ) I’m tempted to cut a corner here, using a local equivalence to get rid of the W quantifier; but no, let’s press on by brute force, using methods that apply in general. So my next step is to get rid of the type-1 identities.

"F"G"H$Y "z ( z Î Y º $W (("v(v Î W º v Î F) Ú "v(v Î W º v Î G) Ú "v(v Î W º v Î H ))& z Î W))

Now I’m ready to get rid of type-1 variables, and turn membership of an individual in a type-1 set into a disjunction of type-0 identities. I use the fact that a type-1 set has at most two members. "f"f ¢ "g"g¢ "h"h¢$y$y ¢ "z (( z = y Ú z = y ¢ ) º $w$w ¢(("v (( v = w Ú v = w ¢ ) º ( v = f Ú v = f ¢ )) "v(( v = w Ú v = w ¢ )º ( v = g Ú v = g¢ ) Ú "v(( v = w Ú v = w ¢ ) º ( v = h Ú v = h¢ )))) &( z = w Ú z = w ¢ ))) OK? I also know how to combine this with non-set-theoretic predicates allegedly applicable to higher-type entities. For instance, let’s suppose (what I think defensible) that armies are sets of soldiers; and that fighting is a thing that armies do, and any number of armies can fight each other (as in the Battle of Five Armies in The Hobbit). We have a monadic predicate allegedly applicable to sets of armies: Fight(𝒳) We trade it in for a multigrade predicate applicable simply to armies: Fight(X, Y, Z, . . .) And we trade that in for an ‘articulated’ multigrade predicate applicable to soldiers. ‘Articulated’ means that we can permute some arguments but not others salva veritate, viz. any in the same block, where blocks are separated by semicolons; and we can also permute whole blocks.

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Fight(a, b, c, . . .; e, f, g, . . .; h, i, j, . . .) Also we have a monadic predicate applicable to sets: Army(X) And we trade it in for a non-articulated multigrade predicate applicable to soldiers: Army(a, b, c, . . .) (Here we can interchange ad lib.) Now, an army is odd or even according to the number of its soldiers. Consider ‘An even number of odd armies fight’. Superficially, that’s ∃𝒳 (Even(𝒳) & ∀X (X ∈ 𝒳 ⊃ Odd(X)) & Fight(𝒳))

whence

∃a ∃b… ∃e ∃f … (α & β & Fight(a, b, …; e, f, …))

where α and β are obtained by translating the mathematical parts into type theory and applying the treatment on the previous page. This much I maybe understand. What I don’t understand is what happens when you make the types cumulative, as Gödel claims you can; and what happens when you stop forgetting about empty. The two problems combine in a big way when you take ‘pure’ set theory and start making everything out of empty! Not attacking mereology. You say one can decline to explain away quantifiers over mereological sums if one holds one or both of (i) refusal to believe in sums of all combinations of objects, or (ii) accepting of entities that are sums of others. Right; in my case, it’s (ii) without (i). Elimination of logical modalities in the sentential case. If I’ve understood what you’re doing, its sentential case is decidable by truth tables. We use complete truth tables only: no rows missing. (So it’s not like using sets of partial truth tables for S5.) If sentence Φ gets a full column of T, give □Φ a full column of T, otherwise give □Φ a full column of F.  If Φ gets a full column of F, give ◇Φ a full column of F; otherwise give ◇Φ a full column of T. If that’s the system, modalities are eliminable as follows. Take any modal subformula □Φ or ◇Φ which is innermost, i.e. has no further modals in the Φ. Do its truth table, which will be either a full column of T or a full column of F.  If T, replace it by P ∨ ¬P; if F, replace it by P & ¬P. (Or whatever your favorite tautology and

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263.  To Hartry Field, 6 July 1983

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contra­dic­tion may be.) The result is equivalent to the original, but has one fewer modal. Carry on thus until all the modals are gone. You have a modal-free equivalent of the original. Obviously, this is real Mickey Mouse for logicians, but that’s no reason not to think it the correct treatment of logical modality. Schematic logical modality. A schematic logical truth is an instance of a schema, all instances of which are logical truths. (In your sense of logical truth.) So ◇P (P atomic) is a non-schematic logical truth; whereas ¬◇(P & ¬P) is a schematic logical truth. You say you think the schematic logical truths are more than S5. I think that’s wrong; I think the proof is easy that they’re S5 exactly, but I haven’t stopped to think it through. I also think that early Carnap in effect shows this. I tried to look it up in his ‘Modalities & Quantification’, JSL 1946. Can’t check quickly, given the avalanche of alphabet soup; but I think the giveaway is the queer definition of L-truth, D4-1, which seems to be a definition of schematic logical truth rather than plain logical truth. My remark on your footnote 13. It was too condensed, but the point was this. Your (S)3 was a sentence which, if it existed in the only way you countenance, would be 10 1010 characters long, or longer; so if (S) existed, something of the same form as the part of it after the diamond would be true (and if it didn’t exist it wouldn’t be true); so it’s a poor example for you to use in arguing that there are more ways to know of a possibility than to know of an actuality of the same form. I could make the same 10 point against your text, page 17, lines 7–8 up. ‘The claim that there are at least 1010 physical entities is not obvious’.4 I say that if ‘The claim . . . entities’ is an abbreviated name for an unabbreviated long sentence, then either this name denotes nothing or it denotes a truth; the latter if a sentence can be written in shapes of empty space that don’t contrast with the space around them and space is a continuum, otherwise probably the former. So I think this is your first interpretation of my remark. And the remedy, I take it, is as you suggest: allow numerical quantifiers – including fancy ones with exponents – as primitive notation. How many possible individuals? The semantic and object-of-thought applications of possible worlds go crook if there’s no set of all worlds; so I daren’t say that for just any cardinal c, there might be a world with c donkeys in it. Just because you can say it in mathematics doesn’t mean it’s possible. I take this to present a problem: anything that seems arbitrary looks as if it might have been otherwise, facts about the totality of worlds can’t have been otherwise, so they’d better not look arbitrary. So

10

 ‘(S) ◇(there are at least 1010 apples)’ (Field 1984b, 525).   

3

  (Field 1984b, 526).

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what bound on population of a world will look sufficiently non-arbitrary to be decently a candidate for non-contingency? Something ‘intrinsic’ underlying beliefs. Sure: the brain-writing, synaptic interconnections, or whatnot are intrinsic. They occupy functional roles, and thereby make it true that your beliefs have certain content (or, join with your relations of acquaintance to make that true) under various indexing schemes; and thereby are the truthmakers of ordinary belief sentences about you. But though the brain-writing or whatnot is intrinsic to you, its occupancy of a functional role isn’t, for the two r­ easons noted. (I take the reason about madmen to be highly controversial; the reason about the non-local character of causation given a law theory of causation and a regularity theory of law to be not too controversial.) So the property of having something in you that occupies a role isn’t intrinsic, even if the something that occupies the role is intrinsic. Logical omniscience. Yeah. I hope it’s possible to get by on a mixture of three treatments, no one of which would work by himself. (1) Fragmentation. The logical ig­nor­ amus is a doublethinker; he has a belief system in which he believes A but not B, another in which he believes B but not A, none in which he believes both together. Thus in a sense he believes A, in a sense he believes B, in no sense does he believe A & B or various logical consequences thereof. (2) Lip service. He looks at the naive comprehension axiom; he believes of those words that they express some truth; but he doesn’t believe the (impossible) proposition that those words in fact express. (3) De re failures. He believes the (necessary) proposition that 3 squared is 9; but doesn’t believe de re of 3 that its square is 9, or de re of 3 and 9 that the square of the former is the latter. I hope that, somehow, these three dodges together, used in an ambiguityand-mess theory of ordinary belief sentences, can capture what’s true about failures of logical omniscience. Yours, David

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264.  To Peter Unger, 5 October 1983

515

264.  To Peter Unger, 5 October 1983 Princeton University Princeton, NJ Dear Peter, I’ve read your ‘What am I?’1 with interest – as always, with your work – but with less inclination to agree than in the case of some other recent things. I think you’re right about the cases, to at least the extent that we do have somewhat the intuitions you say we have: that the subject survives as the one with the worse continuity. That’s interesting, and needs explaining. The hypothesis that we divide our allegiance between naturalistic and Cartesian conceptions would explain it. The question is whether there are alternative explanations. I think there are. I think the unequal split case, page 6.2, is easy. I say it’s a fission case. Both branches have continuity enough; you survive as both. So it’s true that you will survive, and that you will be the one who was conscious throughout. But you’ll be the other as well. It was misleading to ask ‘who will you be?’ in such a way as to suggest that a choice is called for. ‘You’ is plural. There are two all along, but beforehand they’re united by stage-sharing, so it’s very understandable that we treat the two as one. The disembodiment case, page 5.1, is harder. I can think of at least three things that might be happening, separately or in combination, to produce the puzzling intuition. (1) You tell the reader to think of the disembodied being as a seeming person, as a viewer, as doing things that normally only a person does. It’s no surprise if your reader cooperatively suspends disbelief, ignores a conflict with his concept of a person, and thinks of the case as you ask him to. (2) We can in some sense imagine the impossible. For instance, by doublethink: we keep the conflicting features of the supposition separate in the mind. ‘Imagine that your cousin has just discovered that her father was an only child, and her mother was too . . .’. You will imagine something. Your answers to questions about the imaginary situation will not be good evidence that you have a nonstandard conception of cousinhood. But I think maybe the main thing that explains the intuition is something else. (3) Suppose our conception of a person is neither naturalistic nor Cartesian but rather neutral. It is a functional conception: there is something X, we know not what, the states of which are our experiences, continuity of which explains memory and retention of traits of character, . . . . This X, whatever it is, is me; or better, it is the 1   This paper remained unpublished; for Unger’s work on personal identity, see Identity, Consciousness and Value (Unger 1990).

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i­ndispensable part of me, without which I would not survive. Though the concept doesn’t say what kind of thing X is, we may nevertheless entertain hypotheses e.g. that it is the material brain, or that it is immaterial and unextended. Mostly we think the first; but we are prepared to imagine that it is the second, and that is what you have asked the reader to imagine. (In suggestions (1) and (2) I somewhat follow Patricia Kitcher, ‘Being Selfish about your Future’, Phil. Studies 197?;2 in (3) I somewhat follow John Perry, in his paper in Amelie Rorty, The Identities Of Persons.)3 Where does the uninterrupted consciousness come into it? Not, I suggest, as built into any conception of persons that influences us; but as a guarantor of con­ tinu­ity, and of the presence of the X we know not what that supports continuity. For I think that when you ask us to imagine uninterrupted consciousness as a feature of the case, we imagine more than just that there is experience at every moment. We imagine besides that the experience obeys continuities like those of an ordinary stream of consciousness; and that this happens not by accident, but because the experience at each moment causally depends on the experience just before. At two points you offer psychological speculations that seem to me so unlikely on their face that they detract from your case unless you can give further evidence or theoretical support for them. One is the suggestion that insomnia is caused in part by the thought that unconsciousness is death. The other is the idea that we find it reassuring that we can always tell whether what we need for survival is there. On the other hand, I liked the suggestion on page 3.4 that we want to think of our survival as an all-or-nothing absolute matter, not admitting of degree, and the Cartesian concept seems to do better this way than the naturalistic one. I stress the ‘seems’ because I think that in fact there could very well be a state that was a borderline case of being an experience, hence a history that was a borderline case of un­inter­ rupt­ed consciousness. But this is less obvious than the non-absoluteness of the naturalistic conception. So I think that people might well like the Cartesian conception for the sake of absoluteness, even though I think they’d be making a mistake. I thought the order of presentation was unfortunate: it tries the patience of your reader and will tend to produce sales resistance. You say you have ‘striking’ evidence for a surprising and disturbing thesis. The reader thinks ‘Oh yeah? Put up or shut up’. You then spend quite a while toing and froing before you produce your evidence. A small change, which would improve the presentation somewhat, would be to start with the present section 2, reserving material from the present introduction and section 1 for later in the paper. (To the extent that it’s needed at all – some

 (Kitcher 1977).   3  ‘The Importance of Being Identical’ (Perry 1976).

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265.  To Peter Unger, 24 October 1983

517

isn’t.) A better change, but one that would take more work, would be to start with the cases and the intuitions, and afterward to offer your explanation of these intuitions, and draw morals only at the end. Yours, David

265.  To Peter Unger, 24 October 1983 [Princeton, NJ] Dear Peter, I’m comfortable enough with the naturalistic conception of myself that I may not be the best informant about what’s going on in those philosophers who have trouble regarding themselves naturalistically! But I think it might be true that they cling to some sort of simplistic conception and, ‘with some misgivings, call just those entities people’ that don’t fail too badly to act as simplistic selves would act. I’m not sure that the simplistic conception need carry all the Butler-Reid baggage you mention, just as I’m not sure it need carry all the Cartesian baggage. The important tenets of simple-mindedness are (1) no fadeaways; (2) no arbitrariness; and (3) no branching. Endurance (in MJ’s sense)1 would guarantee these, but isn’t the only guarantee. Lack of structure seems a gratuitous extra, just as permanent consciousness did. Yours, David PS You said that ‘since the Butlerian self has no structure, there is no grounded disposition’ of it to be conscious. Seems right, but too quick. I would think a simple might have some grounded dispositions – maybe an electron is a simple with a grounded disposition to accelerate in a field – but they might have to be dispositions to do simple things, as in my example. Does a disposition to do a variety of things – which is what a disposition to be conscious is – need a complex structure as its grounding basis? Plausible, but why? Maybe for this reason: the complexity of the mani­fest­ation has to reflect either complexity in the basis or complexity in the governing laws; but, by the Mill-Ramsey-Lewis theory of lawhood, laws can’t be too complex; for to be a law is to belong to the system of regularities that gets the best combination of simplicity and strength.   Mark Johnston.

1

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266.  To Alan McMichael, 16 January 1984 Princeton University Princeton, NJ Dear Professor McMichael, Yes; your answer to Hinchliff, whether in the infinitary-relation version or in the single-thing version, seems to be the equivalent in your framework of my answer. My answer could likewise come in two versions: one in which we extend the counterpart relation from individuals to infinite sequences, another in which we take the mereological sum of the sequence as a single thing. I would be inclined to doubt that there’s any determinate answer to the question whether a proper part of something can be a counterpart (in the same world) of that thing; and I’d be likewise doubtful about your corresponding question of accessibility of roles. I agree with ‘Why Physics . . .’1 so far as doctrine goes; but I’m afraid I think it’s way off target as a rejoinder to Field. It’s one thing to oppose ‘numbers, functions, sets or any similar entities’ as Field does; it’s a different thing to oppose universals. I don’t think there’s any evidence of opposition to universals. Remember, he’s a Harvard man. He speaks the lingo of Quine and Goodman. Goodman called the main system of Structure of Appearance2 ‘nominalistic’ even though its elements, the qualia, were unmistakably universals – because it was free of sets! Quine, early and late, speaks the same language; except that, to make matters worse, he calls sets ‘universals’. What moves them toward ‘nominalism’ has nothing to do with opposition to such universals as are required in physics. Rather, they’re responding to the something-from-nothing of pure set theory (and correspondingly much-from-little in impure) and to the set-theoretic paradoxes. The worries would carry over to properties if properties were understood as like sets only not extensional – which is how they understand properties – but not at all to the sort of properties that Goodman calls ‘qualia’, or the sort that physicists discover. Besides, he’s doing philosophy of mathematics; in which field, the Harvard sense of ‘nominalism’ as renunciation of sets has got well established. Look at the leading anthology in the field: Benacerraf & Putnam, first edition, introduction, pages 21–22.3 The nominalist of the latter half of the twentieth century makes no such sweeping denials [that there are any abstract things], however. He directs his wrath

  ‘Why Physics Can’t Be Nominalized’ (McMichael 1984).    2  (Goodman 1951).   Philosophy of Mathematics: Selected Readings (Benacerraf and Putnam 1964).

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267.  To Hartry Field, 7 February 1984

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against relations that may be employed to ‘generate’ new (heretofore undiscovered?) elements out of those we already may have admitted. Good man that he is, (Nudge, nudge, know what I mean?) he allows us to start with anything we like as the fundamental building blocks of the universe, but once we have made our choice, we are limited in the ­methods we may employ to generate (discover) new members. . . . What is most obviously ruled out is the employment of class membership as the generating relation. . . . One sees but dimly what relation this view bears to that of trad­ ition­al nominalists . . . Amen. He (Field) does say that ‘Nominalism is the doctrine that there are no abstract entities’, but God knows what that means; ‘abstract’ is even more of a disaster area than ‘nominalism’. Thus Quine and Goodman, 1947, ‘We do not believe in abstract entities’;4 where they make plain that ‘sensory qualities’, as in the dissertation5 which was the precursor of Structure of Appearance, are not what they don’t believe in; and only four years later, in Structure itself, Goodman says that ‘Some individuals, such as the atomic qualia of the present system, are appropriately termed abstract’. (There is a footnote on the change of tune.) Sincerely, David Lewis cc: Field

267.  To Hartry Field, 7 February 1984 [Princeton, NJ] Dear Hartry, No disagreement at all, I think – the ‘Harvard man’ line was meant only to bear on what you could be expected to mean by ‘nominalism’, not on your reasons for opposing mathematical entities. I don’t think, as McMichael does, that you get ontologically committed just by introducing predicates. There I’m with Quine, Devitt, you – and Armstrong, as witness the predicate ‘instantiates’. And I don’t think universals, strictly speaking, are   ‘Steps Toward a Constructive Nominalism’ (Goodman and Quine 1947).   A Study of Qualities (Goodman 1940).

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indispensable – because there are other ways to construe ‘natural properties’ than as universals, e.g. as classes of possibilia (doubly unwelcome to you, of course) or as classes – or mereological sums? – of ‘tropes’, more or less as in D.C. Williams. Is it part of nominalistic physics to say, as real physicists do: ‘there is a family of properties of quarks (the colors) that govern the strong forces between them in much the same way that charge governs the electromagnetic forces’? Or do you just start using new predicates: ‘some quarks are red, some green, some yellow, and . . .’ (declining, even implicitly, to define your theoretical terms in the Ramseyish way that quantifies over properties). That’s where I see the question of dispensability as arising – I see it as mysterious how those predicates enter the language without some implicit quantifying over natural properties construed some way or other, not necessarily as universals. Yours, cc: McMichael

268.  To Alan McMichael, 8 February 1984 [Princeton, NJ] Dear Professor McMichael, While I agree with you that serious acceptance of physics involves some sort of commitment to properties, it seems that we don’t agree on how this happens – see letter to Field.1 Maybe I should have spotted this point of difference when I read the ‘Why Physics . . .’ paper.2 My sentence comparing a satisfactory inventory of universals to a primitive vocabulary may have been unfortunate.3 I meant to suggest that a satisfactory inventory would achieve exhaustiveness without redundancy (except maybe those redundancies that Armstrong thinks have to be allowed); but not that for any vocabulary that could achieve this, there would be corresponding universals. The latter would certainly be unwelcome to Armstrong, and likewise to me if the natural properties are to be picked out by universals; because there would be ever so many hoky ways to choose primitives for an exhaustive language. Yours, David Lewis   Letter 267. To Hartry Field, 7 February 1984.   ‘Why Physics Can’t Be Nominalized’ (McMichael 1984). 3   The sentence reads: ‘A satisfactory inventory of universals is a non-linguistic counterpart of a primitive vocabulary for a language capable of describing the world exhaustively’ (Lewis 1983c, 346). 1 2

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269.  To Paul Teller, 9 February 1984

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269.  To Paul Teller, 9 February 1984 Princeton University Princeton, NJ Dear Paul, Green is an intrinsic property.* You might be green. But is it so that you might be green in any company, you might be green no matter which (possible) set of objects you coexisted with? Maybe not. Suppose essentialism of origins is true; then you could not exist, a fortiori couldn’t be green, without your parents. Then you couldn’t be green accompanied by whatever consistent collection I like. It’s not that lack of your parents would hinder you from being green; hinder you rather just from being, and you can’t be green without being. I think essentialism of origins – or, more generally, extrinsic similarity – is built into some reasonable counterpart relations and not into other, equally reasonable, ones. But I think it’s bad if the extrinsic/ intrinsic distinction comes out relative to a counterpart relation. It seems sharper than that. Suppose that for each thing, there’s at least one intrinsic property that it can have and can lack – that’s to say, essences don’t get so rich as to crowd out accidents. Let f be a function that assigns to each thing some such property. Let P be the proposition holding at a world w iff everything existing at w has the property that f assigns to it. It may well be that for every consistent collection X of things, X exists at some P-world and at some not-P-world. Now consider the property of inhabiting a P-world. It is not intrinsic. Anything could have it. And anything could have it in any company. I might respond to the first example by saying: instead of counterparts we should have considered intrinsic duplicates. Then things will indeed exist in­de­pend­ ent­ly of other things, in the sense that anything has a duplicate that coexists, or fails to coexist, with duplicates of any (consistent) class of other things. Sure; but the repair introduces circularity. The second example goes to show that things have their intrinsic properties not only independently of which things accompany them, but independently also of what are the properties of things that accompany them. Properties generally? – No, my intrinsic properties are tied to the extrinsic properties of things accompanying me. But my intrinsic properties are independent of the intrinsic properties of things accompanying me (provided I can be there to have properties at all). Again, the repair would be circular.

* 

irrelevant Landish worries aside

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But here’s another way around the second problem. Suppose, like an old-time logical atomist, you believe in facts. Now in my ontology, facts are just true ones of whatever things have truth values – true propositions, true sentences, true speaking, what have you. A fact could have existed and been false, though in that case it wouldn’t have been a fact. But suppose a fact in some other sense can’t exist at all without being true. Then questions of the properties of things turn into questions of the existence of things – namely, of facts. Does this help? Should we say that if a property is intrinsic, then anything that can have it at all can have it in the company of any consistent collection of facts? – No; consider the fact that Reagan coexists with nobody green, an extrinsic fact about Reagan. You can be green, but you can’t be green in the company of that fact. So to make this go we need a distinction between intrinsic and extrinsic facts about things – circular again. Or maybe we need a sparse theory of facts, so that any genuine fact is ex officio intrinsic? That might go; but it’s very close to solving the problem by means of a sparse theory of properties. And it allows a simpler solution: intrinsic properties are the ones determined by those of the properties of a thing that are involved in genuine facts. Yours, David cc: Kim

270.  To J.J.C. Smart, 14 February 1984 Princeton University Princeton, NJ Dear Jack, I leave for Oxford on the evening of Sunday 29 April. So I might go to the very beginning of the Davidson conference,1 but only that, and not even that if there’s too much to do at the last minute. I hope we’ll see you. If you won’t be going off to visit any cats, maybe you’d like to stay with us before, or during, the conference. I think enough Princeton people will go to the conference that rides might be arranged. Steffi will still be here after I leave, though with her usual weekday early departures and late returns: with luck, she can join me in Oxford for almost two weeks late in May.

  Davidson Conference, Rutgers University, 28 April to 1 May 1984.

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270.  To J.J.C. Smart, 14 February 1984

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Frank Jackson will be giving a paper at Princeton on 27 April, and he too will be at the conference. I think he’ll be staying with us before the conference, and maybe during. No bother if you’re both here – two guest rooms. Thank you for the paper.2 My only comment (apart from predictable disagreement about chopping the worlds, etc.) is the one I made at the Moral Sciences Club. It might be useful to write it down, with copy to Bas. I’ll use p, q, r as in your paper, with overline for negation. If our theories are empirically adequate, there are four ways that might be so: (qpr)  Our theories are adequate because they are (close enough to) true; there are indeed unobservables, electrons etc., obeying simple laws in just the way (or near enough) our theories say they do. ( qpr )   Our theories are empirically adequate, but far from the truth; what we see is what there is, there are no unobservables, or not many; the basic laws governing the observables are laws according to which they behave just as if there were the unobservables we think there are. ( qpr )   Our theories are empirically adequate, but far from the truth; the complex behaviour of observables does indeed manifest in simple laws about the unobservables, but these unobservables are not at all the way our theories say they are. ( qpr )   Our theories are empirically adequate; they are true in saying that there are electrons etc., and true also in the rough-and-ready generalisations they make about the behaviour thereof; but they are wrong when they say that the unobservables obey a beautiful system of strong and simple laws. At Cambridge I left off the fourth alternative; but I’ve since read Nancy Cartwright’s book.3 (But Nancy’s position isn’t exactly qpr ; there’s a partial rejection of q itself. Insofar as theory says that the unobservables obey simple laws, that part of theory is not even empirically adequate! But I expect she’d take ‘accepted theory’ not to include the claims of lawfulness that she rejects – the villains of the piece are scientific philo­ sophers, not working scientists.) A scientific realist, like you or me, after giving most of his credence to q, then gives the lion’s share of his credence in q to the first alternative, qpr. A sceptic, like Bas, gives substantial shares of his credence in q to some of the other alternatives. But which ones? You see the situation as a contest between the first two alternatives: it’s qpr versus qpr . Then you say, and I agree, that qpr has cosmic coincidences of the simple   ‘Laws of Nature and Cosmic Coincidences’ (Smart 1985).   How the Laws of Physics Lie (Cartwright 1983).

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and credible sort, whereas qpr has cosmic coincidences of the complex and incredible sort, so it’s reasonable to give credence much more to qpr than qpr . So far, so good. And you could have said just the same about the contest between qpr and the fourth alternative, qpr. But we’re still not done. The third alternative, qpr, is untouched by what you say. It does say that the cosmic coincidences are of the simple, credible sort; only not in the way our theory says. If a sceptic gives a big share of his credence to qpr, he’s not answered by what you say against incredible cosmic coincidences. And I have the – faint – impression that Bas’s scepticism may indeed be of this sort. That is, he may be thinking: very likely a lot of very different hypotheses about the unobservables, all of which have them obeying simple laws, would make more or less the same predictions about the observables; hence would be equally adequate. It’s no easy thing to think up an empirically adequate hypothesis about the unobservables; the fact that we’ve invented only one doesn’t prove there aren’t a lot of equally good ones that we’ve never considered. No wonder we have only the one – we put our effort into developing the first promising one we hit upon, not into finding rivals for it. But if indeed there are many, why think we’ve hit on the right one? – they would have been thought of; and what’s more, would have been brought to my attention. But how to justify such confidence? If you analogize the first alternative to belief in divine creation, and the second to the belief that the world exists all by itself (with the difference, of course, that in that case the second alternative wins in simplicity), then you can analogize the third alternative to Philo’s position when he asks: why not an apprentice god, why not a committee of gods, why not a giant spider, . . .? Yours, David cc: Bas

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271.  To Terence Horgan, 22 May 1984

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271.  To Terence Horgan, 22 May 19841 as from: Princeton University Princeton, NJ [Oxford, England] Dear Terry, Sorry; your letter caught up with me in England and my copies of ‘Putnam’s Paradox’ are about 4000 miles away. I’ll try to remember to send you one when I get home; failing that, it will be in the Australasian later this year anyway. If I had a ‘mailing list’ I’d be glad to put you on it; but I don’t so I won’t. Generally I circulate drafts within my own department, and otherwise send them only to ­people who have some special connection with the paper in question, e.g. by getting discussed in it. The ‘mailing list’ would expand beyond all feasibility, it seems to me; or else would be kept within limits by means of decisions that could give offence. A losing game, so best not to begin it! I’m sorry. Naturalness ‘not so much in the properties themselves, but rather as something in us: say, certain innate propensities to make simplicity judgements in one way rather than another’. I don’t like a psycholinguistic theory of naturalness as one’s only departure from egalitarianism (1) because if naturalness enters into the analysis of laws and causation in anything like the ways I think it does, then our psych­ology enters into the causal affairs of remote galaxies, and (2) because without the aid of some prior discriminations of naturalness, I doubt that anything we do could be interpreted unequivocally as one judgement of simplicity rather than another. Thus it might be because green is more natural than grue that what I do counts as judging that green is simple rather than as judging that grue is simple, rather than vice versa. Neither point counts against a mixed story, in which some distinctions of nat­ ural­ness are psychologistic. I can’t see psychologistic distinctions as getting you off the frictionless ice of indiscriminate egalitarianism; but once off the ice, lots of things are possible, naturalness-for-us among them. So no protest, if you stress your ‘not so much’ which suggests mixture. Colors (of things, not of images) might be a case in point: in themselves they’re betwixt and between, far better than utterly miscellaneous hordes, but far too extrinsic and disjunctive to be on a par with charge and mass. In themselves, they’re moderately natural; but they’re better than moderately natural-for-us. Likewise for the shape of a key that fits certain locks. I don’t think an utterly unnatural property could   Sent 13 June 1984.

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gain promotion, or a perfectly natural property gain demotion, in this way; but as for the comparative fortunes of the middle classes . . . Your paper,2 and the Spindel volume,3 will be waiting for me at Princeton; thank you for both. Yours, David

272.  To D.M. Armstrong, 6 January 1985 [Princeton, NJ] Dear David, Thank you very much for the draft of your ‘In Defence of Structural Universals’.1 Let me respond, though I think you can predict from conversations most of what I will say.2 Part 1. We agree that structural universals would violate an otherwise plausible principle of uniqueness of composition: no two things are composed of the very same parts. (The violation is avoided if we take a ‘linguistic’ or ‘magical’ line about structural universals, but neither of us would want to go that way.) But you say that uniqueness of composition is best thought of as an argument against postulating any universals, structural or otherwise. Therefore you reject uniqueness of composition; in which case (as I agree) there’s no longer any special problem about structural universals. The reason uniqueness of composition is an argument against postulating any universals is that structures violate the principle as much as structural universals do; and those structures don’t have to involve structural universals, merely relational ones. (I think you could have gone further. If structures really violate uniqueness of composition, why isn’t the problem already there with monadic universals? If there are structures, we ought to be able to conjoin them to get more complex structures, and the conjunctive structures ought to have their conjuncts as parts. (Compare conjunctive universals, composed mereologically out of their conjuncts – something we agree is OK.) Suppose that a instantiates both F and G; and so does b. Then Fa and Ga and Fb and Gb all are actual simple structures; Fa & Gb and Fb & Ga are two different actual complex structures composed of the very same parts, contra uniqueness of   ‘Compatibilism and the Consequence Argument’ (Horgan 1985).   Spindel Conference 1983: Supervenience (Horgan 1984).

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 (Armstrong 1986).   2  Cf. ‘Comment on Armstrong and Forrest’ (Lewis 1986b).

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272.  To D.M. Armstrong, 6 January 1985

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composition. No need for relations, still less for non-symmetrical ones, to show that structures violate uniqueness of composition.) Structures violate uniqueness of composition – so much the worse for structures! What makes that an argument against universals? Why can’t we postulate the universals and do without the structures? The main system of Structure of Appearance, for instance, certainly does postulate universals (under the name of ‘qualia’), but it does not postulate structures. It does have things composed mereologically out of universals and the particulars that instantiate them (viz. the ‘place-times’). For instance, we have the sum F + G + a + b. But that’s not what you call a structure; because it exists regardless of how or even whether the particulars a and b instantiate the universals F and G. If we accept set theory, unlike Goodman, then we also have the many ­set-theoretic constructions out of F, G, a, and b. But these also aren’t what you call structures. For these too exist (if set theory is to be believed) regardless of how or whether the particulars a and b instantiate the universals F and G. If we like, we can treat (some of) these constructions as sentences of an interpreted Lagadonian language. The in­ter­ pret­ation will be arbitrary, as is all interpretation, even if one system of interpretation is especially easy and natural to specify. For instance, we could interpret the set of sets [[F, a], [G, b]] (I’m using brackets for braces – sorry) as a sentence meaning that a instantiates F and b instantiates G; so interpreted, this set will depend for its truth, but not for its existence, on what instantiates what. That’s only one way among many; other ways would use some sort of construction of ordered pairs, say the WienerKuratowski construction you mention. No harm done if somebody calls these things ‘structures’ or ‘states of affairs’ or what have you; but what you mean by a structure, I take it, is something that will depend for its very existence on what instantiates what. I think you’d do well to stress this earlier. As is, it comes clear only after you’ve gone on to a different topic: on page 5, explicitly in the point you credit to Hager3 and implicitly in the previous complaint about arbitrariness. (What makes the arbitrariness of a set-theoretic construction of the structure aRb unacceptable? – Not the seriousness of the enterprise, I think, but rather the goal of it. It’s perfectly OK that something should be true relative to one arbitrary stipulation and false relative to another – truth is always relative to in­ter­ pret­ation, interpretation is always arbitrary – but it’s nonsense that something should exist relative to one arbitrary stipulation and fail to exist relative to another.) Goodman postulates universals; but nowhere in the Structure . . . system are there entities that depend for their existence on what instantiates what. I still call that system a theory of universals. It serves the purpose I mainly have in mind for   Paul Hager.

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universals: explanation of (the simplest kind of) resemblance in terms of shared universals. But you have two purposes in mind: explanation of resemblance, and also provision of truthmakers. If a theory of universals fails to provide entities that depend for their existence on what instantiates what – structures, in the sense you have in mind – it will not provide truthmakers for even the simplest of truths. (You might even deny that it explains resemblance; for if it gives you no truthmakers for statements of instantiation and of universal-sharing, you might doubt that it really allows you to speak of universal-sharing at all.) So a Goodman-style theory of universals without the structures is, by your lights, a failure. It would be pointless for me to use uniqueness of composition against structural universals if it’s equally lethal against universals generally. That’s what your draft suggests, but I don’t think it’s quite right. We have a two-way conflict between structural universals and uniqueness of composition; we do not have a two-way conflict between universals generally and uniqueness of composition. Rather, what we have is a three-way conflict between universals generally, uniqueness of composition, and the principle that truths need truthmakers. Once the conflict is described that way, I think we’re in full agreement that something has got to go. I say (even though I’m not committed to universals): so much the worse for the alleged need for truthmakers. (Goodman presumably concurs.) You say: so much the worse for uniqueness of composition. The real stand-off is uniqueness of composition versus the truthmaker principle – not uniqueness of composition versus universals. Part 2. Couldn’t a natural class theory get around the arbitrariness of the Wiener-Kuratowski construction of ordered pairs by saying that you get a natural class no matter what construction of ordered pairs you use? Suppose there are three constructions: the pairs1, the pairs2, and the pairs3. Then I can say that the class of all pairs1 of things a meter apart is a natural class; and so is the class of all pairs2 of such things; and so is the class of all pairs3. This is the usual remedy for arbitrariness: don’t make the choice, generalize over the different ways of making it. Maybe not all different ways: among the constructions themselves, some might be disqualified as unnat­ ural, leaving us with only a short list between which the honours are even. For the resemblance theory, what I think you get is an even more complicated and nasty primitive of resemblance. Suppose you start with a nice two-place predicate of resemblance: a resembles b. To get resemblance of pairs without introducing any such entities as pairs – hence without making any arbitrary choices about how to construct pairs – you go to a four-place predicate: a vis-a-vis c resembles b vis-a-vis d. And for resemblance of triples you need six places, and so on. The ordering is the ordering of places of the predicate. You could say there’s a family of resemblancepredicates, or better that there’s one variably-many-place predicate. Unfortunately,

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273.  To John Bigelow, 8 January 1985

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this is not the whole story; you don’t really start with a nice two-place predicate even in the monadic case. There are the complications needed to deal with imperfect community etc., as described in ‘New Work . . .’; these would have to be superimposed on the complication I’m describing now. Not nice, I agree. Part 3. Suppose that matter is nonatomic; suppose further that different elem­ ents can be blended so thoroughly as to get a mixture that is absolutely homo­ge­ neous. Then how about being some lead and some tin blended in equal amounts as a structural universal – or maybe a different kind of complex universal built from constituents in the same way as a structural universal – in which the constituents don’t particularize? Your hypothesis might be right for structural universals in the real world, where matter comes in particles, but not right a priori. *** I can’t guess whether the coming reunion of departments makes this an especially good or especially bad year for you to be away, but I’m sure it makes it one or the other. I’m very curious about what will happen. Good luck! Yours, cc: Bigelow, Forrest, Johnston

273.  To John Bigelow, 8 January 1985 [Princeton, NJ] Dear John, I don’t really get the picture in your sketch of a defence of Pictorialism.1 I think I understand what you say, but I don’t see how to develop the plan further. A ‘natural’ part of a universal is a part that is itself a universal. Hydrogen is part of four different natural parts of Methane: call them U1, U2, U3, and U4. Not so for Carbon. That, you say, is how Methane involves Hydrogen four times over. Since the U’s are universals in their own right, I want to know what instantiates them. Parts of methane molecules, presumably. Which parts? What you say by way of analogy between parts of Methane and parts of each methane molecule suggests that the four U’s are instantiated by the four bonded CH pairs in each molecule. But I don’t think that can be right. First objection. Each CH pair includes a carbon; so if only such pairs could instantiate the U’s, we’d have an entailment from each of the U’s to Carbon, and you   ‘Towards Structural Universals’ (Bigelow 1986).

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agree that such entailments should be explained mereologically, which they can be only if Carbon is part of the U’s. But if it is, then Carbon as well as Hydrogen turns out to be part of four different natural parts of Methane. Second objection. The four CH pairs are exactly alike. So they ought to instantiate exactly the same universals. But then each of the four pairs turns out to instantiate all of the four U’s; in which case the fact that there are four of the U’s doesn’t seem to do anything to explain why there are four instances of each of the U’s (and hence four hydrogen atoms) per molecule. I can get around the first objection if I suppose that it’s not the four CH pairs that instantiate the U’s, but rather it’s just the four hydrogen atoms. (Then how do the U’s differ from the universal Hydrogen? Perhaps because they’re not instantiated by just any old hydrogen atom, but only by the sort of bonded hydrogen that is found in a methane molecule. That makes them a bit too extrinsic to be nice universals, but let me waive that.) The first objection remains; the four hydrogens in a methane mol­ ecule are just as much alike as the four CH pairs are, so each hydrogen atom in the molecule should instantiate all or none of them, so what has the multiplicity of the U’s got to do with the multiplicity of the hydrogen atoms? I can get around the second objection if I suppose that the bonded CH pairs instantiate only one of the four U’s and the other ones are instantiated by larger substructures of the molecule. Like this: U1 is instantiated by each of the four CH bonded pairs; U2 is instantiated by each of the six HCH bonded triples; C H bonded quadruples; U3 is instantiated by each of the four H H U4 is instantiated by the whole molecule. That way, Carbon and Hydrogen (and presumably Bonded) are natural parts of U1, which in turn is a natural part of U2, which in turn is a natural part of U3, which in turn is a natural part of U4, which is the same thing as Methane. But my first objection applies: Carbon is as much part of the four U’s as Hydrogen is. So what else can we find to instantiate the four U’s? I have another objection, independent of any specific hypothesis about what instantiate the U’s. What are the ultimate, simple, mereologically atomic parts of the universal Methane? I can think of three: Carbon, Hydrogen, and Bonded. (It was a supposition of my example, bogus of course, that those were simple.) Suppose those are the only ones. From three atoms c, h, b, seven and only seven things are composed: namely c, h, b, c + h, c + b, h + b, and c + h + b. The U’s are supposed to be four natural parts of Methane that contain Hydrogen; there are only four parts altogether that contain Hydrogen, namely h, c + h, h + b, and c + h + b; so these must be the four U’s. Two of those contain Carbon, and besides we know that Carbon is a universal in its own right;

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274.  To Peter Forrest, 30 January 1985

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so we have three natural parts of Methane that contain Carbon (and it’s hard to see why we don’t have a fourth – why isn’t c + b as much a universal in its own right as h + b is?); yet Methane does not involve Carbon three (or four) times over. So we’d better suppose instead that there are some other ultimate, simple, mereologically atomic parts of Methane besides the three considered so far. What can they be? We know this much: they are present wherever Methane is present. Hence presumably they are universals. Have we any notion what parts of a methane mol­ ecule instantiate them? (A simpler way to make that last point. How can any part of a universal not be ‘natural’? A universal is something that occurs repeatedly, and any part of a universal occurs as repeatedly as the universal itself. Possible reply: it’s one thing to occur repeatedly, another thing to be instantiated repeatedly. What an unnatural part of a universal does is to occur repeatedly without ever being instantiated. Can we understand what this means?) *** As to the Linguistic Conception. I guess I don’t know any strong reason why unfundiert set theory is worse than the ordinary sort. But if you take your ersatz structural universals as constructions in fundiert set theory, you can explain what it is for them to be ‘instantiated’ (or as I would say, satisfied) by means of a recursion based in the genuine instantiation of the genuine universals that are the urelements of the construction. You cannot do this if you take them to be constructions in unfundiert set theory – it’s constructions all the way down, genuine instantiation of genuine universals never enters into it, the recursion on ‘instantiation’ of the constructions never gets going. Yours, cc: Johnston

274.  To Peter Forrest, 30 January 1985 Princeton University Princeton, NJ Dear Peter, Thank you for the ‘Neither . . . Nor . . .’.1 I like it. Comments probably rather predictable. 1) If there are universals, their sums are sometimes conjunctive universals; sometimes not, for instance when conjuncts are incompatible (or have different   ‘Neither Magic Nor Mereology: A Reply to Lewis’ (Forrest 1986b).

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degrees). Then is it an embarrassment that I can’t say, in general, what a sum of universals is? I don’t see why – good enough to say it’s a sum of universals. The sum of a trout and a turkey – neither fish nor fowl? Partly fish, partly fowl. Sum of a particular and a universal? Partly particular, partly universal. And so on. An advocate of unrestricted composition will of course say that many of the things there (speaking with unrestricted quantifiers) are will not fall under any of the classifications we ordinarily use. 2) I’ve written to DMA about the structures2 – did I send you a copy? (I think so, say if not.) Briefly: yes, uniqueness of composition is as bad for structures as it is for structural universals. (If structures are supposed to be things that exist only if the particulars in question instantiate the universals in question.) But being bad for structures isn’t the same as being bad for universals. Universals can do most of their good works without there being any structures. What they can’t do that way, though, is what DMA most wants – I now think – and that’s provide truthmakers for what don’t superficially seem to be existential truths. 3) The ad hominem. Sets ‘formed’ out of their members bothers me about as much as sets ‘composed’ of their members – especially in the case of unit sets, where mereological composition of set from subsets is out of the picture. The relationship of things to their unit sets strikes me as a sublime and horrid mystery, but one thing not to suggest is that the two have anything in common. I think a better ad hominem (due to van Inwagen) is to say not that the relationship of things to their unit sets is like the nonmereological composition I reject, but rather that it’s like the magic I reject. Equally embarrassing. But unlike the case of structural universals (including your worlds) in the case of the unit sets I think I have no alternative to believing in the magic. 4) The other ad hominem. Ordered pairs are sets. The composition of pairs is like the composition of sets generally: so far as it’s composition it’s mereological, so far as it’s unmereological it’s not composition, but rather the mystical promotion of things into unit sets. The catch is: we haven’t decided, and needn’t decide, just which sets they are. We speak a systematically ambiguous language, and no harm turn so long as the things we want to say come true on all disambiguations. (Just as you needn’t settle just which part is called the outback in order to say truly that the outback hasn’t started yet by the time you get to Balmain.) Make the Kuratowski convention if you like (and indeed it’s not a discovery). Serious ontology is not done by convention – no indeed, but why should deciding which lot of sets deserve the name of ‘ordered pairs’ have to be a piece of serious ontology. The serious ontology (sad to say) is the ontology of sets – the closure of ordinary things under the unit set op­er­ ation plus mereology, as I see it – which furnishes the candidates for the name.*

  Letter 272. To D.M. Armstrong, 6 January 1985.

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The final paragraph looks interesting, but I’m afraid I found it too concise for me to be sure I understood it. Your first paragraph, last three lines, might cause confusion among the ­readers. You understand my view perfectly well, but your statement of it will seem to conflict with mine. I could as well have said that set-theoretic composition is another mode of composition, but one that is analysable into mereology plus something that isn’t composition at all; but what I did say was that the ‘generation of sets out of their elem­ ents . . . is not some unmereological form of composition’ and earlier that the gen­er­ ation of unit sets was ‘not composition at all’. I may have used the phrase ‘set-theoretic composition’. I would have been willing to use it at any time before 21 August 1984. I hope I’ve purged it from the final draft of the paper!3 Yours, David * PS As ordered pairs go, so go relations, understood as sets of pairs (or triples or . . .) of individuals (this- or otherworldly). So I say the same as before: my ontology provides various candidates to deserve the name of relations. (So far, serious ontology.) As to which candidate is to get the name, that is a matter for conventional decision or (better) for indecision.

275.  To George Boolos, 6 June 1985 [Princeton, NJ] Dear George, I’ve been tinkering with the simplified stage theory in your ‘B:ITCON5’ draft that you gave me in March. It turned out that mostly I was just transforming it back into Scott ’67;1 but there were some differences that I’d like to tell and ask you about. What I most wanted to do, I haven’t been able to bring off. Whether that’s because I was trying to do the impossible or because I’m terribly rusty at proving things, I don’t know. (Somehow I doubt that it’s possible but difficult.) The target is the whole of 2nd-order ZFC, though I want to follow Scott (and you, and van Aken)2 in separating the ‘axioms of extent’ from an ontologically neutral theory.   ‘Against Structural Universals’ (Lewis 1986a).

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  ‘Existence and Description in Formal Logic’ (Scott 1967).   ‘Axioms for the Set-Theoretic Hierarchy’ (van Aken 1986).

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The first step is to take ‘F’ as ‘c’. Then stages, aka ranks, are certain sets and so fall under Ext(ensionality). That gives the antecedent of your exercise; so we have the theorem of linearity: rEs ⋁ r = s ⋁ sEr. That means that Net simplifies to Suc(cessor): there is no last rank. Also Spec simplifies, with the aid of When, to a special case of ordinary Aussonderung; or rather, since we want to go second-order Comp(rehension): whenever there is a set that contains all of some things, then there is a set of exactly those things. Tra and Inf don’t look any different; and we have All: for some r, x c r When: each rank is the union of the power sets of previous ranks. In reading these, I want to understand ‘c’ and ‘power set’ in a funny way: any memberless thing, whether it’s the null set or an honest-to-god individual, vacuously c anything, and so belongs to every power set. (Actually, I think the null set is an honest-to-god individual. We only make believe that it’s a set. But let’s set that aside.) Ext is of course doctored to say that two memberless things needn’t be coextensive to be identical. If we like – I don’t like, but conservatism demands it – we can introduce a primitive name 0 and say that something is a set iff it has members or it is 0. (Or else a primitive sethood predicate and an axiom to say that exactly one set is memberless.) The next step is to define ‘E’ and get rid of Tra. Scott does this one way: ‘E’ means membership, When is doctored so that transitivity of membership of ranks falls out. But if we want to go second-order anyhow, there’s a different and nicer way. (This is the first instalment of trying to make good on what I said to you in March: that if we accept second-order quantification, otherwise than as set theory in sheep’s clothing or substitutional quantification in wolf’s clothing, we should put it to more use than just replacing the schematic parts of the first-order axioms.) Let E be the strict ancestral of membership: xEy iff whenever there are some things such that every member of y is one of them, and every member of one of them is one of them, then x is one of them. Transitivity of E follows; and not just for ranks, but generally. Next, I want to get rid of Choice. Of course I don’t mean by that that I want to reject it or derive it. I just want to get it off the list of set-theoretical axioms. Isn’t it really a principle of second-order logic having nothing especially to do with set theory? State it schematically thus, Φ(x, y) being any formula with just the two free variables displayed.

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Whenever there are some things X such that (1) whenever x is one of themX, there is at least one y such that Φ(x, y), and (2) it never happens that u and v are two different ones of themX and Φ(u, y) and Φ(v, y), then there are some other things Y such that whenever x is one of themX, there is exactly one y such that it is one of themY and Φ(x, y). (And then if theyY all fall within some set, Comp applies and we get a choice set.) This goes with something else I think: that it’s misguided to claim that NBG and MorseKelley are two different set theories. The set theory part is no different; what’s happening is that one set theory is being stuck onto two different incomplete fragments of class theory, in other words two different incomplete fragments of second-order logic. Likewise set theory with and without Choice isn’t two different set theories; it’s set theory stuck onto two different fragments of second-order logic. At this point, set theory consists of the neutral axioms Ext, Comp, All, and When (much as in Scott) and the axioms of extent Suc, Inf, and Replacement. Primitives are membership, rankhood, and (ugh!) 0. *** Replacement is a blotch on the landscape. Handy to use, maybe, but a devious way to say what it’s trying to say about the extent of the hierarchy. (Reflection is even more devious – it reeks of mystery.) What I’d like to see, but I don’t know how to do it, is something in the style of Suc and Inf – a statement about the ordering of the ranks – that takes the place of Replacement. Burgess tells me that what I want to say is that the ordering of ranks isn’t cofinal with any lesser ordinal. If I were happy with dyadic second-order variables I could define order-isomorphism (with respect to the order E), and then say whenever there are some of the ranks, and they are not order-isomorphic to all the ranks, then some rank follows all of them. Unfortunately, I’m only really happy with monadic variables. But at least I do know how to say that the order of ranks has cofinality more than omega. First, some ranks have a non-initial limit iff there is one of them x such that (1) another one of them precedes x, and (2) whenever another one of them, y, precedes x, then one of them is between y and x. (Just as in your Inf.) Then we can have an axiom whenever there are some of the ranks, and they have no non-initial limit, then some rank follows all of them. For what it’s worth, this can replace Suc and Inf, and also take us a goodly way beyond rank omega + omega; but it doesn’t take us as far as replacement. If I understand what

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Burgess told me, it says that the number of ranks is at least aleph-1, and is either a successor cardinal or else a ‘weakly inaccessible’ cardinal. What I’d really like is something quite different, and more radical, but I think much less likely to come good. I’d like to see the axioms of extent go the way of Choice, and turn out to be not part of set theory at all, but rather of second-order logic. All says that you’ve got enough ranks to exhaust the universe; how many ranks it takes to do that depends on the size of the universe; second-order quantification enables us to say things that depend for their validity on the size of the universe; so the question of extent turns on which of these things are valid. Complication. When I speak of what’s valid, I have a funny notion of validity for quantifiers. I say that what’s valid is what comes true under all interpretations of the non-logical vocabulary; however, I think ordinary quantifiers, which get to range over different domains under different interpretations, are for that very reason nonlogical vocabulary. What’s logical vocabulary is the absolutely unrestricted quantifier that ranges over everything. (This goes for first- and second-order quantifiers both.) So consider the first-order sentence which uses seventeen existential quantifiers in front of a lot of nonidentities to say that there are at least seventeen things. If its quantifiers are the ordinary ones, then it is invalid, because some interpretations tacitly restrict the quantifiers to, as it might be, the twelve Apostles. But if its quantifiers are the logical ones, then it’s valid; because there are at least seventeen things, and the in­ter­ pret­ation of the non-logical vocabulary is neither here nor there because the sentence didn’t have any non-logical vocabulary. (Don’t say that it’s contingent whether such a sentence is valid; because when I say absolutely unrestricted, I mean among other things that there’s no restriction to our little bit of the pluriverse. But that’s another story.) None of this matters much in first-order; we know there are infinitely many things, and we can’t say anything that depends for its validity on the difference between infinite sizes. But in second-order it’s otherwise. We can make sentences that distinguish lots of infinite sizes. These sentences will be devoid of nonlogical vocabulary – their quantifiers, both first- and second-order, will be absolutely unrestricted – so the true ones will be valid, the false ones will have valid negations. The true ones are the valid second-order principles that combine with All to yield conclusions about the extent of the hierarchy. Problem. I said that we can make second-order sentences that distinguish lots of infinite sizes. I’m sure that’s so if we have dyadic second-order variables; but as I said, I’m really only happy with monadic ones. What can we say about size with only monadic variables? Another problem. It isn’t really the size of the universe that settles the extent of the hierarchy. We could get a big universe by having a hell of a lot of individuals even if the hierarchy didn’t go very high at all. It’s a matter of comparative size: how much

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bigger is the whole universe than its ground floor? I don’t know what to do about this beyond confining my attention, for now, to the pure case – which is pretty sleazy after I’ve just been beating the drum for absolutely unrestricted quantification! *** The other thing I’d really like to do is get rid of When and the primitive of rankhood. After all, When looks just like an inductive definition of rankhood; and doesn’t ­second-order quantification enable us to turn inductive definitions into direct ones without presupposing any set theory? Try this. Some things X are cumulative iff each one of themX is the union of the power sets of all previous ones of themX. And r is a rank iff, whenever theyX are cumulative, then r is one of themX. Now: does it follow that the ranks are cumulative? If so, When follows from the definition of rankhood, and we’re home. Set theory is nothing but Ext, Comp, All, and maybe some axioms of extent. Hallelujah. Maybe it does follow, and I’m just missing a trick. More likely it doesn’t, and I only think it must because I’m presupposing some kind of induction that I’m not really entitled to at this stage of the game. Can you help me? If it doesn’t follow, and we can’t get When out of this definition of rankhood, maybe we can at least keep the definition, be rid of primitive rankhood, and get When from the definition with the aid of some new axiom that looks simpler than When did. Any suggestions along this line? Another approach would be to define rankhood more directly. What is it like to be a rank? If r is a rank, then (1) whenever x precedes r, x is a member of r; and (2) whenever each one of X either is memberless or else precedes some member of r, then there is a set of exactly themX, and it is a member of r. Are (1) and (2) sufficient for rankhood? If rankhood is defined by (1) and (2), does When follow? If not, does it follow with the aid of some new axiom that looks simpler than When did? Yours, cc: Benacerraf

276.  To J.J.C. Smart, 13 July 1985 [Princeton, NJ] Dear Jack, Thank you for all the footy, family, and railway news. Especially, our welcome to Robert’s new tool-kit!

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Steffi has found a new job. Not absolutely ideal, because it’s in New York rather than closer to home, but good enough. It’s still public finance – that is, the issuing of tax-exempt bonds – but this time not with an investment banking firm; rather, with a small new firm whose job is to advise clients in their dealings with the investment bankers. The investment bankers are supposed to advise the clients themselves, but there are conflicts of interest, hence the use for independent advisers. I am leaving for New Zealand and Australia tonight. I’ll reach Melbourne on 29 July, stay there except for miscellaneous travel until the AAP week, then go home after the AAP. Steffi must start work immediately at her new job, but she can take three weeks off a little later. That means that she will join me for most of my time in Melbourne. Our ‘miscellaneous travel’ is meant to include Canberra, and also western NSW; further plans await word from Barry Taylor about whether, and if so when, he’s been able to book us one of the Ormond College flats. So we’ll see you soon. This year was meant to be a light one, after my big push last year on Philosophical Papers, Volume II, and On the Plurality of Worlds. No such luck – it turned out that there was a lot more to do on both books. A year ago there only were a couple of small gaps in my draft of Plurality . . . but small gaps they were not, as it turned out. Anyhow, both books have at last gone to the publishers, and are now at the stage of copyedited manuscript. I fear one lot of galleys will catch up with me in Melbourne, the other as soon as I get home. The books should be out early in 1986. And now for something completely different . . . . No more afterthoughts on modal realism, counterfactuals, chance, causation, and so forth, anyway not for some time. *** One new venture has to do with set theory. (You heard the main idea at the AAP last year, in my reply to DMA.) I’ve always liked mereology better than set ­theory – it’s comparatively parsimonious, it doesn’t have any equivalent of the settheoretical paradoxes, and it doesn’t give us differences without difference-makers the way set theory does. (That is, – Goodman’s point – whenever we have two different things, there always will be some part of one that’s absent from the other.) Goodman and Quine (and in other circles Lesniewski) have taught us all not to confuse mereological sums with sets: the set of a and b has a unique built-in division back into a and b, whereas the sum of a and b will in general have many divisions (unless a and b are atoms), and the division into a and b will have no privileged status. I think we should halfway unlearn that lesson. It’s true, of course, that the set of a and b is not the same thing as the sum of a and b. But this doesn’t mean that the set of a and b is not a sum at all. I think it’s natural, and also it’s unproblematic tech­ nic­al­ly, to say that a (nonempty) set is the mereological sum of its (nonempty) subsets. Then unit sets are mereological atoms; other sets are sums of these atoms. For

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instance the set of a and b is the mereological sum of the unit set of a and the unit set of b. The set of the aforementioned set and c is the mereological sum of the unit set of the aforementioned set and the unit set of c; and so on. The many-into-one aspect of set theory is just good old mereology. The distinctive aspect of set theory isn’t that, but rather it’s the operation that transforms something – individual or set – into its unit set. I take this as bad news for set theory. The forming of unit sets is explained not at all by informal remarks about how sets are formed by treating many things together collectively as one. Of course, the forming of unit sets never was explained, but we tolerated them as a special case, thinking that we understood set-formation in general. But I say that the general case comes from the special place (plus unproblematic mereology) and if so, then the general case is just as mysterious as the special case. At this point it would be nice if I could share Hartry Field’s view that mathematics is needed only for the sake of physics, so that a workable instrumentalism about mathematical entities would mean we needn’t believe in them. The mathematical universe is the set-theoretical universe (dogma which I accept); if we needn’t believe in mathematical entities, then we needn’t believe in sets, and in particular we needn’t believe in unit sets; and then we needn’t claim to understand the alleged operation which is supposed to transform things into their unit sets. Unfortunately, I think that philosophical scepticism about the truth of mathematics is no less absurd than scepticism about the truth of physics, or scepticism about having two hands. So I think it’s not on to dispense with sets. So I find the whole situation pretty unsatisfactory. *** The other new project I have in mind is an analogy between mass and value. Recall what Hartry Field said about ‘mass’, as used not nowadays but by Newton. ‘Mass’ is a theoretical term of a theory – classical mechanics – that has turned out to be false, but close to the truth, not wildly far off. That theory defined a role, and the word ‘mass’ was supposed to denote the magnitude that occupied that role. It turned out that no magnitude occupied the role perfectly, but two different magnitudes – the ones we now call ‘rest mass’ and ‘relativistic mass’ – both occupied the mass-role fairly well. Some of the classical principles about mass are satisfied exactly by rest mass and approximately (under commonplace circumstances) by relativistic mass; the other principles are satisfied exactly by relativistic mass and approximately by rest mass. So what’s to become of the name ‘mass’, when nothing deserves the name perfectly, and two rival candidates both deserve it fairly well? There might of course be a stipulation: let ‘mass’ henceforth mean rest mass. But let’s say there hasn’t been a stipulation. It’s extravagant to say, as Feyerabend might, that it turns out that there’s no such thing as mass. Hartry says that ‘mass’ comes out mildly ambiguous, ‘partially

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denoting’ each of the two candidates; and we can ignore the ambiguity whenever what we’re saying is true on both disambiguations, which is very often the case. Now, imagine that ‘value’ is a theoretical term of another false-but-close-totrue theory, which I’ll call the ‘naïve theory of value’. I don’t know who the great theorist is who put forward this theory; it’s a myth, like the myth of the great theorist who introduced the theoretical terms of folk psychology. But I dare say that if you find somebody who thinks that recent moral philosophy undermines morality, it might turn out that the naïve theory of value is what he believes – or at any rate, it’s what he wishes were true, and thinks it would be beneficial for others to believe. I need some background before I can state the naïve theory of value. The background may be problematic, but if so its problems are irrelevant to what I want to say next. I need some ontology: properties, especially properties of stretches of human lives (temporal parts of people) such as the properties of health, serenity, wisdom, ­honour, happiness. And I need properties of properties as well, because if value is anything, it seems to be a property of properties – a property that is shared, perhaps, by all the properties just listed. And I need facts, such as the fact that a certain particle has positive charge, or the fact that a certain person-segment has serenity, or the fact that serenity has value. I hope we can take these entities in the least controversial way possible: set-theoretical constructions out of mathematical representations of pos­ sible worlds and individuals should do, and should be acceptable to both of us. I need the notion of a fact being objective. (If materialism is true, the objective facts will be those that supervene on the whole physical truth, though maybe without finite definability in physical terms.) They hold simpliciter – not relative to the standpoint of this person or that. And I need the notion of a fact being general; the fact that a first-order property has a second-order property, for instance that serenity has value, is one kind of general fact. I need the notion of a person valuing a property. This is a psychological notion, and not itself evaluative. Roughly, valuing a property means wanting to have it; but sometimes it may be no more than wanting to want to have it, and it may also involve wanting (or wanting to want) others to have it. The naïve theory of value holds (1) that value is a second-order property such that, when a first-order property has it, that is an objective, general fact; and it is a fact which can, somehow, be known. Further, (2) there is a necessary connection between the knowledge that something has value and the psychological state of valuing it. Suppose, for instance, that it is a fact that serenity has value. It is absolutely impos­ sible for anyone to know this fact without valuing serenity. You might fail to value serenity out of ignorance, because you didn’t know that serenity has value. You might know that serenity has value and nevertheless not want serenity, because you

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value serenity only to the extent of wanting to want it, without succeeding in wanting it. Or you might know that serenity has value, accordingly value it, indeed want it, but not pursue it because there are other things (maybe themselves valued, maybe merely wanted) that you want more. All these gaps between value and motivation are possible, indeed commonplace. But what cannot happen – so says the naive theory – is that you know that serenity has value and yet do not value serenity. I take it that the naïve theory of value is false. It can’t be dismissed out of hand because of its necessary connections; there could be necessary connection between knowledge and valuing if, for instance, folk psychology defines the names of mental states and the connection is so well written into folk psychology that no states would deserve the names of ‘knowledge’ and ‘valuing’ unless the connection held between them. It could be that way, but I don’t think it is. Folk psychology is looser, and leaves room for the possibility of villains who have any amount of knowledge and yet value the wrong things. But the naïve theory of value is close to the truth, not wildly off. There is a property, knowledge of which is necessarily connected with being valued, just as part (2) of the naïve theory requires: namely, the property of being valued. Of course, this property doesn’t satisfy part (1) of the naive theory very well. The fact that serenity is valued might be true for you and me, but not for Frantic Fred, so it isn’t an objective, general fact. Here we have one imperfect candidate to occupy the role and deserve the name of ‘value’, just as rest mass is one imperfect candidate to occupy the role and deserve the name of ‘mass’. And I suppose there is probably another property that fits (1) perfectly and (2) only roughly. I don’t know what that property is; and it might be something rather messy and disjunctive. But somebody might think that conduciveness to general happiness is the property that fills the bill, and that will do at least for an example. We’re OK on (1): if serenity is conducive to happiness, that’s an objective, general fact. As for (2), we don’t get it in full. There isn’t a necessary connection: it’s at least possible to know that serenity conduces to happiness and nevertheless not value serenity. But there may be a pretty good contingent connection: given the relevant laws of nature, given the actual constitution of people (or at least most people, or at least most people hereabouts) it isn’t possible to know that serenity conduces to happiness and yet not value serenity. So (2) is roughly satisfied. Now we have another imperfect candidate to occupy the role and deserve the name of ‘value’, just as relativistic mass is another imperfect candidate to occupy the role and deserve the name of ‘mass’. If all this is right, we end with a sort of compromise between three of the main positions in metaethics. ‘Value’ partially denotes something of which a kind of nat­ural­ ism is the true account; partially denotes something of which a kind of non-cognitivism

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or subjectivism is the true account; and purports to denote something which doesn’t exist at all, so that there’s truth also in an error theory. *** This letter was meant to end with long-overdue comments on two papers you sent me. But there’s no time – my plane leaves in 3½ hours. The short of it is (1) that even if there are many worlds, I don’t think the anthropic principle affords genuine explanations, and (2) I agree with you in doubting that Regan’s theory is really different from act utilitarianism. Perhaps we can talk about this in Canberra or at the AAP if you’ll be there, though I’d have to reread the papers first. Yours,

277.  To D.M. Armstrong, 1 October 1985 Princeton University Princeton, NJ Dear David, News. Frank has been offered and has accepted the RSSS chair (subject to negotiations about transferring superannuation, expected to cause delay but nothing worse). Mark1 and I have been granted money from a Departmental research fund to pay an experienced and recommended transcriber, Matthew Bell, for about 13 hours of work on the Williams Notre Dame tapes;2 but not until after Bell takes his general exam in January 1986. Your ticket stubs came, and the reimbursement form has gone in. My visit to Madison seems to be on – see one enclosure.3 A second enclosure is the textual notes on ‘Universals and Existents’.4 A third is correspondence with Katherine Williams having to do with her mixed feelings about the Nachlass.5 *** Here is my own scorecard on the six views about natural classes, followed by comments. You’ll note that I’ve had to distinguish three grades of difficulty, with   Mark Johnston.   Three lectures read by Williams at the University of Notre Dame, February 1974. Lecture 1 and Lecture 2 have been published in (Williams 2018). 3   Most likely, Lewis’s itinerary for his brief visit to UW-Madison in Fall semester, 1985. Armstrong was visiting UW-Madison where he ran a seminar on modality focusing on On the Plurality of Worlds (Lewis 1986c) and his own research that led to A Combinatorial Theory of Possibility (Armstrong 1989a). 4   (Williams 1986). Recently reprinted: (Williams 2018, ch. 3). 5   Donald Cary Williams Papers, Harvard University Archives. 1 2

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scores of -1, -2, -3, and with thin, thick, and double arrows; that makes the scores reflect my current ranking of the views.

Unmereological composition. This is of course the point from ‘Against Structural Universals’: if a theory of universals is to make room for the possibility of infinite complexity, it must have genuine, not ersatz, structural universals; in which case the composition of these out of simpler universals is unmereological. Diseconomy: particularised natures. I’m not persuaded that an advocate of the resemblance or primitive naturalness views must or ought to buy particularised natures, respectively of individuals or of classes. If he doesn’t, then he should reject your questions of priority. That is, he should (a) take a thin view of natures, saying that the nature of a thing (or class) is given by what natural classes of this- and otherworldly things it falls into; (b) take a thin view of what it is for a relation to be internal, saying only that R is internal iff it supervenes on the natures of the relata; and (c) take a thin view of supervenience, leaving out anything about explanatory value or priority or direction or asymmetry, and saying only that X supervenes on Y iff there cannot be X-difference without Y-difference. Classes Depend on Properties. As to the difficulty as stated in the first paragraph of section III, I say that it’s fair to answer by denying that there’s any ‘in virtue of’ in either direction between having the property and belonging to the class. What does priority mean when there’s a necessary connection? Sometimes I understand it: the disjunction is true in virtue of this disjunct being true, the existential quantification is true in virtue of this instance being true. But we don’t have such an easy case here.

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As to the ‘sharpened’ difficulty in the following paragraph, you agree that it vanishes given my modal realism. But I say that it vanishes just as much given your modal Meinongianism. For then also ‘the classes involved can be taken to be classes which span all possible worlds’ – the existent one and the nonexistent ones too – ‘and it is not possible that such classes could be any different from the way they are’ so far as the identity and Sosein of their members is concerned. All that is contingent is which members of the classes happen to exist. If you’re going to be a Meinongian, you shouldn’t neglect the nonexistent parts of your classes any more than I should neglect the otherworldly parts! (If you dislike that, good for you. But I think that to dislike that is to dislike Meinongianism.) Causality. I agree it’s a desideratum that causation should come out to be a wholly local matter, but I think it’s a lost cause. Even having the properties of the rock and window be universals or particular natures won’t do it unless, in addition, the laws are a local matter. That means rejecting plain and fancy regularity theories of lawhood in favour of the DTA theory (or an adaptation of it to particular natures) and you know my objections there. Co-extension. As Dan Garber said, it’s not a problem for someone whose only aim is to distinguish the natural from the unnatural classes. It becomes a problem for someone who then wants to say that the natural classes are (or correspond one-one with) the natural properties. But anyone who favoured the primitive naturalness or resemblance views probably would want to take that further step. As you say, the difficulty vanishes given modal realism. (Unless you want to distinguish between necessarily co-extensive natural properties, which seems pretty negotiable.) I say, again, that it vanishes just as much given your modal Meinongianism. I say, again, that you shouldn’t forget the nonexistent parts of your classes. There will be no such thing as accidental co-extensiveness; though it may happen, by accident, that the existent parts of two different classes are the same. Michael Smith objected to this as follows: Armstrong thinks the worlds, this one and the nonexistent ones alike, are constructed from states of affairs, which in turn are constructed (partly) from properties. So worlds in turn are constructed (partly) from properties. So worlds are constructed (partly) of properties. But if, contra Armstrong’s real view, properties are natural classes bound together either by primitive naturalness or by resemblance, and if – as just argued – we have to remember the otherworldly, nonexistent parts of these classes so as not to conflate different properties which are co-extensive so far as this world is concerned, then also it turns out that properties are constructed from (parts of) worlds. This looks like an objectionable sort of circularity or unfoundedness in the two constructions from properties to worlds and back.

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277.  To D.M. Armstrong, 1 October 1985

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I’m inclined to agree that this circularity is bad, though I can’t say for sure without understanding the alleged unmereological composition whereby states of affairs, and then worlds, are constructed (partly) from properties. So I think Michael’s objection is right, in a way – but only in the way it’s right to say that if Bizet and Verdi were compatriots they’d both be French. As every student of counterfactuals knows, you can’t on pain of contradiction change just one thing and hold all else fixed. The real Armstrong holds that properties are entirely thisworldly universals, not cross-world classes. But we’re considering a hypothetical Armstrong who tries on a primitive naturalness or resemblance view, and therefore holds that properties are cross-world classes. (The otherworldly parts being ‘nonexistent but none the worse for that’.) Would this hypothetical Armstrong still be committed to the view that worlds are constructed partly of properties? Maybe so – hold that fixed (like Bizet’s nationality), and then Michael’s point is well taken. But maybe not. I should think a better way to combine your modal Meinongianism with a hypothetical rejection of universals would be to give up the view that worlds, existent or nonexistent, are constructed (partly) from properties. (Unless you want to call tropes ‘properties’, but I think that’s unfortunate ter­min­ ology.) Worlds are constructed from regular particulars, or maybe from tropes; not from universals, if ex hypothesi those are rejected; and certainly not from cross-world classes of parts of worlds, for Michael’s reason. If we suppose that your hypothetical rejection of universals would include rejection of the view that worlds are constructed (partly) from properties, then Michael’s objection no longer applies. (He agrees.) Identical tropes. Why can’t duplicate tropes be concreted together? Mark and I both suggested that, at least so far as absolute possibility is concerned, they can be; though there might be laws of nature (exclusion laws) against it. Mark added that the result of such supersaturation might not deserve to be called a ‘particular’, or anyway not an ‘ordinary particular’. Whereas I said that the results of such supersaturation might be very ordinary particulars indeed – some sorts of supersaturation might be commonplace. Example. There is a minimal positive charge. (Or negative. Let me omit ‘positive’ henceforth. Unfortunately, what’s called ‘unit charge’ is not minimal but thrice-minimal – same sort of misnomer as with the word ‘atom’.) There are abundant particles with min­imal charge, and there are abundant particles with thrice-minimal charge. Hypothesis: the latter have three duplicate charge-tropes each. Sometimes (the proton) the thriceminimally charged particle isn’t a point particle, so maybe it can have three chargetropes at different positions within it (namely, one on each of its three quarks). But sometimes (the positron) the thrice-minimally charged particle does seem to be a point particle. Then maybe its three duplicate charge-tropes are concreted together.

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Someone, I think you, asked how this could apply to a quantity Q that can take any value in a continuous spectrum. Duplicate infinitesimal-Q-tropes, concreted together in infinite numbers? Well, why not? But what I said was that concretion of duplicate tropes didn’t have to be right for all quantities to be right for some. (I might also have tried a tu quoque: what problem would I have with the putting together of little Q-tropes to give bigger values of Q that you wouldn’t have with the putting together of little lengths to give bigger lengths in your treatment of similarity and incompatibility of lengths?) John Collins said that it might be all very well to have concretion together of duplicate noncomposite monadic tropes, like the charge tropes, but what if we were dealing with composite structural tropes, such as shape-tropes? I offered a simplification of his point. I thought that concretion of structural tropes reduces to concretion of the constituent monadic and relational tropes. Thus we have F1-R-F2, a structural trope made of two monadic F-tropes and one dyadic R-trope; and likewise we have G1-S-G2; and the concretion of them amounts to the concretion of F1 and G1, and of F2 and G2, and of R and S. Now suppose we’re trying to double up two duplicate structural tropes: F1-R1-F2 and F3-R2-F­4. We need concretion of the duplicate F-tropes F1 and F3, and likewise of F2 and F4, and so far it’s the monadic case which John granted me wasn’t problematic. But also we need concretion of the duplicate relational tropes R1 and R2; and that, I grant, seems pretty hard to imagine. So my version of John’s point is that concretion of duplicate relational tropes, for instance distance-tropes, still seems puzzling even if concretion of duplicate noncomposite monadic tropes is acceptable. It remains a question whether concretion of duplicate relational tropes is downright impossible, in which case the trope view seems stuck with a brute modal fact, or whether it’s just so foreign to the ways of this world that we can’t imagine it beyond just saying in words that it would be. And Mark’s point still applies in the relational case: even if concretion of duplicate relational tropes is possible, we needn’t grant that we would then have, as it might be, two different distances between the same two particles; because maybe the entities involved in such an affair would ipso facto not deserve the name of ‘particles’. One might favour a principle forbidding the concretion of duplicate tropes because one holds a stronger principle, as follows: any given case of concretion (or, any case that produces something deserving of such a name as ‘particle’) must involve exactly one trope from each of certain listed categories. That stronger prin­ ciple, at any rate, seems false. Example: suppose I’m right to suggest that there are spacelike distance relations and timelike distance relations; in a Newtonian world, two spacetime points (or particle-stages) are related by two distances, one of each kind, whereas in a relativistic world, two points are related by only one distance,

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277.  To D.M. Armstrong, 1 October 1985

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which may be of the one sort or the other. (I set aside the case of lightlike distances.) And suppose both cases are possible. Then either the spacelike and the timelike distances fall in a common category or they don’t. In the first case, the Newtonian pointpairs violate the principle by doubling up within a single category; in the second case, relativistic point-pairs violate the principle by omitting one or the other cat­ egory. For that matter, point-pairs from two worlds (for you and me both, though for you such pairs would include one nonexistent point) or from different island universes (for you) would also violate the principle by omission. I think there’s something left of the difficulty, but not much. I’ve marked it accordingly on my scorecard. Fit of tropes to universals. Why can’t a trope instantiate a universal just the same way you think an ordinary particular does? ‘What is it about a certain trope that makes it fall under just such-and-such universals?’ – Having that universal wholly present within it. Ontological diseconomy. However I think there’s a fair complaint of diseconomy against a view that posits universals and tropes both; as well as a milder complaint against any view that posits either universals or tropes. Diseconomy of connective. (First a point of terminology. ‘Connective’ to me strongly suggests a sentential connective, nothing else, and I think this will distract if not mislead many in your audience.) This has several parts. There’s complexity of the primitives themselves, and there’s complexity of the principles governing them. There’s complexity introduced by the fact that naturalness of classes admits of degree, and there’s complexity that arises for other reasons. As to complexity in handling degrees of naturalness, I think there’s nothing to favour one view or another. The universals view first delivers only the perfectly nat­ ural classes as the classes united by one shared universal; afterward, when we have some account of resemblance of universals, it delivers also the imperfectly natural classes with their differing degrees of naturalness. There are two alternatives. Case I: your plan to explain resemblance of universals in terms of part-identity of structural universals succeeds completely. Then I claim the resemblance and primitive naturalness views can adapt your solution, using in place of structural universals either perfectly natural classes of structured regular particulars or else perfectly natural classes of structural tropes. Case II: the plan succeeds partially or not at all, leaving you stuck with a need for primitive resemblance of universals, and for axiomatic principles governing it. In that case you cannot fault rival views for needing parallel complexity before they can introduce degrees of imperfect naturalness of classes. Everybody’s problem is nobody’s. As for other complexity, I think the clearest thing to say is that primitive resemblance for regular particulars is a very horrid complex primitive – see ‘New Work’.

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Simpler sorts of primitive resemblance for ordinary particulars, as opposed to tropes, won’t do: they give you the Companionship and Imperfect Community ­problems. To a lesser extent, I think we can complain of complexity against any view whose primitive applies to classes instead of individuals, that is against either of the primitive naturalness views; and against any view that needs two primitives instead of one, that is against any of the trope views. For they will all need primitive concretion of tropes, as well as primitive naturalness or resemblance or instantiation of universals by tropes. As to the further diseconomy of needing axiomatic principles governing resemblance or primitive naturalness (e.g. that resemblance of tropes is an equivalence relation, or that the primitively natural classes of tropes are mutually exclusive and jointly exhaustive), I suspect the dishonours are pretty much even. Doesn’t the theory of universals also have its axiomatic principles? How about victory of particularity? Instantial invariance? Order invariance (weak or strong)? Yours, David cc: Collins, Johnston, Smith

278.  To Peter van Inwagen, 25 February 1986 Princeton University Princeton, NJ Dear Peter, The content of a time t is the mereological sum of all the things that are wholly at t. If it is not always true that things have a mereological sum, then it may happen that a time has no content. For instance, if composition takes place only when an organism is composed of particles, then t has a content only when the only things at t are an all-inclusive organism and the particles that are its parts. But if, as I think, composition is unrestricted (PoW 211–13) then every time has a content. If a particle, or a universal, or the universe is wholly at different times, then the contents of different times overlap. Indeed if the universe is wholly at all times, and everything else is part of the universe then all times have the same content. If, on the other hand, nothing is wholly at two different times, then the content of different times never overlaps. In that case, indeed, not only does the content of an

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279.  To Michael Tooley, 4 March 1986

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instant persist only for an instant; not even any part of the content of t persists beyond t. My view is that contents may overlap by having universals as common parts, if there are any universals; but they overlap in no other way. So if there are universals, it can’t be said that the whole of the content of t persists only for an instant – some of it will persist longer, viz. those universals that are instantiated at t not for the last time. The supplementary clause you requested goes as follows, but I doubt that it will help you: How can an object that is wholly present at t1 and t2 be spherical at t1 and cubical at t2 given that (1) sphericality and cubicality are properties of the object itself, not relations of the object to something else, and given that (2) they are properties of the whole object, not of distinct parts of it; and given that (3) they are properties the object has, not properties it is falsely represented to have. I imagine you as denying (1) and regarding that denial as unproblematic – does that description seem to you to fit? Yours, David PS Steffi said you wanted to see my stuff on nuclear war. I’ve sent two things, one old1 – which I may have sent before – and one new.2

279.  To Michael Tooley, 4 March 1986 [Princeton, NJ] Dear Michael, Let’s speak of ‘Russellian velocity’ or ‘Russellian acceleration’ to mean those properties which Russell takes to be velocity or acceleration: properties extrinsic to the particle at a moment, derived from the spatiotemporal shape of the trajectory in the vicinity of the moment. Whether or not they are rightly called ‘velocity’ and ‘acceleration’ simpliciter, they are still there. That is, they normally are; let’s say they are imperfectly defined when the left- and right-hand derivatives are defined but un­equal, and altogether undefined when the derivatives are undefined.   ‘Devil’s Bargains and the Real World’ (Lewis 1984a).   ‘Finite Counterforce’ (Lewis 1989b).

1 2

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It is at least somewhat plausible that a particle still has a determinate velocity or acceleration even when its Russellian velocity or acceleration is imperfectly defined or undefined. Your main argument for the non-Russellian view is that it provides for these prima facie possibilities. But note that you don’t guarantee, any more than Russell does, that every par­ ticle at every moment must have a velocity and an acceleration. Presumably the velocities, and likewise the accelerations, are a family of determinates, in the same way that the masses, the charges, the quark colours are. In general, when we have such a family, it’s possible that a particle might have none of the properties in the family – neutrinos have no charge, photons have no mass, electrons have no quark colour. (I take it to be an artificial convention that having no charge is called having charge zero, and having no mass is called having mass zero. No such convention exists for the quark colours.) In return for securing the possibilities you want, you make room for a supposed possibility that seems to me entirely unwanted: that a particle might have (what you take to be) genuine velocity and acceleration throughout a period of time, and might also have well defined Russellian velocity and acceleration throughout the same period, but the former might be entirely unrelated to the latter. Thus the particle might just sit there, stationary with respect to its surroundings, while undergoing extreme Tooleyan velocities and accelerations every which way! Or vice versa. That might be a nomological impossibility, but I believe you agree that the laws are contingent, so that a nomological impossibility is still possible simpliciter. I think this supposed possibility is much more unwanted than the possibilities you wanted are worth. Consider the laws or causal relations whereby a charged particle in an electromagnetic field accelerates and changes its velocity. You argue that if the velocity and acceleration are Russellian, those laws or causal relations will violate plausible formal principles; and not so if the velocity and acceleration are Tooleyan. Suppose this is true, and suppose it matters. I ask you: what about the laws or causal relations whereby Tooleyan velocity and acceleration cause Russellian velocity and ac­cel­er­ ation? Russellian velocity and acceleration are still there. The problem of how they get caused doesn’t go away just because you solve a different problem about how Tooleyan velocity and acceleration get caused. Here ends a limited defence of Russellian velocity and acceleration. Two side issues. First: what’s the relevance of infinitesimals? I think you’re joining Russell in a mistake at this point. Suppose there are infinitesimal spatial and temporal distances, ds and dt, so that a quasi-Russellian velocity can be taken as (the standard part of) the ratio ds/dt. That still makes the velocity and acceleration supervene on the particle’s trajectory (on where it is when), though the trajectory is more complicated than we

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280.  To Peter van Inwagen, 1 April 1986

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thought since it’s a trajectory through a Robinsonian rather than a standard con­ tinuum. It still allows the velocity or acceleration to be imperfectly defined because the left- and right-hand derivatives are unequal. It still allows the velocity or ac­cel­er­ ation to go altogether undefined if the particle goes flashing around discontinuously – provided it appears at a point only for a moment, not a moment plus an infinitesimal interval around that moment. Second, I think you’d do well to mention Graham’s ‘Hegelian’ spread theory of velocity (with or without the paraconsistent angle which especially endears it to him;1 and regardless of how close it is to the historical Hegel). This theory makes velocity supervene on the trajectory; though again the trajectory is more complicated than we think, since a moving particle supposedly is present at many different places at once. And yet it makes the velocity intrinsic to the moment; so that there can be a Priestian velocity even when the Russellian velocity is imperfectly defined or undefined, as you and Graham want. The price paid is the same as for your theory: we make room for the unwanted possibility that the Priestian and the Russellian velocities might disagree completely. May I share this letter and your paper2 with various people who will be ­interested? Yours, David Lewis

280.  To Peter van Inwagen, 1 April 1986 [Princeton, NJ] Dear Peter, When we have a pair of truths of the form X is ADJECTIVE PREPOSITION Y but not X is ADJECTIVE PREPOSITION Z we may presume that the adjective and preposition together express some relation that X bears to Y but not to Z. It is that way, I hope you’ll agree, when Brisbane is far from Cunnamulla but not far from Toowong; or when time t0 is future at t1 but not future at t2; or when Fred is envious of Ted but not of Ned; or . . .

 Graham Priest.   2  ‘In Defense of the Existence of States of Motion’ (Tooley 1988).

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You think it’s not that way, however, when x is spherical at t1 but not spherical (rather, cubical) at t2. Well, OK; I only said ‘we may presume’ that there’s a relation being expressed. I’d be glad to let that presumption be defeated, provided it’s defeated by some alternative account, not just the bare declaration that we have here an exception. Sometimes an alternative account will leave us with the relation that X bears to Y but not to Z, but will explain this relation in terms of some property. That’s how it is, on my view and perhaps also on yours, when the road is rocky in the mountains but smooth on the plains. The road – the whole of it, which stretches over both the mountains and the plains – has the ‘rocky in’ relation to the mountains and the ‘smooth in’ relation to the plains; but this relation can and should be explained in terms of the properties of parts of the road: the part in the mountains is rocky, the part in the plains is smooth. Of course I think, and of course you disagree, that this is how it is also when a lump is spherical at t1 and cubical at t2. I also think, and this time I hope you agree, that this is how it is when a yearlong course is tedious in the first semester but exciting in the second. When a politician is honest according to the Times but not according to the Age, again we have a rival explanation to defeat the presumption. Not full defeat: we do have the ‘honest according to’ relation between politicians and newspapers, but it’s to be explained in terms of content involving the property of honesty simpliciter. There could also be a presumption-defeating account that doesn’t leave us with the relation X bears to Y but not to Z.  In Oxford it was once suggested, for instance, that we have been misled by superficial grammar into thinking that there is some entity denoted by the name ‘Australia’. It’s not like that; in the true logical form for ‘Australia’-sentences, the phrase ‘in Australia’ is simply a negation operator. Thus ‘In Australia, Christmas comes in the summer’ is true iff ‘Christmas comes in the summer’ is false; ‘In Australia, Cardiff is a suburb of Newcastle’ is true iff ‘Cardiff is a suburb of Newcastle’ is false; ‘In Australia, most snakes are poisonous’ is true iff ‘Most snakes are poisonous’ is false; ‘In Australia, the Labor party is the capitalist’s friend’ is true iff ‘The Labor party is the capitalist’s friend’ is false; and so on. The evidence is abundant. See how easily the bewitchment of grammar leads us into bizarre beliefs! (Another example, though not one involving a seeming proper name. ‘In a pig’s eye Reagan is competent’ is true iff ‘Reagan is competent’ is false – don’t think Reagan bears the ‘competent in’ relation to some pig’s eye.)

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281.  To Max Cresswell, 27 May 1986

553

OK – the presumption is defeasible, but I say it takes an account to defeat it. You reject the two serious defeating accounts known to me, viz., that being cubical is in the first instance a property of improper temporal parts, and that other times are false representations of what properties the thing has. You propose no other defeating account. So I take it you think no defeating account is required. The presumption that ‘spherical at’ and ‘cubical at’ express relations of things to times just wasn’t there in the first place. I would like to hear what you have to say to someone who says that (1)*ʹ Nearness and fairness are properties that an object may have to or from one place and lack to or from another; where an object has one of these properties, that property is there a property of that object itself, not a relation of the object to something else. I suppose you say that (1)*ʹ, though somewhat similar to (1)*, differs from it by being false.1 Can you say more? Yours,

281.  To Max Cresswell, 27 May 1986 [Princeton, NJ] Dear Max, In the March 1986 AJP, second paragraph of page 92,1 you will find something very like your Turk-Greek sentences simply used – not presented as an example. It is disambiguated by variables, as if it were (1V) Each of two Turks T and Tʹ was fighting each of two Greeks G and Gʹ. As best I remember, I had no thought when I wrote it that it was any kind of puzzle sentence. What I think I’ll do with the tax certificate is file it away and never trouble any tax authorities anywhere with it; because I think that if I tried to get credit, I might well get more than $12.11 worth of hassle. 1   ‘(1*) Sphericality and cubicality are properties that an object may have at one time and lack at another; when an object has one of these properties, that property is then a property of that object itself, not a relation of the object to something else (when an object doesn’t have one of these properties, it’s neither a property of that object itself nor a relation of the object to something else)’ (Letter from Peter van Inwagen to David Lewis, 25 March 1986, p. 1, his italics).

  ‘Comment on Armstrong and Forrest’ (Lewis 1986b, 92).

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To connect surface structure and first-order formalization for your Turk-Greek sentences, you might think of it like Two Turks are such that     Two Greeks are such that        each of them was fighting each of them; and then put that into second-order as For some T, T are two Turks, and     For some G, G are two Greeks, and        each of T was fighting each of G; and then replace the second-order by pseudo-second-order quantifiers, where a pseudosecond-order quantifier is simply a long enough block of first-order quantifiers For some x, for some y, x and y are two Turks, and     For some z, for some w, z and w are two Greeks, and        each of x and y was fighting each of z and w; and finally do the obvious with the formulas ‘x and y are two Turks’, ‘z and w are two Greeks’, and ‘each of x and y was fighting each of z and w’ to obtain a slightly longwinded equivalent of (5). What makes it easy this time is that ‘long enough’ has a finite bound: two. ‘Each of 462 was fighting each of 978 Greeks’ is just as easy, except for the typist. If it’s ‘Each of many Turks was fighting each of many Greeks’, and you’re willing to presuppose that there were finitely many Turks and Greeks but not willing to impose a definite bound, then it gets harder: we can formulate each of the sentences ‘Each of m Turks was fighting each of n Greeks’ as above, then take an infinite disjunction. And if the war gets worse, so that after a while each of countably many Turks is fighting each of continuum many Greeks, the use of pseudo-second-order quantifiers gets very badly infinitary, very fast. I think the trade-off between second-order and infinitary formulations is pretty well known. I don’t really suggest that it serves any good purpose to trade in the covertly second-order quantification in natural language for the infinitary firstorder counterpart. In fact, I don’t really think it’s always possible. For we can quantify second-order over the sets, or for that matter over the proper classes; and then no block of first-order quantifiers, not even one we take as an uncountable sequence, can be ‘long enough’. So there’s not really any use having a treatment of the original Turk-Greek sentences that doesn’t carry over to (1ʹ) Each of all the sets was fighting each of all the proper classes or whatnot.

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282.  To D.M. Armstrong, 28 July 1986

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But what pseudo-second-order quantification is good for, I think, is a softeningup exercise in preparation for Boolos’s view that second-order quantifiers are plural quantifiers over ordinary things, not singular quantifiers over special plural things; so that a plural quantification over dogs, nonselfmembers, or what have you, carries commitment only to dogs, nonselfmembers, or whatever, not also to any kind of sets or classes or properties or . . . of them. It’s easy to say how a second-order quantifier is noncommittal in this way when it can be replaced by a pseudo-second-order quantifier; then it’s only a small step to thinking it’s equally noncommittal even when it can’t be. --Plans. Steffi gets two weeks’ vacation, and she’ll be in Australia for the AAP and for the week before. She may get a little more time, but we can’t plan on that now. I don’t want to be away very much longer than she can be with me, as has happened too often in recent years. So I won’t come to the Auckland logic conference, as I’d been hoping to (or not unless Steffi gets a good deal more time than expected, and gets it promised quite soon). Probably Australia from late July through the conference, dividing my time between Sydney, Canberra, and Melbourne; and no NZ this year. See you at the conference, anyhow. I liked your departmental prospectus! Yours,

282.  To D.M. Armstrong, 28 July 1986 Melbourne, Australia Dear David, More on structural universals, mostly to write down things I said in our conversation last week. I’ll start with some background to make this letter self-contained. Your proposal, since late last year, has been that we can get structural universals by conjoining ‘types of states of affairs’ – for shorts, tsoa’s – and that the conjoining can be taken as mereological summation. Example. We have the universal H(ydrogen) and the dyadic universal B(onded). We want the structural universal H2, which is instantiated by molecules consisting of two hydrogens bonded together. We have the tsoa’s TH1:  Something being H, TH2:   Something else being H, TB:    Something being bonded to something else;

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and we conjoin them by summation to get TH2:  One H being bonded to another H. Second example. We have H and B as before, and also O(xygen). We want H2O, the structural universal instantiated by molecules consisting of two hydrogens both bonded to a single oxygen. We get it by conjunction, that is by summation, of several tsoa’s as follows: TH1ʹ: TH2ʹ: TO: TB1: TB2:

Something being H, A second thing being H, A third thing being O, The first being bonded to the third, The second being bonded to the third;

and by conjunction, that is summation, we have TH2O:  Two H’s being bonded to one O. I’ve had a difficult time understanding what a tsoa was meant to be. I offered you three guesses, all of which you rejected. The first guess was that, after all, the mereological summation applied not to types but to tokens – particular states of affairs – and only at the end did we pass to types by means of some unexplained sort of abstraction. I complained that I didn’t understand the unmereological composition of particular states of affairs from universals, and also I didn’t understand the abstraction step that took us from complex, conjunctive particular states of affairs to structural universals. The second guess was that tsoa’s simply were universals, simple or structural as the case might be. Then TH1 and TH2 in the first example would be identical, being simply the universal H; and likewise in the second example TH1ʹ = H = TH2ʹ and TB1 = B = TB2. Against this I said just that the objections to mereological com­ pos­ition of structural universals out of simpler universals couldn’t be beaten just by calling universals by a new name. My third guess was that tsoa’s were what I’ve called ‘amphibians’: like universals they can occur repeatedly, but like particulars they can be duplicates of one another. Then TH1 and TH2 could be two different duplicate hydrogen amphibians; likewise TH1ʹ and TH2ʹ; and TB1 and TB2 could be two different duplicate bonding amphibians. I think the theory that structural universals are composed of am­phib­ ians might be workable. But it goes off in a novel and unexplored direction. I resist it out of conservatism. All three guesses disregard your statement that tsoa’s involve ‘particulars, but no particular particulars’. The reason is that I find that paradoxical – there is no such

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thing as a particular which isn’t any particular particular. What’s meant, however, seems to be that the tsoa’s involve patterns of identity and difference which, in an instance, would become the identity and difference of particulars – of some particular particulars. How to capture this? A fourth guess. Tsoa’s are relations. Not, in general, genuine polyadic universals – some may indeed be that, but others are hoked-up redundant affairs, unsuited for inclusion in our fundamental inventory in the same way that internal relations or disjunctive properties are. Still, they may serve as building blocks. The ‘particulars, but no particular particulars’ turn out to be the places of these relations. So in our first example TH1 = λxy Hx, TH2 = λxy (y ≠ x & Hy), TB = λxy xBy; so TH2 = λxy (Hx & (y ≠ x & Hy) & xBy). And in the second TH1ʹ = λxyz Hx, TH2ʹ = λxyz (y ≠ x & Hy), TO = λxyz (z ≠ x & z ≠ y & Oz), TB1 = λxyz xBz TB2 = λxyz yBz TH2O = λxyz (Hx & (y ≠ x & Hy) & (z ≠ x & z ≠ y & Oz) & xBz & yBz). Thus conjunction by summation is carried out on relations, all of the same polyadicity; and what it yields is a complex structural relation, namely the relation that obtains between the two atoms of an H2 molecule or between the three atoms of an H2O molecule. (This needs a qualification. It’s true, thanks to the symmetry of the molecule, that TH2 = λxy x and y are the atoms of an H2 molecule but it isn’t true that TH2O = λxyz x, y, and z are the atoms of an H2O molecule because TH2O holds between the three atoms of an H2O molecule only if they’re taken in the proper order, with the hydrogens before the oxygen. It would be nice to be rid of this arbitrary ordering. But we must have it, at least until all our summing is done; since it’s the correlation of orders in the two conjuncts that gives us what we want from the summation.)

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Note that H ≠ TH1 ≠ TH1ʹ. The first is monadic (H = λx Hx), the second dyadic, the third triadic. Even when one place of a relation is idle, as the second place is in TH1 and as the second and third places are in TH1ʹ, still we carry it along. Else it’s not clear how the subsequent conjunctions make sense – how do you conjoin two relations of different polyadicity? Any two things whatever have a mereological sum. But when we want to take sums as conjunctions, we’d better make sure that the polyadicity matches. We need an operation of extension that adds extra, idle places to up the polyadicity. It can add one or more of them; it can put them before or after or between the places we had originally. We can extend a property to various dyadic or triadic or . . . relations:

Or we can extend a triadic relation to various triadic or . . . relations

(Thanks to the symmetry of bonding, I don’t have to distinguish λxy xBy from λxy yBx. If I started with an asymmetric dyadic universal – something I’m not sure will ever be required – it might be necessary to provide also an operation for permuting or identifying places.) Extension doesn’t yet yield TH2, TH2ʹ, or TO, because of the nonidentities they involve. One option is to analyse these as conjunctions by summation of tsoa’s derived by extension with nonidentity tsoa’s. Objections to nonidentity as a genuine universal do not carry over against nonidentity tsoa’s, since tsoa’s are ­relations in a liberalised sense. So we can derive TH2 (and similarly TH2ʹ) and TO as follows

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282.  To D.M. Armstrong, 28 July 1986

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by extension and conjunction together. Another option is to limit ourselves throughout, as you do already for polyadic genuine universals, to irreflexive relations. (Let’s call a triadic relation R irreflexive if Rxyz entails x ≠ y & x ≠ z & y ≠ z; and likewise for tetradic, . . ..) In addition to operations of extension and conjunction, we need a third op­er­ ation: otherwise we have only our structural relations, not yet any monadic structural properties. To finish the job we need what Peter calls projection: ‘Consider an n-adic relation R. Suppose a1, . . ., an are related by R. Then, as a consequence, the sum a1 + . . . + an has a property, namely being the sum of parts related by R. I call this property the (monadic) projection of R’ (‘Ways Worlds Could Be’, page 18).1 With projection at the final step, the derivation of the structural universal H2 – being a diatomic hydrogen molecule – is as follows. (Arrows for extension, braces for conjunction by summation, double arrow for projection.)

So we have a construction of structural universals out of simpler universals (and maybe also nonidentity tsoa’s) by means of extension, conjunction, and projection.   ‘Ways Worlds Could Be’ (Forrest 1986a).

1

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Compare Peter’s construction by means of product, contraction, and projection. The two are akin, but not exactly the same. (There are many more in the family.) The main advantage of Peter’s choice, I think, is that it’s rather plausible that anything you get from genuine universals by his operations is itself a genuine universal. No need for a liberalised sense of properties and relations! Whereas the extensions of genuine universals, and also the nonidentity tsoa’s, don’t seem plausibly to be genu­ ine universals. Nor do some of the conjunctions in which not every conjunct is a genuine universal; although maybe the finished structural relations, ready for projecting, are. The main advantage of yours is that, unlike any of Peter’s operations, your conjunction of tsoa’s can plausibly be taken as plain mereology. (The most Peter can say is that his products bear an analogy to mereological sums. But the analogy is limited, as he immediately says.) But if I’m right about your construction, it’s more than mereology. Before the mereology comes the extending, for instance to turn monadic universals into dyadic tsoa’s. And after the mereology comes the projecting, to get us back down to monadic structural universals. Only the middle part is mereology. The whole thing is partly mereology, partly something else, viz. extension and projection. In fact, it’s like set theory, which is partly mereology and partly something else, viz. the operation which generates unit sets from their members. (I thought for a time that we might do without projection and hence, strictly speaking, without monadic structural universals. Instead we could use our nonmonadic structural relations – tsoa’s such as the dyadic TH2 or the triadic TH2O – as ersatz structural universals, defining a special sort of ersatz instantiation. A single thing x ersatz-instantiates an n-adic relation R iff, for some y1, . . ., yn, (1) x = y1 + . . . yn, and (2) y1, . . ., yn instantiate R (where this is the ordinary sense in which several things instantiate a relation. If there is an operation of projection, then x ersatz-instantiates R iff x instantiates (in the ordinary way) the projection of R. But if we didn’t believe in projections, we could still speak of ersatz instantiation. The trouble with this, I now think, is very simple. In the extreme case of infinite complexity, all monadic universals are structural; so if we do without structural universals, whether or not we try to drag in ersatz instantiation of ersatz structural universals as a substitute, we’ve got no monadic universals at all.) Extension cannot just be the mereological addition of something; it must indeed be some sort of unmereological operation. Tsoa’s produced by extension must be distinct not just in your Humean sense of modal independence but in the ordinary mereological sense of having no part in common. For mereological summations can be rearranged: (a + b) + (c + d) = (a + d) + (c + b). Take the H2O example, abbreviated by leaving out the nonidentity tsoa’s.

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Now suppose extension did work by mereological addition. It’s enough to take two of the five extensions. Suppose

In the first place, I have no notion what sort of things the added bits X and Z might be. In the second place, by rearranging our sum we get TH1ʹ + TH2ʹ + TO + TB1 + TB2 = (H + X) + TH2ʹ + (O + Z) + TB1 + TB2 = (H + Z) + TH2ʹ + (O + X) + TB1 + TB2 = TH* + TH2ʹ + TO* + TB1 + TB2 where TH* = H + Z and TO* = O + X. Now if H + X = λxyz Hx, we would expect O + X likewise to be λxyz Ox. And if O + Z = λxyz Oz, we would expect H + Z to be λyxz Hz. In short, we’ve lost the distinction between two structural relations – and then, after projection, two structural universals – that ought to be different: the one for the structure

in which two hydrogens are bonded to one oxygen, and the structure

in which the oxygen has traded places with one of the hydrogens. The remedy: deny that a universal is part of the tsoa that comes from it by extension. Even if you agree that extension from a universal to a tsoa is unmereological, you might still hope that it’s nothing new – just a commitment you took on already when (motivated by the principle that truths need truthmakers) you accepted the unmereological construction of particular states of affairs from universals and (thin) particulars. (Or maybe you’d rather put it the other way round: the unmereological abstraction of universals and thin particulars from particular states of affairs.) I don’t agree. The terminology is misleading. The commitment to particular states of affairs and the commitment to tsoa’s, understood as relations in a liberalised sense, are two different, independent commitments. You could still accept particular states of affairs

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for the sake of truthmaking even if you abandoned relations in the liberalised sense, structural universals, and the possibility of infinite complexity. On the other hand I, unmoved as always by the alleged need for truthmakers, might consider accepting the extension of genuine universals to tsoa’s as part of a partly mereological construction of structural universals, without ever granting that some new entity is engendered in virtue of the fact that a universal (or a tsoa) is instantiated. The extension of universals to tsoa’s, understood as this letter proposes, does not involve particulars; whereas the generation of particular states of affairs must involve ­particulars. Well – what do I think of the idea that the construction of structural universals out of simpler universals is mainly mereological? Mereology in the middle, plus extension at the beginning and projection at the end? Like set theory, it involves unmereological operations that I find mysterious. Unlike set theory, it isn’t the only game in town – it has to score higher than sparse trope theory, or natural-class (or resemblance) nominalism. But, given a commitment to universals, including structural universals, it seems a good idea to give mereology as big a part as possible in constructing them. One reservation: I’d like to know more about properties and relations in the liberalised sense. Supervenient or not, these are some of the things you say there are. They aren’t composed mereologically out of the basic genuine universals and thin particulars. Nor are they mere fictions: else structural universals constructed from them are fictions too, and in the case of infinite complexity all monadic universals are fictions – which won’t do. In particular, I need to know more before I can see why conjunction of properties and relations in the liberalised sense is mereological summation. I see why conjunction is summation for genuine universals. I see it for particular states of affairs. But also I see why conjunction isn’t summation (rather, disjunction is summation) for properties or relations taken as classes – my own candidate for the liberalised sense. I’m not opposed to the idea that properties and relations in some liberalised sense will conjoin by summation as if they were genuine universals, but I haven’t heard enough. Yours, David cc: Bigelow, Forrest, Hazen, Johnston PS            29 July I left out one thing that figured in our conversation, the reason being that it’s a variation that I now think has no advantage. Still, it might be best to write it down. The idea is to replace the projection step at the end by what I’ll call E(xistential)projection. (Actually E-projection would ordinarily be called just ‘projection’ – Peter’s use of the term is nonstandard.) The E-projection of the n-adic relation R is the property λx ∃y2 . . . ∃yn R(xy2 . . . yn). So if R is the triadic relation

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283.  To Barry Taylor, 5 August 1986

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TH2+: λxyz (x = y + z & Hy & (z ≠ y & Hz) & yBz) or in other words λxyz (x = y + z & TH2(yz)) then the E-projection of TH2+ is H2, the structural property of being a molecule consisting of two hydrogens bonded together. We already know how to construct TH2, the dyadic structural relation, by extension and conjunction; now proceed as follows to complete the construction, triple arrow being E-projection. I need a com­pos­ ition­al tsoa, the ‘is the sum of’ relation (in this case triadic). This would be like the nonidentity tsoa’s, a relation in the liberalised sense but not a genuine universal.

(Or we could extend everything to triadic right at the start, and reach TH2+ by one big conjunction step.) --It was loose talk to call extension an operation – that suggests a function, whereas I made clear that extension is one-many. You could say we have an infinite family of extension operations, differing in how many idle places they put in, and where they put them. If you like, you can replace the infinite family by a finite family – I think three – applied with repetition and alternation. Good fun, but irrelevant to ontology. See ‘Variables Explained Away’ in Quine’s Selected Logic Papers2 – Quine’s aims are unlike yours, but the technology transfers.

283.  To Barry Taylor, 5 August 1986 [Melbourne, Australia] Dear Barry, I’ll write down what I said to you yesterday about the jejune phenomenalist (in your ‘The Truth in Realism’,1 bottom of page 5), mostly in order to test your ­prediction   (Quine 1966).

2

  (Taylor 1987).

1

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that Devitt will not agree with me. I say it is possible for the primeval forest to exist when no subjective standpoint accessible to us is occupied. (Indeed, when no subjective standpoint whatsoever is, or ever was or will be, occupied.) And I take this view to be part of my realism about the primeval forest. But ‘the most jejune antirealist phenomenalism has ready a tale explaining how the primeval forests existed in the absence of human observers’. The jejune phenomenalist tells such a tale, sure enough. He says ‘the primeval forest existed’. But shall we take him at his word? Given his explanation of what he meant, we need not agree that he asserts that the primeval forest existed. Two main cases, of which the second subdivides. 1) What it turns out that he means by ‘the primeval forest existed’ isn’t existential at all. Maybe it’s a counterfactual to the effect that certain sense data would have existed under certain circumstances. Then he definitely doesn’t mean by ‘the p.f. existed’ what we mean by it, so it’s wrong for us to say that he’s an antirealist about the p.f. who nevertheless asserts that the p.f. existed. He’s an antirealist about the p.f., sure enough; and he does say ‘the p.f. existed’; but he doesn’t thereby assert that the p.f. existed. No more so, in fact, than if he explained that by ‘the p.f. existed’ he meant that the p.f. had not existed! (Compare Argle’s first position in ‘Holes’, AJP 1970, especially the long speech that starts ‘when I say that there are holes in something . . .’.) 2) The other case is that when the jejune phenomenalist explains his meaning, it turns out that by ‘the p.f. existed’ he does assert the existence of something; but of something – a cluster of unsensed sensibilia, perhaps – that fits our conception of the p.f. so badly that it’s doubtful whether it deserves the name ‘p.f.’ Two subcases. 2A) It does not deserve the name, though he thinks it does. Then again he’s an antirealist about the p.f.; and though he says ‘the p.f. existed’ he doesn’t thereby assert that the p.f. existed. However he’s a realist about something else, and he asserts its existence, and he wrongly thinks that this something else deserves the name ‘the p.f.’. 2B) His candidate does deserve the name. This time he’s a realist about the p.f. and he does assert that the p.f. existed. It’s just that he holds peculiar views about the nature of the p.f. He’s like a realist who believes that the p.f. existed but was made of metal. (Compare Argle’s second position, when he asserts the existence of material hole-linings, and claims – questionably – that these deserve the name of ‘holes’. Whether this is like 2A or 2B depends on whether he’s wrong or right in the questionable claim.) So in each case, the jejune phenomenalist comes out as a realist about the p.f. if and only if, when he seemingly asserts that the p.f. existed, he really does assert that the p.f. existed.

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284.  To Peter van Inwagen, 4 November 1986

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The remaining cases add nothing new. They are just the cases where our ig­nor­ ance, semantic indeterminacy, or both* make it impossible to settle which of the main cases we have: 1), 2A), 2B) or straightforward realism without a phenomenalist tale. These blurred mixtures of the previous cases don’t introduce any way to make him an antirealist about the p.f. who nevertheless asserts that the p.f. exists. Yours, David cc: Devitt, Hazen

284.  To Peter van Inwagen, 4 November 1986 [Princeton, NJ] Dear Peter, This is yours, as witness the inside front cover. Sorry about the delay returning it to you – it got into a heap of to-be-attended-to, whereas it should have gone off as soon as we found it. You’ll have to come back to see the trains, won’t you? I think the idea I missed the turn over won’t work. We have a primitive ordering of set-theoretic rank, and unit sets share the location and some other properties of their members; so {Possum} is the Possum-like thing that immediately outranks Possum, {{Possum}} is the Possum-like thing that immediately outranks something that immediately outranks Possum, . . . OK; but then {Possum-cum-Magpie} is a (Possum-cum-Magpie)-like thing that immediately outranks Possum-cum-Magpie (‘cum’ being the mereological summation sign); and {Possum, Magpie}, that is {Possum-cum-Magpie}, also is a (Possum-cum-Magpie)-like thing that immediately outranks Possum-cum-Magpie; yet these two should have been different. Reply: {Possum-cum-Magpie} is a unit set, {Possum, Magpie} isn’t; unit sets are mereologically atomic; there’s the distinction. OK; but now take {{Possum-cumMagpie}} versus {{Possum, Magpie}}. Both are unit sets, both are two ranks above Possum-cum-Magpie, and both are (Possum-cum-Magpie)-like. Yours,

  Or compartmentalised thinking on the phenomenalist’s part.

*

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285.  To Keith Campbell, 11 December 1986 [Princeton, NJ] Dear Keith, Thank you very much for the interesting paper on tropes and fields.1 My reactions are as follows. To the problems raised in your first part, my response would be the Russellian one that you anticipate. I’d retreat to point-sized tropes located at points of spacetime – a tropist version of what I call an ‘arrangement of qualities’ in my introduction to Papers II (DMA has a copy of the 1984 manuscript) – and mereological sums of these. I would think it a questionable matter whether this atomism was a contingent thesis about this world, or instead a necessary truth about how any world must be built. But if, for instance, tropism can’t accommodate a continuous gradient of some magnitude without dissolving that gradient into point-sized tropes, I could just conclude that a non-atomistic possible world would have to lack such gradients. Of the problems you raise against atomism, the main one is the NerlichMortensen problem about enantiomorphs.2 I don’t see the problem. It’s some while since I read Graham’s book3 (and I haven’t read all their subsequent joint pieces) but the lesson I came away with was not a problem for atomism. Rather it was this. The relation of like- or opposite-handedness cannot be an internal relation of the gloves, or even an external relation that supervenes on the intrinsic qualities and the distance relations of the parts of the gloves alone; rather, it must be a relation that involves distances not only between the parts of the gloves but also between the parts of the gloves and other things everywhere else, and among those other things. Then there must be relata for distances everywhere – either parts of spacetime itself, or else parts of some omnipresent thing. Bad news for a kind of relationism; but not bad news for the theory that absolute spacetime divides into points with distance relations between them. Some of the rest of the rejection of atomism seemed to turn on some richer notion than I hold of what it means to be a part – but here I’m not very sure what was going on. As to your final view, I have no objection whatever to the idea that fields are all-pervasive abstract particulars, abstract in the sense that they are not the exclusive occupants of their places; or to the speculation that the world consists entirely of a

 See Abstract Particulars (Campbell 1990, ch. 6).   ‘Space-Time and Handedness’ (Mortensen and Nerlich 1983). 3   The Shape of Space (Nerlich 1976). 1 2

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286.  To William G. Lycan, 11 February 1987

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small number of such abstract particulars. But I do have trouble understanding how fields can vary over spacetime otherwise than by having parts that differ one from another; and how they can vary and still be tropes. I’d rather have it that point-sized parts of fields are tropes, and fields are mereological sums of these point-sized parts. Yours,

286.  To William G. Lycan, 11 February 1987 [Princeton, NJ] Dear Bill, I’ve looked at ‘What is Eliminative Materialism?’,1 a paper I’d probably read when new but didn’t remember. I thought first that Rorty’s position is better off than you and Pappas made it out to be; and second that it isn’t an instance of what I had in mind as ‘eliminative reduction’. First, as to Rorty. I think there’s a coherent position that fits the quotations you gave. (It also fits my memories of reading Rorty, but I haven’t rechecked.) It does rely on semantic indeterminacy, as you suggested in your letter; but not the extreme Quinean sort, only something so moderate that it ought to be uncontroversial. The position goes as follows. (1) ‘Sensation’ is defined in terms of a certain theoretical role written into folk psychology. (2) There is nothing that perfectly fits this role; however (3) brain processes fit the role imperfectly, and (4) the imperfection is fairly bad. (5) As a result, we have a case of semantic indeterminacy: since we have never decided the question, there is no fact of the matter about whether brain processes do or don’t fit the role well enough to deserve the name of ‘sensations’. (6) Thus we have two versions of English: call them ‘strict speaking’ and ‘loose speaking’. Strictly speaking, ‘sensation’ is denotationless; there are no sensations; brain processes are the nearest thing to sensation there are, but not near enough to be sensations. Strictly speaking, strong eliminativism is true. But loosely speaking, ‘sensation’ denotes brain processes even though brain processes fit the definitive

  (Lycan and Pappas 1972).

1

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role rather badly; so there are sensations, and sensations are brain processes. Loosely speaking, the identity theory is true. (6a) Or rather, there are countless versions of English, some stricter and some looser, some strict in some ways and others strict in others. But it suffices to distinguish only as far as we must for the issue at hand. (7) Since strict and loose speaking are equally versions of English, it settles nothing at all to insist on speaking English throughout your paper or your letter. (8) Have we a false belief in sensations? – Yes, so long as we believe that, strictly speaking, there are sensations; in other words, we believe in things that fit the ­sensation-role well enough to definitely deserve the name. (9) Have we also a true belief in sensations? – Yes, since we also believe that, loosely speaking, there are sensations; in other words, we believe in things that fit the sensation-role well enough to not definitely not deserve the name. (10) We can speak strictly about our loose speaking, if we like. If we do, we will say that the things we have hitherto (loosely speaking) called sensations are not really (strictly speaking) sensations. (11) Reform is desirable, or would be except for its social unfeasibility, since the semantic decision we left unmade turns out to make more difference than we might have hoped. It turns out that we are constantly saying things that are indeterminate between an interpretation that makes them true and another that makes them false, and that is a confusing position to be in. (12) Pending reform, we need not commit ourselves once and for all to strict speaking or to loose speaking. We can mix the two and count on making ourselves understood on the principle that the correct interpretation is the one that makes the message make sense. Then the parenthetical bits in (10) are optional; it’s OK just to say that what we have hitherto called sensations are not really sensations. What of this position? Not Rorty? Not coherent? It seems pretty good to me, except that I don’t buy premise (4). I think brain processes do fit the folk-psychological role of sensations, maybe not perfectly, but well enough to definitely deserve the name. But I think there are other cases where a candidate fits a definitive role less well, and a hybrid strict-elimination-plus-loose-identification theory is called for. For instance, I think that there is nothing such that, necessarily, we are disposed to value it (disposed under certain special conditions – never mind details) but I think there are plenty of things such that, de facto and fairly uniformly, we are disposed to value them. Therefore there is nothing that perfectly fits what I take to be the definitive role associated with the term ‘value’, but there are plenty of things that fit the role

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fairly well. I think perhaps it’s somewhat indeterminate whether this ‘fairly well’ is well enough to deserve the name. If indeed this is indeterminate, then my position is realism about values loosely speaking but eliminativism – and ‘error theory’ – about values strictly speaking. Someone – not me – might take Hartry’s example of mass as another case, but with an added wrinkle. (A common added wrinkle, I should think.) It turns out that nothing fits the role definitive of Newton’s word ‘mass’ perfectly, but two rival candidates with equal claims fit it imperfectly. If they both fit well enough, as I think and as Hartry thinks, we get two-way indeterminacy in the denotation of ‘mass’ – what Hartry calls ‘partial denotation’ – whereas if they fit the role not definitely well enough and definitely not well enough, then we get a three-way indeterminacy, the third alternative being the one on which there turns out to be no such thing as mass. A final example. Suppose someone splits the difference between me and Al. Unlike me, he thinks no set could perfectly fill the definitive role associated with ‘proposition’. (I simplify by supposing for now that there’s only one established version of the role; as you know, I don’t believe this.) Unlike Al, he thinks a set could fill the role fairly well; but he might think it indeterminate whether this ‘fairly well’ was well enough. Then he couldn’t give a straight answer to the question whether he believed in the existence of propositions. He would have to distinguish loose and strict speaking and answer ‘yes and no’. --OK; but what I had in mind when I defended the possibility of eliminative reduction was something quite different. I said you could have a position that says It’s true to say, with the vulgar, that ‘there are’ people; but, rightly understood, this doesn’t assert the existence of some special kind of thing; it just means that sometimes a lot of atoms do a certain sort of dance. I did not have in mind loose and vulgar versus strict and philosophical standards for what it would take for something to deserve the name of ‘person’, so that it might be indeterminate whether swarms of atoms do or don’t deserve that name. Rather, I had in mind a position which denies the existence of all composite individuals, so that there don’t even exist any remotely decent candidates to deserve the name ‘person’. There exist atoms, a lot of them; but there do not exist any swarms of atoms, hence the issue whether a swarm of atoms could be a person doesn’t arise. (This position would be one that rejects composition altogether – exactly opposite to my own view. For a sympathetic development, but not adoption, of it, see Adam Morton, ‘Complex Individuals . . .’ in Noûs 1975. Also van Inwagen used to – so far as I know, still does – reject composition except in cases of living organisms; but didn’t want to deny that

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in some ordinary sense there are bicycles and corpses; and so would be an eliminative reductionist about these things though not about people.) An eliminative reductionist believes that we have idioms that look like quan­ti­ fiers but are not genuine quantifiers; or maybe they are genuine quantifiers, but not the quantifiers they seem to be. Here are some examples of eliminative reductionist views – not necessarily held by, still less directly quoted from, the authors I associate them with.* Let’s stipulate that capitalised quantifiers really will be decent, honest, straightforward, single, singular, objectual quantifiers. Lower-case ones are up for grabs. Argle I did say that there are holes in the cheese; but that is not to imply that THERE ARE holes. When I say that there are holes in something, I mean nothing more nor less than that it is perforated. The synonymous shape-predicates ‘. . . is perforated’ and ‘there are holes in . . .’ – just like any other shape-predicate, say ‘. . . is a dodecahedron’ – may truly be predicated of pieces of cheese, without any implication that perforation is due to the presence of occult, im­ma­ter­ ial entities. I am sorry my innocent predicate confuses you by sounding like an idiom of existential quantification, so that you think that inferences involving it are valid when they are not. But I have my reasons. You, given a perforated piece of cheese and believing as you do that it is perforated because it contains immaterial entities called holes, employ an idiom of existential quantification to say falsely ‘There are holes in it’. Agreeable fellow that I am, I wish to have a sentence that sounds like yours and that is true exactly when you falsely suppose your existential quantification over immaterial things to be true. That way we could talk about the cheese without philosophizing, if only you’d let me. You and I would understand our sentences differently, but the difference wouldn’t interfere with our conversation until you start drawing conclusions which follow from your false sentence but not from my homonymous true sentence. Routley When I say that some things – in fact, most things – do not exist, I do not mean that THERE ARE such things. My ‘some’ is meant to be an ontologically neutral, noncommittal, particular quantifier – not an EXISTential quantifier. Mill When I say that there are physical objects, I do not mean that THERE ARE; I mean rather that sense-experience would take certain courses and would not take certain others. When I say that there is a penny in my pocket, for instance, *  Argle gave up the view here stated because he couldn’t extend it to numerical quantification. ‘Mill’, ‘Ryle’, ‘Marcus’, and ‘van Fraassen’ are unsubtle pastiches of their namesakes. ‘Morton’ holds a view which Morton presented but didn’t endorse. ‘Black-Boolos’ uses ideas from Boolos to develop a view which Black holds and Boolos doesn’t. ‘Parsons’ holds a view which Parsons used to establish the consistency of his real view, and then rejected.

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286.  To William G. Lycan, 11 February 1987

571

I mean not that THERE IS a penny, but rather that looking-in-the-pocketish sensations would be followed by finding-a-pennyish sensations. Ryle When I say that there are sensations, I do not mean that THERE ARE; I mean rather that behaviour would take certain courses and would not take certain others. When I say that I seem to see a Doberman on the front doorstep, for instance, I mean not that THERE IS a dobermanish sensation, but rather that approaching-the-house behaviour would be followed by goingaround-to-the-back-behaviour. Morton When I say that there are composite individuals, I do not mean that THERE ARE composite individuals; I mean that many simples satisfy a many(and variably-many-) place predicate. What looks like one quantifier over composites is really an infinitely long block of quantifiers over simples. For instance when I say ‘Some man sits’ I mean For some x1, for some x2, . . . (ad infinitum), x1 is a simple and x2 is a simple and . . . and either [are-a-man (x1, x2) and sit(x1, x2)] or [are-a-man(x1, x2, x3) and sit(x1, x2, x3)] or [are-a-man(x1, x2, x3, x4) and sit (x1, x2, x3, x4)] or . . . (ad infinitum). Here the predicates ‘are-a-man’ and ‘sits’ are just polyadic predicates of ­simples. They must not be analyzed in terms of the EXISTENCE of a man or a sitter composed of those simples; because THERE ARE no composite individuals. Black-Boolos When I say that there are classes of individuals, I do not mean that THERE ARE classes; THERE ARE none of those, only individuals. When I say in the surface-grammar singular that there is a class such that it does so-and-so, what I mean is covertly plural: there are several individuals such that they do soand-so. And when I say that something is a member of a class, I really mean that it is one or another of several individuals. For instance, if I say that someone (other than me) is my ancestor iff he belongs to every class that has me as a member and has every parent of a member as a member, I mean: . . . iff, whenever there are some individuals such that I am one of them and every parent of one of them is one of them, then he is one of them. Here I quantify plurally over individuals. I don’t quantify over classes, which don’t EXIST. Plural quantification is an overlooked logical primitive. It can’t be analyzed as singular quantification over sets or classes; because even if THERE WERE sets or classes, THERE still wouldn’t BE a set or class of all sets or classes, yet we could still quantify plurally over all sets or classes. Parsons THERE ARE NO incomplete or inconsistent Meinongian Objects, or even any merely nonEXISTENT ones. However, the nonexistent Objects cast

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Philosophical Letters of David K. Lewis EXISTENT shadows: property-bundles. For instance, the nonEXISTENT round square has as its shadow the bundle of roundness and squareness. When I say that there exists a nonexistent, inconsistent Object that is a round square, I mean that THERE EXISTS an uninstantiated, uninstantiable property-bundle containing roundness and squareness. I don’t say that the Meinongian Object is its property-bundle; for one thing, because the bundle EXISTS and the Object doesn’t, for another thing because the bundle is two-membered and neither round nor square, whereas the round square is round and square and not twomembered. But when I seem to quantify over Meinongian Objects, really I’m quantifying over property-bundles. Marcus THERE ARE NO mythical beasts, neither in this world nor in any other. However, the nonEXISTENT mythical beasts have EXISTENT surrogates: the names that figure in mythology. When I say that there exists a mythical winged horse, I mean that SOME sentence obtained by substituting SOME name from mythology into the formula ‘x is a winged horse’ is true. (And such a sentence is true, roughly and subject to certain exceptions, iff the myth from which the name comes implies it.) I don’t say that the mythical beast is the name, of course: ‘Pegasus’ EXISTS and Pegasus doesn’t, Pegasus has wings and ‘Pegasus’ doesn’t. But when I seem to quantify over mythical beasts, really I’m quantifying over beast-names out of mythology. Sturch THERE IS NO SUCH THING as Australia; likewise THERE ARE NO inhabitants of Australia, parts of Australia, etc. It is a mistake to suppose that the name ‘Australia’ has the same logical grammar as ‘France’, ‘Switzerland’, ‘Siberia’, ‘Rutlandshire’, or ‘North Dakota’. The words ‘in Australia’ are used simply to signify that the contradictor of what is stated to be the case ‘in Australia’ is in fact the case. Looking at the effect on truth value of prefixing ‘in Australia’ to such sentences as Christmas comes in the summer Cardiff is a suburb of Newcastle swans are black the Labor party befriends the capitalists and ever so many more, it should be perfectly obvious that the phrase is merely an idiom of negation. (Compare the logical grammar of ‘in a pig’s eye’.) So when I say ‘In Australia there is a mammal that lays eggs’ I do not mean that there EXISTS a mammal that is located in a certain queer place and lays eggs; I mean in fact that there does not EXIST (anywhere) a mammal that lays eggs.

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286.  To William G. Lycan, 11 February 1987

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Prior There do not EXIST any past or future objects; EVERYTHING is present. However, it has been the case that there EXIST objects; and it will be the case that there EXIST objects. (What is more, it has been the case that there EXISTed objects such that it was not then going to be the case that they EXISTed thereafter; likewise it will be the case that there EXIST objects such that it will not then be the case that they have EXISTed before; the past and future objects, so to speak, are not just some among the present objects.) When I say that there exist past or future objects, I do not mean that such objects EXIST, but only that they have EXISTed or will EXIST. Van Fraassen There do not EXIST any minute particles, or at any rate we have no good reason to believe that any EXIST. When I say – speaking as a working scientist – that there are minute particles, I do not mean that there EXIST mi­nute particles; I only mean that it may be accepted that there EXIST minute par­ticles – that is something said by the most empirically adequate available theory. (If I said it speaking as a philosopher, I would mean something else – something I take to be false.) In each case, the idea is as stated by Argle. We have the realist about X’s: someone who believes in X’s, quantifies over them, and thereby says things that it would seem preposterous to deny outright. The eliminativist doesn’t believe in X’s and therefore won’t quantify over them, and yet doesn’t want to go in for preposterous denials. So he needs some way to achieve that verbal agreement with ‘There are X’s’ itself, even though he doesn’t believe THERE ARE any X’s! He needs to mean something by his seeming quantification that will be true by his lights just when the realist falsely supposes his homonymous sentence to be true; but which, unlike the realist’s genuine quantification, will not imply the EXISTENCE of X’s. He needs a story about what his seeming quantifications really mean. The stories are varied, and some are more satisfactory than others. Routley’s is no story at all – just some catchwords. The rest are better, though some have more offhand plausibility than others and some are more technically workable than others. Prior’s and Sturch’s are the least plausible of the lot, by my lights; Sturch’s and Black-Boolos’s are the least technically work­ able; Sturch’s because ‘in Australia’ doesn’t reverse truth value quite all the time, Black-Boolos’s because it doesn’t handle classes of classes. The varied stories about how the ostensible quantification is simulated fall into several classes. For Argle, there’s no quantification there at all; for the rest there is. For Routley, Morton and Black-Boolos, there’s quantification of a peculiar sort – least peculiar for Morton, since what seemed to be a single ordinary quantifier comes out as nothing worse than an infinite string of ordinary quantifiers. For Parsons and Marcus, there’s ordinary quantification, but over surrogates for the things ostensibly

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quantified over, with matching adjustment of the formula to which the quantifier is prefixed. For Mill and Ryle, there’s ordinary quantification over courses of experience or behaviour, but these aren’t really surrogates for the things eliminated. For Sturch, Prior, and van Fraassen, there’s perfectly ordinary quantification, but it falls within the scope of some sort of overt or covert sentential operator which blocks exportation. What should we think of these theories? I don’t think they should be opposed wholesale, on the basis of any general principle. Certainly it’s somewhat counterintuitive to claim that any seeming quantification is not what it seems to be. It imputes a kind of deviousness to the language, or at least to some users thereof. That’s a genu­ ine cost that attaches to any theory that so claims. But, as always, we balance costs, and what’s acceptable depends on how bad the alternatives look. Nevertheless, for my own part I don’t accept any of these eliminative reductions (except maybe for surrogate quantification over inconsistent Meinongian Objects). That’s because I (almost?) always find some alternative at least slightly preferable: usually the realist alternative, often with some reductive identification. I’m well placed to go in for reductive identification. In the first place, as Al can attest, I’m without certain paralysing scruples; and in the second place, my ontology has abundant resources for identification, what with all the parts of all the worlds, and all the sets and mereological sums of things already in my ontology. You will perhaps say to all these eliminative reductionists in my parade: speak English! I think that’s question-begging. The naïve ones think they are speaking English – they’ve discovered that under careful analysis, what seemed to be quantifications are revealed to be something else. The sophisticated ones think there’s a certain amount of semantic indeterminacy about English – not the radical indeterminacy that can’t tell a cat from a cherry, but enough indeterminacy so that there’s no fact of the matter about whether an ostensible quantification over X’s really is what it seems to be (and is therefore false if there are no X’s) or whether it rather is what they claim to mean by it. They claim to speak, if not the only version of English, at least something that is as much a version of English as the one where the quantifications are taken at face value. They remind you that nobody in his right mind thinks that every seeming quantification has to be taken as a genuine quantification, on pain of not speaking English – not so, for instance, when we superficially seem to quantify over kicked buckets or bats in belfries. It may seem that with all these imposters threatening to show up disguised as quantification, we may not retain our grasp on the real thing. What is it to be quantification, if not to look like quantification? Well, I can very easily tell you – but if you’d lost your grasp on quantification you wouldn’t understand, because the semantic clauses for quantification themselves use quantification. If you’d lost your grasp on

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287.  To Keith Campbell, 31 March 1987

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quantification I couldn’t cure you, any more than I could force Geach to understand what identity is. All I can say is: it seems to me that I can very easily distinguish genu­ ine quantification from all the varieties of simulated quantification presented above (not Routley’s, for there nothing has really been presented). If there’s some argument that purports to prove I can’t distinguish, too bad for that argument. Here ends the sermon, Yours, David Lewis cc: Plantinga, van Inwagen, some people at Princeton

287.  To Keith Campbell, 31 March 1987 [Princeton, NJ] Dear Keith, As you’ll expect, I don’t believe that ‘genuine parts are in some real meta­phys­ ic­al or logical sense prior to the wholes they compose’. It’s not that I think the wholes are instead prior to the parts. I don’t see what sort of priority there is either way. I just can’t think of any significant sense in which the train is prior to its coaches, or the coaches prior to the train. Likewise with space-time and its points, or a field and its point-sized parts. I’m willing to say ‘prior’ and just mean ‘part’ if anyone wants me to, but I don’t attach any importance to this. I like to think of composition as a kind of identity. As DMA puts it, the relation of part to whole is partial identity.1 Or, even better, as my colleague Don Baxter puts it, the relation of the many parts to the one whole they compose is many-one identity.2 They are it; it is them – the ‘is’ of identity, grammatically plural or singular depending which way round you write the identity. It’s because we’re dealing with a kind of identity that it’s redundant to count the whole and also the parts; it’s because we’re dealing with a kind of identity that it would be absurd to ask for an explanation of why the whole automatically turns up if and only if all the parts do. (Also whenever and only whenever, if the whole and its parts happen to be universals, or otherwise capable of being wholly present at more than one place, time, or world.) It’s because we’re dealing with a kind of identity that, once we’ve settled the natures of all the parts, there’s no further question to be asked about the nature of the whole they compose; and vice versa.   Universals and Scientific Realism II: A Theory of Universals (Armstrong 1978b, 36–9).   ‘Many-One Identity’ (Baxter 1988).

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Now you wouldn’t expect something to be in any sense prior to itself, would you? – and likewise in the case of many-one identity, there’s no difference between the many parts and the one whole, therefore no room for priority, which always means priority of one thing to another. Is place within the whole essential to a point? – Maybe so, maybe not. I understand this in terms of counterparts. I suppose that something enough like me to be my counterpart ought to be similar to me not only in its intrinsic but in its relational properties – e.g. its place in a line of ancestral descent, or maybe its place in philosophy. (Or both, or neither – different counterpart relations suit different contexts.) Likewise even more so for points, I suppose, seeing that they’re rather short on intrinsic differences. But I don’t see this as having much to do with priority. And if it did have to do with priority still it needn’t be priority of parts over wholes; because even if things have some of their relational properties essentially, these could involve relations to other things of a kind with themselves rather than relations to wholes they’re parts of. If we understood essence in terms of overlapping worlds, then I’d say that if X is composed of parts x, y, z, . . . then it’s essential to X to be composed of exactly those parts; and likewise symmetrically it’s essential to x, y, z, . . . that they compose X. Because after all X just is x, y, z, . . . and they just are it. You find this implausible? Well, so do I, and that’s the fundamental reason why I don’t understand essence in terms of overlapping worlds. If we understand essence in terms of counterparts, I don’t think there’s any general reason to say that a counterpart of X has to be composed of counterparts of x, y, z, . . .; or any general reason to say that counterparts of x, y, z, . . . have to compose a counterpart of X. But though that may not be so in general, it may happen for some kinds of things and some reasonable counterpart relations; and especially, as noted above, when x, y, z, . . . are interchangeable parts, short of distinctive intrinsic character. Are holes in space-time a possibility? I suppose so, though I doubt this is connected with anything else I think. I suppose I’m convinced that boundaries of spacetime are a possibility; and if boundaries, it seems arbitrary to prohibit boundaries of complicated shape; and then it seems arbitrary to prohibit holes. But again, I don’t see what this has to do with any sort of priority. I have no plans yet to come over this year, but you have excellent inductive evidence that I’ll turn up. Maybe a little later than usual. I have leave for 1987–88, so don’t absolutely have to be back in mid-September. Yours, cc: DMA, Baxter

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288.  To D.M. Armstrong, 6 May 1987

577

288.  To D.M. Armstrong, 6 May 1987 [Princeton, NJ] Dear David, I owe you answers to no less than three letters, of which the first written (11 Feb) was the last to arrive, by quite a lot. Sorry for the delay! Enclosed is a copy of a letter to Keith,1 which tries to spell out, as a set of analogies, our view that mereological relations are somehow a matter of identity. Baxter, it turns out, does not like my way of thinking of it – identity in general a one-many relation, so that the ‘are’ of composition is the plural of the ‘is’ of identity. He really wants to hold out for something much stranger: ordinary one-one identity between the thing and each of its parts! Yes, that does mean that the several parts are in some way identical to one another; and so we find him speaking of the ‘discernibility of identicals’, akin to the discernibility of Russell-qua-philosopher and Russell-quapolitician. Remember that fellow at the 1984 conference who claimed there was only the one Fosters can? – maybe it’s something like that. In /the/ last sentence of the marked paragraph of the Keith letter, of course I should have said ‘. . . once we’ve settled the natures and relations of all the parts . . .’. Correction due to Bob Stalnaker, in conversation. Complicates the point but I think doesn’t spoil it. --[. . .] --Your first March letter. I can’t think of much to say, but holding up my reply still longer probably isn’t going to help, so here goes. The main thing to say is that I agree with you that states of affairs give me the same problem that I see with non-Humean laws of nature: necessary connection between mereologically distinct existences. In the case of soa’s, the question is: if Fa and a are mereologically distinct, how can it be necessary that the latter must exist if the former does? In the case of laws, the question is: if Fa & N(F, G) and Ga are mereologically distinct, how can it be necessary that the latter must exist if the former does? (Remarks. (1) We’ve agreed to ignore the complication of oakenness. (2) The common G doesn’t remove the mereological distinctness if it isn’t a mereological part of the soa’s N(F, G) and Ga; and even if it were, I wouldn’t think it gave enough non-distinctness to explain a necessary connection.) The same problem is my main worry about sets: if a and its unit set are mereologically distinct, how can it be necessary that the latter must exist if the former does?   Letter 287. To Keith Campbell, 31 March 1987.

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Almost the same problem is my main worry about structural universals: if an-F-bearing-R-to-a-G and F are mereologically distinct, how can it be necessary that the latter must be instantiated wherever the former is? (That is, the latter must be instantiated by part of any instance of the former.) In each case, if one doesn’t reject the suspect entities or the suspect connection, there are two alternative moves. (1) Here there just is a mysterious necessary connection between distinct existences, or (2) there is a not-so-mysterious necessary connection between existences that are not distinct, but unmereologically not distinct. I had thought that for structural universals and soa’s you preferred (2), but for laws you preferred (1). But yes, I see that (2) is available also for the case of laws, which is what you say in the letter. Likewise (1) is available for the case of soa’s and structural universals; (1) for structural universals is what I called the Magical Conception. Myself, I can’t see any real difference between (1) and (2), because I have so little idea what it might mean for things to be ‘unmereologically not distinct’. The best I can do to understand it is to think of it as just a metaphor for necessary connection itself – a metaphor inspired by the case of necessary connection between mereologically not distinct existences. So understood, it doesn’t help. So if I had to accept the mysteries of necessary connection, I think I’d prefer to stop with (1), thinking of any help from (2) as illusory. And of course there is one case out of the four where I am committed to accept the mystery: I believe there are unit sets, they are wholly distinct from their members, and they exist automatically if and only if their members do. Here you have a good tu quoque against me. If I were as happy with the mystery of unit sets as you are with the mystery of soa’s, I’d try to assimilate the other cases to that case – just as you have been interested in assimilating the cases of structural universals, sets, and now laws to the case of soa’s. But I’m not happy with the case of the unit sets ­­– it’s just that I see no way around it. I have no problem agreeing that we experience forces, and no great problem agreeing that when we do, we thereby experience bringing about. But whether this may count as experiencing an N(F, G) depends on the prior question whether the DTA theory of laws should be accepted. I’d like to meet with your wonderful 4th-year class on possibility, if timing permits.2 I’ve met Peter Godfrey-Smith; haven’t met Fiona Cowie, but I’ve heard about her from several people. I’m hoping they’ll apply to Princeton. We really need some geographical balance – our next entering graduate class will be three Melbourne and only one Sydney (plus a German and four yanks). --2   The class included Fiona Cowie, Stephen Glaister, Peter Godfrey-Smith, Richard Hanley, and Rodney Rutherford.

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288.  To D.M. Armstrong, 6 May 1987

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Your second March letter. I’m sorry that Rosen’s paper turned up un­announced.3 I’d intended that it and my Possibility comments should arrive at almost the same time, but was much delayed in finishing the comments. Your query: do I not need a truth-maker principle to get me from true statements of possibility to my ‘really there’ possible worlds? How do I rebut the suggestion that statements of possibility are true but require no ontological ground? In the first place, I insist that some statements ‘are true but require no onto­ logic­al ground’. Namely, negative existentials (equivalently, universal generalisations). The truth of atheism requires no ontological ground; it’s true just because theism does require an ontological ground, and the required ground is lacking. Some truths need truth-makers, some don’t. Theism, if true, would be one that does. Atheism is one that doesn’t. I don’t rebut the suggestion in any conclusive way. Rather, I look around for the best analysis of possibility statements (best analysis or non-analysis, I should say – one option is to leave them unanalysed and burden ourselves with a primitive distinction) and then see what the chosen analysis has to say about whether possibility statements do or don’t need truth-makers. On my analysis, possibility statements turn out to be existential quantifications; existential quantifications are true, when they are, because they have instances to make them true; so on my analysis, it turns out that true possibility statements need truth-makers. But also, on my analysis, necessity statements turn out to be universal quantifications; universal quantifications are true, when they are, because they have no counter instances to make them false; so on my analysis, it turns out that true necessity statements do not need truth-makers, but false ones need false-makers. A rival analysis says the opposite. Suppose we thought that ‘Necessarily A’ was true iff A has a proof in axiomatic theory T, whereas ‘Possibly A’ is true iff not-A has no proof in T. (This is a bad analysis, because – for one thing – you need modality to specify what T should be. But for my present point it doesn’t matter whether the analysis is good or bad.) On this analysis, a true necessity statement needs a truthmaker, namely a proof; whereas a true possibility statement doesn’t need a truthmaker, but a false possibility does need a false-maker. Nobody should deny that some truths – existential truths, and whatever may imply existential truths – require ontological ground to make them true. No truthmaker principle required here – the statement in question just is (or just implies) the statement that there are such-and-suches, and so of course there have to be suchand-suches for it to be true. But not all statements are existential statements, not all statements are equivalent to existential statements, not all statements imply   ‘Modal Fictionalism’ (Rosen 1990).

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e­ xistential statements. Negative existentials are the most striking exception. The truth-maker principle seems to be the thesis that every statement is really an existential statement. I don’t see why that should be so – any more than I see why every statement should turn out to be really a negative existential statement. --Winter plans are taking shape, but still tentative. I’m on leave for 1987–88 so I don’t need to be back for the beginning of classes. I thought I might arrive early August (perhaps the 7th), leave late September (perhaps the 25th), divide my time before the conference between Sydney and Canberra, spend my time after the conference mostly in Melbourne. Steffi might arrive just before the conference and leave in the second week of September, but as always the big uncertainty is when and how long she can take off from work. Possible times for a lecture, or a visit to the 4th-year class, or both are just after I arrive in early August (when does your August break begin?), just after the conference (when does the break end?), or just before I go home. Just before the conference is another time for me to pass through Sydney, but I assume that will be in break. We may have seen the last of that miserable lounge in Honolulu in the middle of the night. Qantas is about to start running three non-stops per week to and from San Francisco. See you soon, Yours,

289.  To William G. Lycan, 18 June 1987 [Princeton, NJ] Dear Bill, I liked the ‘little potboiler’. Yes, off to Oz early August, returning late September. Steffi joins me for three weeks in the middle. T&M, ANU, conference, and Melbourne. [. . .] Why a reluctance to accept composite entities? Myself, I’m not reluctant – I accept arbitrary sums, no matter how scattered and miscellaneous. But I can understand and sympathise with the reluctance. Two reasons. One is a sense of redundancy and double-counting – as if (Don Baxter’s example) you thought you couldn’t go through the express check-out, 6 items maximum, because you had seven items: the six cans, and also the six-pack. If the six-pack is not identical to any of the other six, wherefore is it not a seventh item? (It is an item of the right sort to count, and so

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290.  To Nelson Goodman, 22 September 1987

581

is each can.) This motivates me to look for a sense in which the cans and the six-pack can be called identical. Slogan: the ‘are’ of composition is the plural of the ‘is’ of identity. But it might motivate someone else to say that the six-pack doesn’t really exist, really there are only the cans, or only the atoms, or . . . . The other reason is that with composition it’s Sydney or the bush. It’s hard to say that sometimes when you have several things you get a composite of them, sometimes you don’t; you seem to be stuck with things such that it’s vague or borderline or a matter of degree or . . . whether there is any such thing, and that I take to be nonsense. So it’s composition always, or composition never. Composition-always means there are a lot more things than you used to think. OK by me, but it takes some getting used to. The remaining alternative is composition-never. I think even worse – there are a lot less things than you used to think. But you can bring them back at least to the extent of an ill-conceived effort etc. Yours,

290.  To Nelson Goodman, 22 September 1987 as from: Princeton University Princeton, NJ [Melbourne, Australia] Dear Nelson, Thank you for your letter asking me to compare what is said about endurance and persistence in Structure of Appearance with what is said in Plurality of Worlds. The answer is that there’s somewhat more difference than our use of the same terms might suggest, but no fundamental dispute. The first thing to notice is that insofar as there’s a correspondence of terms, the correspondence is not homophonic. SoA endure* –––––––– persist* ––––––––

PoW (following Johnston) perdure endure persist

The second thing to notice is that the correspondence is not exact, even when limited to the individuals of the SoA system. Let t1, t2, . . . be different time qualia; p1, p2, . . . different place qualia, and c1, c2, . . . different color qualia. Suppose t1 + p1 + c1 and t2 + p2 + c2 are concreta. Then t1 + p1 + c1 + t2 + p2 + c2 enduresSoA through t1 + t2, and also perduresPoW – so far, so good. However in the same case p1 + c1 + p2 + c2 persistsSoA * 

through a period containing two or more times.

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through t1 + t2, yet it does not endurePoW. Now suppose instead that t1 + p1 + c1 and t2 + p1 + c1 are concreta. Then p1 + c1 persistsSoA through t1 + t2, and also enduresPoW – so far, so good. However in the same cases, t1 + t2 + p1 + c1 enduresSoA through t1 + t2, yet it does not perdurePoW, strictly speaking, because it has the part p1 + c1 which is wholly present at more than one time. (It is one of those ‘mixed cases’ which are explicitly ignored at the bottom of page 202 of PoW; and after we ignore the en­dur­ ancePoW of p1 + c1, we may count it, loosely speaking, as a case of perdurancePoW.) The third thing to notice is that when you define enduresSoA and persistsSoA, the values of your variables are the individuals of the SoA system, so we are not told how, if at all, these predicates might apply to entities of another system, say a particularistic system. Suppose, however, that we extend your definitions by applying them, as they stand, with particulars as values of the variables. Then we find a further discrepancy between enduranceSoA and perdurancePoW. Let e1, e2, . . . be momentary electronstages; e1 is with p1 + t1 and no other place-time (if we thus extend ‘with’); e2 is with p2 + t2 and no other place-time. Then t1 + p1 + e1 + t2 + p2 + e2 enduresSoA and per­ duresPoW – so far, so good. However, e1 + e2 also perduresPoW, yet it does not endureSoA. And e1 + e2 persistsSoA although it does not endurePoW, so here we have a discrepancy also between persistenceSoA and endurancePoW. Sincerely, David

291.  To John Bigelow and Robert Pargetter, 28 September 1987 University of Melbourne Melbourne, Australia Dear John and Robert, Here are my running notes on your ‘Theory of Structural Universals’.1 Looking back, I found I was not well pleased by an unpleasant shrillness of tone and ­hammering-in of the same point, especially toward the end. I apologise. I do think that what you’ve done is a version of the ‘magical conception’. Magic is not eliminated; rather it’s systematically and economically packaged in the ne­ces­ sary principles governing the 3rd-level relations. (I think you can get down to two of these relations, so only two spells; I’ll try my hand at that later after rereading John’s ‘Toward SUs’2 which gave me the idea how to build up other relations from the two.)   (Bigelow and Pargetter 1989).   

1

  (Bigelow 1986).

2

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292.  To Earl Conee, 9 December 1987

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I think now that I can’t accept the present theory for the same reason I can’t accept the DTA theory of laws. But I can’t see why DMA shouldn’t accept it, or something like it; because its magic is no worse than some that he accepts. I shall try to persuade him of this when I reach Sydney next week. --In the notes I express confusion and indecision about your saying that the 3rdlevel proportions were ‘internal’. I shouldn’t have got so muddled by clash of ter­min­ olo­gies: your ‘internal’ =df ‘essential to the relata’ vs. the ‘internal’ =df ‘supervenient on the intrinsic natures of the relata’ that I’m more accustomed to. I’m still confused by p11, lines 7–8, since ‘not grounded in intrinsic properties of the universals related’ is different still. But apart from that, I take it you meant ‘essential to the relata’ (as John confirmed by phone). If so, I agree that relations of universals can be essential to the relata without being mysterious, and without being grounded (in any non-trivial way) in intrinsic properties of the relata. In the notes I wasn’t sure whether I had a complaint against you on that score; now I’m pretty sure I do not. As to the second point: I say a relation R is grounded in the intrinsic natures of the relata iff, whenever a and aʹ are intrinsic duplicates and b and bʹ are intrinsic duplicates, then aRb iff aʹRbʹ. But I think that either that’s not so for your 3rd-level relations or else it’s so only for the trivial reason that a universal never has intrinsic duplicates other than itself! As to the second point: it’s a puzzle how universals can be related accidentally – answer: when we really have a triadic relation of universal, universal and world – whereas essential relation is the unproblematic default case. (Cf. PoW on the problem )3 Yours, David

292.  To Earl Conee, 9 December 1987 [Princeton, NJ] Dear Earl, You’re right that the formal work of ‘Survival and Identity’1 could have been done with a different choice about what relation of continuity or connectedness it is   Running notes, dated 23–25 September 1987, are not published here.

3

  (Lewis 1976c).

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that matters and that turns out to coincide with the I-relation. It could have been some sort of cluster, so that excellent bodily c-or-c could override a lack of mental c-or-c or vice versa. Then mental c-or-c would have been sufficient but not necessary for the relation that matters and that coincides with the I-relation. If that were intuitively right, what I did could be altered to fit. But it’s intuitively wrong. At least, for me it is. ‘Survival’ of the sort described in your letter gives me none of what I care about in caring about survival, and I insist that it doesn’t deserve the name. It amounts to my death, followed by unseemingly monkey business with my corpse, and is if anything inferior to a clean death. I’ll make you an offer in compromise. Something survives mental erasure (and doesn’t survive ordinary death) – call this something a ‘human being’. (As in Johnston, ‘Human Beings’, J. Phil., Feb 87.) Just as a person consists of living personstages interrelated by the R-relation (some sort of mental c-or-c), so a human being consists of living person-stages interrelated by a different relation, call it the H-relation. If I will undergo mental erasure, there will afterward be stages H-related to my present stage, but none R-related to my present stage; which means that I-the-human-being (the human being to which my present stage belongs) will have stages afterward, but I-the-person (the person to which my present stage belongs) will not. So I-the-human-being will survive, but I-the-person will not. Well, what I care about in wanting survival is that I-the-person should survive. Survival of the human being without the person isn’t even second best – it’s a repellent prospect. In part, because of how it would distress other people; but even if it didn’t, the prospect still distresses me. Normally we needn’t bother distinguishing people from human beings, because normally they’re identical. Also, it may be a morally useful fiction to pretend they’re identical more universally and more exactly than they really are. So I suppose that often one will say ‘I’ without deciding whether to mean ‘I-the-person’ or ‘I-thehuman-being’. But when I do distinguish, and when I’m talking about what matters in survival, then it’s most certainly the first I mean, not the second. Sincerely, David Lewis

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293.  To Terence Parsons, 21 January 1988

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293.  To Terence Parsons, 21 January 1988 [Princeton, NJ] Dear Terry, Thank you for the paper1 and reference. The reason I couldn’t find ‘Some Things Do Not Exist’2 in the Jungle bibliography3 is that the thing turns out to have two or three different bibliographies, so that what you find to be not there may never­ the­less be there. But once found, it turns out to be disappointing, a sheep in wolf’s clothing. It’s substitutionalist, nothing to bother Quine for a moment, no worries! The Jungle line on substitutionalism (at least at one point) is cute. If all items had names, the quantifier could be explained substitutionally and still be objectual, right? Well, all items do have names, so the (existentially neutral) quantifier is substitutional. Of course, many items – many existing ones, even, and also many of the others – only have nonexistent names! So where does that leave us? Usually we think that substitutional quantification requires objectual quantification over the names, and if that’s so we’re left with objectual quantification over the nonexistent names of (what we might have thought were) nameless items. But maybe these nonexistent names in turn have nonexistent names, and so on down – so maybe Routley can claim to be a substitutionalist through and through. Makes it hard to write about his position. (As do many other things.) I really want to write about a hybrid figure, part Routley part Parsons. [. . .] Yours, David Lewis

294.  To Peter van Inwagen and Hartry Field, 24 February 1988 Harvard University Cambridge, MA Dear Hartry and Peter, Until last week, I was content with Hartry’s answer* to Peter’s question† about substitutional quantification. But now I’m discontented and perplexed. Help wanted.   ‘Underlying States in the Semantical Analysis of English’ (Parsons 1987).    2  (Routley 1966).   Exploring Meinong’s Jungle and Beyond: An Investigation of Noneism and the Theory of Items (Routley 1980).

1 3

* 

Review of Gottlieb, Noûs (1984) 160f., and elsewhere.   ‘Why I Don’t Understand . . .’ Φ Studies (1981) 281 ff.

†

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Peter’s question, freely paraphrased, was: how can the substitutional quantification ΣαΦα be understood otherwise than as an objectual quantification over the expressions which are admissible substituends for α? Hartry’s answer was: understand it as an abbreviated disjunction, perhaps infinite, of all the substitution instances. That is, it’s: Φν1 ∨ Φν2 ∨ . . . (where the ν’s are all the admissible substituends). You wouldn’t think that a finite disjunction ‘Tom dunnit ∨ Dick dunnit ∨ Harry dunnit’ should be understood as an objectual quantification over names – the names are used, not mentioned – and why should it matter if the disjunction is infinite, or if we introduce a concise abbreviation for it? Peter wanted an answer in terms of propositions expressed. That’s OK by me (except that Peter and I don’t agree about what sorts of things deserve the name of propositions) but it won’t be OK by Hartry. Nevertheless, what I’d have said is that the proposition expressed by ΣαΦα is the disjunction of all the propositions expressed by all the Φν’s. Disjunction of propositions? This explanation should be as ac­cept­ able to Peter as it is to me, despite our different conceptions of what we’re talking about: the disjunction of several propositions is that proposition which (1) is implied by each of them, and (2) implies any other propositions of which the same is true. Now I think maybe Hartry’s answer is too good to be true. Because when I apply it to substitutional quantification in a Lagadonian language, it seems that objectual quantification isn’t objectual either! A Lagadonian language, remember, is one in which each thing (in the domain) serves as a name of itself. So the result of concatenating Tom with ‘dunnit’ is an atomic predication, true iff the first term (Tom) denotes something that satisfies the second term (‘dunnit’). Since Tom denotes Tom himself, that’s so iff Tom satisfies ‘dunnit’, so iff Tom dunnit. NB: no missing quote marks! Tom himself, not some other, verbal, name of him, is the subject term. How concatenate a man with a word to make a Lagadonian sentence? Maybe you take the sequence, understood set-theoretically – that’s how Quine taught us to concatenate generally. (But Hartry won’t like it.) How do you utter or write a Lagadonian sentence? – You don’t. So what? (But you can write certain abbreviations of them.) Letting exactly the Lagadonian names be admissible substituends we have that ΣαΦα is true iff for some Lagadonian name ν, Φν is true; iff for some object ν in the domain, Φν is true; iff for some object ν in the domain, the denotation of ν satisfies Φ; iff for some object ν in the domain, ν satisfies Φ; iff ∃xΦx. Lagadonian substitutional quantification is objectual quantification – over the objects in the domain, and ipso facto over their Lagadonian names. Now, why isn’t Hartry telling me to take ΣαΦα as an abbreviation of the Lagadonian disjunction wherein the Lagadonian names are used, not mentioned. If

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294.  To Peter van Inwagen and Hartry Field, 24 February 1988

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so, why shouldn’t I conclude once again that there isn’t any objectual quantification over the Lagadonian names, and ipso facto there isn’t any objectual quantification over the objects in the domain? Can it be that Lagadonian ΣαΦα is exactly equivalent to ∃αΦα except that it unloads all commitment to the existence of the objects in the domain? Oh, wow! Never suffer from burdensome existential commitments ever again! That’s silly. But I can’t see anything wrong either with my analysis of objectual quantification as Lagadonian substitutional quantification or with Hartry’s analysis of substitutional quantification as abbreviated disjunction, or any reason why Hartry’s analysis can’t apply to the Lagadonian case. So I’m left thinking that Lagadonian disjunctions do after all imply the cor­res­ pond­ing objectual quantification; that they do carry a commitment to the existence of (at least one of) the things named, and ipso facto to the existence of (at least one of) the things named. Now in asking whether Lagadonian naming carries existential commitment, I think the fact that this naming occurs within disjunctions (maybe infinite, maybe abbreviated) is an irrelevant nuisance. So let me concentrate on one-disjunct disjunctions – in other words, atomic predications. So does a Lagadonian predication of the form Φν carry commitment to the existence of the object named by ν, and ipso facto to ν itself? Does it imply – in the appropriate sense of imply – ∃x x = ν and ∃xΦx? We were taught that despite the rules of EG and UI that give us Φν                    ∀x x = x ∴∃xΦx                   ∴ν = ν                      ∴∃x x = ν and the like, naming does not in general carry existential commitment. Quine makes his case by Russellizing the names and noting that EG and UI are invalid where ν is a Russellian description; a less conservative logician might simply have admitted denotationless names like ‘santa’ and predicates like ‘is nonexistent’ that are satisfied by nothing yet yield truths when concatenated with denotationless names, thereby invalidating EG and UI. But whichever technique we prefer, we’d better have some way to agree that ‘santa is nonexistent’ doesn’t carry commitment to the existence of santa. Still, ‘Tom dunnit’ couldn’t possibly be true if Tom didn’t exist, that is if ‘Tom’ were a denotationless name like ‘santa’. In some sense, namely the sense of strict implication, ‘Tom dunnit’ does imply ‘∃x x dunnit’ and ‘∃x x = Tom’. Necessarily, if the premise is true (on its intended interpretation) so are the conclusions. But strict implication seems not to be the ‘appropriate sense of imply’ for ascribing implicit existential commitment. I think numbers exist necessarily, wherefore

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any premise whatever strictly implies ‘∃x x is a number’ – so shall I say that every sentence of Science without Numbers carries an implicit existential commitment to numbers? Al thinks God exists necessarily. Should he say that Hartry and I implicitly affirm theism whenever we affirm anything? No way! More likely, the ‘appropriate sense of imply’ is the narrowly logical sense: ne­ces­sary truth-preservation not just on the intended interpretation but also on all rein­ter­pret­ations of all but the logical vocabulary. I have several worries about this alternative also (see the enclosed course handout) and in particular I fear that it upholds not only Quine’s thesis that naming doesn’t always carry existential commitment, but also the alarming thesis that naming never carries commitment – not even the Lagadonian naming in the disjunctions that are abbreviated by the Lagadonian substitutional quantifications that look to be equivalent to objectual quantifications. ‘Tom dunnit’ doesn’t imply ‘∃x x dunnit’ or ‘∃x x = Tom’ in the narrowly logical sense, because ‘Tom’ should be reinterpreted to be a denotationless name like ‘santa’ and ‘dunnit’ could be reinterpreted to be a special predicate like ‘is nonexistent’. The same goes for the Lagadonian predication we get by concatenating Tom himself with ‘dunnit’. If Tom can be interpreted as a name of himself, as in the wholesale Lagadonian stipulation, then also he can be reinterpreted as some other sort of name: maybe a name of someone else, maybe even a denotationless name. So there’s a reinterpretation that makes the Lagadonian predication true, but makes false ‘∃x x dunnit’ and the Lagadonian sentence we get by concatenating ‘∃x x = ’ with Tom. It would be a contradiction to claim that ∃xΦx is equivalent to Lagadonian ΣαΦα, which is equivalent to a Lagadonian disjunction, which fails to imply ∃xΦx – if I meant ‘equivalent’ and ‘imply’ in the same sense throughout. That’s not my problem. (I thought for a while it was, but Catherine Elgin set me right.) Because I can only claim strict, not narrowly logical, equivalence between ∃xΦx and ΣαΦα. Even if the intended interpretation of names is Lagadonian, and of predicates is standard, still a suitable reinterpretation makes ∃xΦx true but ΣαΦα false, or vice versa. My problem is that I want to say that ∃xΦx and Lagadonian ΣαΦα are equivalent in the sense that matters to existential commitments; and yet that Lagadonian predications don’t imply objectual quantifications in the sense that matters. Well, so maybe my problem is just that I can’t make up my mind which sense it is that matters. I knew that already (as witness the handout).1 But Lagadonian substitutional quantification gave me a new way to get embroiled in the old problem. Yours, David   ‘Implicit Ontological Commitment’ (handout, 10 February 1988, attached to this letter).

1

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294.  To Peter van Inwagen and Hartry Field, 24 February 1988

589

IMPLICIT ONTOLOGICAL COMMITMENT

10 Feb 88

You can commit yourself to F’s not only by holding ∃xFx true, but also by holding true something else that implies ∃xFx. Else you could dodge commitments just by silence. But what should ‘implies’ mean here?

Narrowly logical implication? (Truth preservation under reinterpretation of non-logical vocabulary). BAD: somebody could be committed to cavalrymen without being implicitly committed to horses.

Modal implication. (Necessary truth preservation under a fixed interpretation). ì 17 ü BAD: if í ý exists necessarily, then îGod þ ìnominalists ü even í ý are implicitly comî atheists þ mitted to it, despite their denials.

Waiving that, a further dilemma: shall we assess implicit commitments only after translation into canonical language?

No? BAD: Then we lack guidance, even to the extent of a stipulated list, about which vocabulary is logical; but without delineation of that, we can’t assess implicit commitments.

Yes? BAD: We give up too soon on assessing commitments of non-canonical theorist. BAD: sometimes (e.g. Davidsonian analysis of predicate modifiers) the translation appears to foist extra commitments on us. WORSE: . . . or even to foist inconsistencies on us.

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295.  To George Boolos, 24 April 1988 [Princeton, NJ] Dear George, Take a relation – any binary relation, for the moment I’ll impose no conditions on it. Call it ‘precedes’. Something is first among some things iff it is not preceded by any of them. Something is grounded iff, whenever it is one of some things, then something is first among those things. The following are equivalent. (1) Everything is grounded. (2) Whenever there are some things, there is a first among them. Proof. (1) to (2): instantaneous. (2) to (1): suppose that (2) but not (1). Something x is a first among the ungrounded things. Let x be one of X. Something must be first among X; else x is preceded by y and y is one of X.  Is y grounded? No, else there’s a first among X after all. Is y ungrounded? No, because x is first among the ungrounded. Now we have that x is grounded, which completes the reductio. Something x is grounded iff everything that precedes x is grounded. Proof. Left to right. Suppose x is grounded and y precedes x. Let y be one of Y; let Y+ be Y together with x. Since x is grounded, something must be first among Y+. It can’t be x, which is preceded by y, so it must be one of Y. But then it’s first among Y also, so y is grounded. Right to left. Suppose everything that precedes x is grounded and let x be one of X. Case 1: x itself is first among X. Case 2: y is not first among X. Then we have y, also one of X, which precedes x and therefore is grounded. Either way there’s a first among X, so x is grounded. Equivalently, x is ungrounded iff something that precedes x is ungrounded. This means, as we’d expect, that ungrounded things come either in loops or in in­fin­ ite descending chains. The above doesn’t tell us whether self-preceders are grounded. But in fact any self-preceder is ungrounded, because if X are it and only it, then it is one of X but there is no first among X. ‘Precedes’ might be membership, so we know what it means to be a grounded set. Or it might be the ordering of the stages at which sets are formed, so we know what it means to be a grounded stage. (Never mind identifying the latter either with membership or with the ordering of the numbers.) We have (Spec) The set of X is formed at stage m iff each one of X is formed at a stage preceding m; and the empty set is formed at every stage. (That second clause is the price I pay for not allowing valueless plural variables.)

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295.  To George Boolos, 24 April 1988

591

Now stipulate that the precedence of stages is transitive; whence we conclude that if a set x is formed at a stage m, then so are all its members. Proof. If y is any member of x, y is formed at a stage n that precedes m, and all members of y are formed at stages that precede n. By transitivity, the members of y are formed at stages that also precede m. So y is formed at n. If a grounded set is formed at any ungrounded stage, then it is formed at every ungrounded stage. Proof. Else let X be all the exceptions: the grounded sets formed at some but not all ungrounded stages. They’re grounded, so let x be a first among them (wrt membership). Each member of x is grounded, is not one of X, is formed at the ungrounded stage where x is formed; and therefore is formed at all ungrounded stages. But then x itself is formed at every ungrounded stage, after all; because every ungrounded stage has an ungrounded stage preceding it, at which all x’s members are formed. Contradiction. It can’t happen that stage n precedes stage m, yet exactly the same grounded sets are formed at both. Proof (mini-Mirimanoff). The set of all grounded sets formed at m is itself a set formed at m, since its members are formed already at n. It is grounded, since its members are. But then it is a self-member, in which case it must be ungrounded. Any ungrounded stage m must be preceded by an ungrounded stage n. We have shown that the grounded sets formed at m and at n are, and are not, exactly the same. We conclude that all stages are grounded. --This is less neat than (my version of) your version. But it seemed to give me a better sense of what was going on. Or maybe it was just prolonged playing around with the notion of groundedness that gave me the better sense. Anyhow, here it is – for what it’s worth. --I had imagined that a model for unfundiert set theory would look something like a non-standard model of arithmetic. You’d still have stages; first would come the grounded stages; afterward, or off to one side, would come the ungrounded stages, with their infinite descents and their loops; you’d still have Spec; and the ungrounded sets would get formed at the ungrounded stages. I now see that this can’t be right: it might be all very well for ungrounded sets to get formed at ungrounded stages, but there’s nothing you can consistently say about whether additional grounded sets do or don’t get formed at the ungrounded stages. This gives me some sense of what’s inductive about Spec. --I might as well record an idea that, so far as I could tell, doesn’t work. In (my version of) your version, we construct the Rm’s. (Call them the ‘grounded ranks’ – but they turn out to be just the ranks.) They’re indexed by the stages; they’re ordered by

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membership; they’re grounded wrt membership. So we’ve made an order-preserving image of the stages wherein everything is grounded wrt the ordering. So the stages likewise are grounded wrt their ordering. I thought: do we really have to play off two different orderings this way? Suppose we could just map stages into stages (numbers into numbers) in such a way that whenever m is a stage, rm is a grounded stage, and whenever n precedes m, rn precedes rm. Then the rm’s could play the same role as the Rm’s did: an order-preserving image of the stages wherein everything is grounded wrt the ordering. But what’s a suitable mapping r? In hindsight we know the answer: identity, for one. But how to specify an r such that we can show its suitability without circularity? Yours, PS For the record: ‘my version of your version’ rewritten. Assume Extensionality The order E of stages (aka numbers) is transitive F: is formed at xFEm =df Some n(nEm & xFm) Spec: [x: xFEm & --x--]Fm y has a minimal member =df some member of y doesn’t intersect y x is grounded =df every set containing x has a minimal member Rm =df [x: xFEm & x is grounded] Each Rm is grounded. Proof. Else we have Rm a member of a set x with no min­ imal member. Rm itself isn’t a minimal member of x. So we have y in Rm, and hence grounded, and also in x. But then x must have a minimal member after all. Whenever n precedes m, Rn is in Rm. Proof. Because Rn is grounded and RnFERm. Whenever X are some stages, there is a least one of X. Proof. Let k be one of X; let Q = [Rm: m precedes k and m is one of X]. This exists by Spec. If Q is empty, k itself is a least one of X. Else Q has members, and they’re grounded, so Q has a minimal member; let Rj be one such. Then j is the least one of X. Else we have that h precedes j and h is one of X. Then h precedes k by transitivity, so Rh is in Q. But Rh is in Rk, so Rj is not a minimal member of Q after all.

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296.  To Allen P. Hazen, 2 May 1988

593

296.  To Allen P. Hazen, 2 May 1988 [Princeton, NJ] Dear Allen, I’m commuting to Harvard this term, so seeing a lot of the New Haven. Last Friday, I got a bad glimpse of something smooth, low, dull silver with a yellow stripe, that I thought might be an LRC. There was one there years ago – didn’t you and I ride on it coming down from a Boston APA? – but have you heard of one there now? Constructivism as a position on the ontology of mathematics? I don’t know what constructivism is. It seems to me to be sometimes one, sometimes another, of three different things. (1) A branch of parapsychology: by thinking, we cause there to be mathematical objects, where these are not parts or aspects of our own thoughts. (2) A theory of the nature of mathematical objects: they are parts or aspects of our thoughts, and therefore there are far fewer of them than Platonists think there are. (3) Fictionalism: there are no mathematical objects, but we construct false theories that say there are, and what passes for truth in mathematics is really just truth-accordingto-the-fiction. (1) is not a position on what there is, but rather on causal explanation of what there is. (2) is a position on ontology – and indeed is an intermediate position between thoroughgoing Platonism and thorough repudiation. (3) includes a position on ontology, sure enough: the position that there just ain’t no such things (plus a way to make believe that there are). Deviant quantificational logic, deviant notion of existence? But George and I haven’t given up anything. We quantify singularly just the way we always did, and just the way we would if we didn’t also quantify plurally. No green ink there. If affirming and denying singular quantifications is the test of commitment, as it always was, we should be as subject to the test as ever. George affirms ‘Some x, x is a set’ and denies ‘Some x, x is a set or class of all sets’ despite also affirming ‘Some X, X are all the sets’. Likewise I affirm ‘Some x, x is a set’ and I affirm ‘Some x, x is a proper class’ and I deny ‘Some x, x is a class of all the classes’ despite also affirming ‘Some X, X are all the classes’. I don’t think ‘the less ideology the better’; I think ‘the less mysteries the better’ and dislike ideology that seems mysterious. I don’t find plural quantification at all mysterious. Why should I? Perhaps because the only way to understand it would be to internalise a formal system that characterises it completely – which can’t be done. But that standard of what it takes not to be mysterious is so restrictive that I can’t believe it generally, therefore it gives me no special worry about plural quantification. – Well then, what does understanding plural quantification consist in? I can’t answer. But neither can I answer what understanding identity, or part and whole, or negation consists in, and I don’t doubt that I understand those.

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Yes: if I needed a primitive part-of-the-same-world relation, and my oneworlder opponent didn’t, that would make him much better off in ideology. (That’s why I think it worth the cost in plausibility to deny that there can be a world of many spatiotemporally unrelated parts, so I can explain part-of-the-same-world as spatiotemporal relatedness.) Yours,

297.  To Allen P. Hazen, 18 June 1988 [Princeton, NJ] Dear Allen, Good. You know better than I what various constructivists really do have in mind, but certainly I think that some sort of fictionalism is what they ought to have in mind. I too can imagine taking mathematical fictionalism seriously. The more so, now that Gideon Rosen has helped me to take modal fictionalism seriously. I’m sending you a copy of Gideon’s paper, which I like very much. It isn’t an all-out defence of modal f’ism, but gives it a good run for the money. (Gideon is one of our advanced graduate students, in the best-of-many-years class. Maybe you’ve met him as a promising Columbia undergrad a few years back.) (1) Parapsychology? The ‘metaphor’ of worldmaking (numbermaking, setmaking, starmaking, Godmaking, . . .) is so very pervasive in irrealist writing, math­em­at­ ic­al and otherwise, and it’s so very off-the-mark if what’s really meant is that we make theories according to which there exists a world (or numbers, or sets, or stars, or God, . . .) that I find it unbelievable that nobody ever means it literally. Of course, I find it at least as unbelievable that anybody ever does mean it literally. (2) Existing in the mind? I agree with you that the best interpretation of the idea that mathematical objects (or other things of which some sort of irrealism is true) exist in the mind, are parts or aspects of our thoughts, is that they are intensional objects of our thoughts. And that doesn’t really make them parts or aspects of our thoughts, or mental entities the way thoughts themselves are mental entities. No, it makes them things that exist according to our thoughts, whether or not they really do exist. You say that existence in the mind and fictionalism ‘come close together’; I’d say they’d better merge altogether. If not, I think it’s another no-hoper notion to say that mathematical objects exist in the mind, no better than parapsychology. So what we’ve got here, if anything, is yet another highly misleading way to state math­em­at­ ic­al fictionalism. Better state it fair and square.

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297.  To Allen P. Hazen, 18 June 1988

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A very strange sort of fiction? ‘For one thing, some of the characters . . . are as close to real as any abstract entity ever is . . .’ e.g. small numbers. What means ‘close to real’? Come clean: real or not? Is it so, or is it not so but only so according to math, that there is such a thing as the number three? If what you mean is that it’s somehow very much as if the number three existed, that might be OK – depending on which how is ‘somehow’, of course. You go on: ‘. . . and the fiction is true about these characters’. I like this better, because maybe truth about whether the character exists needn’t be part of truth about the character. You ‘may see mathematics as dictating to the physical world: mathematical theorems are . . . necessary. The fiction is in a special sense necessary’. This too is OK, but I don’t agree that it is ‘not captured in a purely fictionalistic account of math’. To me it sounds like Hartry’s idea of a conservative fiction: a fiction such that what’s true according to the fiction about a certain non-fictional subject matter is always true simpliciter, and in fact (in some sense) necessarily true. Something is true according to math about how many animals old MacDonald has if he has two cows and three pigs, and no animal that is both a cow and a pig, and no animal that is neither a cow nor a pig, and if cows and sheep are animals; and you can perfectly well say that math is a fiction, what’s true in the fiction about this sort of question is always true simpliciter, and necessarily true to boot. Likewise for questions about the outcome of feasible computations. Likewise for questions (Hartry’s example) about conditionals from nominalistic-physical premises to nominalistic-physical conclusions. Will this do as a way for fiction to be true about such characters as the small numbers, even though those characters don’t really exist? Will this do as a way for fiction to dictate to fact? Ok, but I don’t see how it gives mathematical objects existence in even the greenest of ink. ‘The story is . . . a character in itself’. Yes; maybe less exceptional than you suggest, see stuff in ‘Truth in Fiction’ about the real-life Sherlock Holmes who doesn’t quite enact the plot because he’s not the one who’s told about in these stories we’ve heard. Anyway, at most an oddity, not a problem for mathematical fictionalism unless I’m overlooking something. ‘The extension of the fiction . . . is very strictly constrained, and some of these constraints (e.g. that of a pair of contradictory elaborations at most one is legitimate) are the constraints of true theories’. Yes – this is strange. The mystery of math­em­at­ ic­al fictionalism is where the constraints come from. Likewise modal fictionalism, as Gideon brings out. But I do think you’ve overstated the constraint. If the pair of contra­dict­ory elaborations are one with the Fermat conjecture and one with its denial, what you say sounds right. But if instead of the Fermat conjecture you put the latest large-cardinal conjecture, maybe you can be happy to put that in with Watson’s blood type and say that the fiction can legitimately be elaborated either way. As a

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realist, I can’t agree that anything goes, but this is a point where I can’t claim to have the intuitive advantage. As may have been clear for some while, I’m nowadays inclined to take all manner of irrealisms as fictionalisms. Their ‘truth’ always works out to be truth-accordingto something or other. Phenomenalism says that what’s true about the external world is what’s true according to whatever external-world story best fits experience. (No ‘sense datum language’ and no definitions of trams in that language required; and understanding what it means for an external-world story to best fit experience is everybody’s business.) Somebody rather like Bas, but less honest, says that what’s true about microphysics is what’s true according to the micro-story that best fits what macroscopic things do. Some sneaky atheist who still likes to go to church says that what’s true about God is what’s true according to the mythology that best arouses ‘agapeistic attitudes’ (or, what’s true according to a certain particular myth­ ology). And so it goes. --I’m sorry, I don’t get the hang of your proposal about points and regions and facts. Let’s try it again in Melbourne. In the meantime, here’s my idea about how to break the symmetry in favour of points, as I join you in wanting to do. I say that if there are the points, then automatically there are the mereological sums of points. Though not points, these are nothing extra, nothing over and above the points. Some of these point-sums (the nicer-shaped ones, at least) are regions – not ersatz regions, not things that ‘might be identified with’ regions, but regions, naturally and indubitably. You can’t have the points and not have the regions too, and the regions are nothing extra. But you might have the regions and not have the points, if every proper part of a region in turn has proper parts of its own. The best you can be sure of having are set-theoretical ersatz points, namely certain classes of regions. These wouldn’t be dinkum points because (1) they aren’t mereological atoms, and (2) the regions aren’t mereological sums of them, and (3) they are sets. It’s true that they correspond one-one to the points there would have been if there had been points. It’s true that by taking them as values of point-variables, as members of the extension of ‘point’ etc., and by fiddling the extension of ‘lies in’ etc., you can make all the right point-sentences come true – but on what I say is an unintended interpretation. You probably won’t like this, for more reasons than one. First, because you don’t share my faith that mereology can do no wrong. Second, because I’m still not respecting the alleged line between linguistic data and explanatory semantic theory, where theory is up for grabs and anything goes in interpretation so long as it predicts the data. As you said, mine is not the metaphilosophy of Structure of Appearance, however much I like the rest of the book! ---

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298.  To Paolo Dau, 23 November 1988

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I don’t know that the talgo I saw was new, or that it was being run. Maybe the 1950’s one was stored until now, and I saw it on the way either to scrap or to preservation? I assumed that the Amturbos with it were for running it, but maybe not. --Verisimilitude and similarity of worlds has been around for a while. I think it was Hilpinen who started it. It gets a mention in PoW. Right, you probably don’t want the same similarity relation as for standard counterfactuals. See you soon, Yours,

298.  To Paolo Dau, 23 November 1988 [Princeton, NJ] Dear Professor Dau, What David Kaplan heard, and told you a little about, is a long, and not yet finished, paper called ‘Parts of Classes’. I’ve made a note to send you a copy when I have a completed – but still preliminary! – draft. It appears to me that you’ll find it somewhat relevant to your work, but maybe less directly relevant than Kaplan’s report suggested. I want to end up with standard, modern set theory. But I want to see it as being partly mereological. The idea is that the parts of classes are all and only their subclasses. (However the null set for this purpose does not count as a class, rather as an individual.) Then the smallest parts of a class are its singleton (= unit) subclasses, and a class is the fusion of the singletons of its members. You are then a member of a given class iff your singleton is part of it. Mereology is primitive, unproblematic, un-set-theoretical, and ontologically innocent – so I claim. All the introductory bumf in the front of the set theory textbook about ‘bringing together’ or ‘gathering’ or ‘many into one’ introduces you only to the mereology in set theory. The other, distinctively set-theoretical, primitive is the notion of singleton. This is not at all explained in the introductory bumf; it is altogether mysterious; it is in no way a matter of making many into one, rather it makes one into one – one member into one singleton, the singleton being something entirely disjoint from the member. It is the notion of singleton, not the mereology, that’s responsible for the mystery, the ontological extravagance, and the mathematical power of set theory. Yours, David Lewis

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299. To Eli Hirsch, 27 December 1988 [Princeton, NJ] Dear Eli Hirsch, Thank you very much for your extremely interesting note on similarity and natural properties.1 What a surprise if naturalness of properties can after all be defined in terms of a nice similarity relation! I cannot find any fault with your def­in­ition. But I don’t feel that I have the idea completely under control. What do I mean by that? Not that there’s any unclarity in what you wrote. I have a hunch your def­in­ition is equivalent to something still simpler, but I can’t figure out what that something is. Best regards, David Lewis

300.  To Phillip Bricker, 13 June 1989 [Princeton, NJ] Dear Phillip, A very belated reply to your very interesting 22 March letter about Parts of Classes.1 Thank you very much! Only now that some jobs with deadlines, and the teaching semester, are over have I been able to return to PoC. Yes, I think absolutely unrestricted composition, and hence restriction of singletons instead – von Neumann rather than Zermelo – is a very important part of my position. Guilt by association? He who’s been caught making mysteries once may well be a habitual offender and do it again? – I think that’s not quite it. I hope not. Rather: if we had a good understanding of what it means to form singletons, then that understanding might somehow have turned out to yield some sort of positive reason why singleton-forming has to be unrestricted. But we don’t. So it doesn’t. That doesn’t do much by itself, but I join it with a positive reason for unrestricted composition: the idea of composition as identity. I can’t put this as any sort of water-tight argument, but here’s how it strikes me intuitively. If com­pos­ition,  Cf. Dividing Reality (Hirsch 1993, ch. 3).

1

  (Lewis 1991).

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300.  To Phillip Bricker, 13 June 1989

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unlike identity, were a sometime thing, and only worked under favourable conditions, it wouldn’t be automatic and trivial the way self-identity is. But the onto­ logic­al innocence of composition only rings true if composition is automatic and trivial. Sauce for the gander: your story of the errors of our naïve days is symmetrical. When we only ever took singletons of small classes (and individuals), and when we only ever fused few singletons at a time, we kept out of trouble; so we naïvely assumed that we understood both, and that our understanding required no restriction. You say that fusing many is significantly different from fusing few, and that’s how we were fooled. Why can’t it just as well be that singletons of large are different from singletons of small, and that’s how we were fooled? Why do you say ‘there was no comparable reason for doubting our understanding of singletons’? Two independent mysteries? – Maybe. It’s certainly one thing to ask why we can’t take a singleton of just anything, another thing to ask what this taking of singletons is in the first place. Better understanding of the second might solve the first, or might not – without the solution, how can I tell what it would do for me if I had it? Anyway, I agree that having them both be mysteries about singleton doesn’t automatically make them be one mystery instead of two. I agree that a limitation of size on composition isn’t vague. Rather, the connection with the argument in PoW goes this way. If we restrict composition to exclude gerrymanders, the battle for composition as identity and the ontological innocence of mereology is already lost; no harm done if we lose it twice over. But however much some of us might wish to, we can’t restrict to exclude gerrymanders; so the battle isn’t already lost; so carry on the good fight. I don’t think I can understand singletons just by choosing to understand. Can I maybe believe I understand singletons just by choosing to believe? Just saying ‘mysteries’ covers up the distinction between incomprehension and ignorance. The continuum hypothesis may well be a case of irremediable ignorance, but I understand it well enough. I never claimed to know everything, or even to be able to find out. Since I don’t claim to have been made in the image of omnipotent God, why should I have any problem about confessing ignorance, even irremediable ignorance? I’ve read the Bunt chapters on ensemble theory2 – partly read, partly skimmed. There’s no doubt that he beat me to the central idea, but also no doubt that what I do with it is a lot different from what he does. So I’ll go ahead. I’ve added a string of footnotes that make the appropriate comparisons. I wonder what he thinks? – I sent him

  Mass Terms and Model-Theoretic Semantics (Bunt 1985, 53–72, 233–301).

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a copy of the March draft and what I thought was a courteous letter, and he has not replied. Responses to your marginal notes. [. . .] You’ll get another draft soon – only the final section is new, but there are a lot of small changes scattered around. I’d be especially interested to know what you make of the new footnote about redundancy of Unions, page 80 or thereabouts. I soon leave for points east, namely Wales, Perth, Melbourne, New Zealand, San Francisco, and Princeton. Best mailing address: before about 12 July, Princeton as usual; Steffi will join me in the middle, bringing mail; from then to about 23 August, c/o Department of Philosophy, University of Melbourne, Parkville, Vic 3052, Australia. (If you write during this time, note that I won’t have copies of previous correspondence to consult.) When do you move to Amherst? Yours,

301.  To W.V. Quine, 8 August 1989 as from: Princeton University Princeton, NJ [Melbourne, Australia] Dear Van, Your 28 June letter about Parts of Classes, and following postcard, have at length followed me to Melbourne. I’m not certain what difficulty you had in mind. If ‘…S. . .’ says that S ‘conforms to appropriate structural conditions’ to be a singleton function, then as you say the relations S such that . . .S. . . are not all mutually compatible. The structuralist plan is to take ‘--singleton--’ as abbreviating ‘∀S (…S. . . ⊃ --S--)’. [Here I disregard the added conjunct ‘∃S (…S…)’; and for the reasons you give, I decline the invitation to switch to ‘∃S (…S. . . & --S--)’.] In short, ‘--singleton--’ is true simpliciter iff it’s true on all appropriate interpretations of ‘singleton’. This has the effect that ‘--singleton--’ and ‘∼(--singleton--)’ may both be false; as is only to be expected since, in unabbreviated notation, the second is not the negation of the first. So far no worries, I think. I think the difficulty you probably had in mind was this. There might be a relation S such that . . .S…, yet such that ‘Possum’s S’ is an improper description because Possum has no S. For it might be that under that S, Possum comes out as a proper class or a mixed fusion.

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302.  To Barry Taylor, 8 September 1989

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Whether that’s the difficulty you had in mind or not, it needs answering, and here’s what I say. I was at fault in saying that ‘…S. . .’ should be purely ‘structural’ and should be obtained just from axioms for set theory. It should express more of what little we take ourselves to know about singletons: e.g. that cats do not have singletons as parts. It should imply not only that if Possum is an individualS then he has exactly one singleton, but also that if he is a cat then he is an individualS (where an individualS is anything that has no S’s as parts, cf. p. 13). The first part comes from the official axioms for set theory; the second part doesn’t, but it should be there too, and I should have said so. I’ll fix it in the next round of revisions. Thanks! Yours, David PS Even without the repair, Possum probably couldn’t come out a proper class if ‘…S. . .’ includes a principle of limitation of size: he doesn’t have enough atoms, and that’s not subject to reinterpretation. The real danger is that he might come out a mixed fusion.

302.  To Barry Taylor, 8 September 1989 [Melbourne, Australia] Dear Barry, I thought it might be handy to write down some responses to your ‘Just More Theory’,1 even though the letter will add little to what we covered yesterday at lunch. Suppose ideal theory includes a chapter on semantics. (Ignore the problem you draw attention to: that since it’s ideal theory, this chapter ought to be the complete and final word on the subject; but making it so appears to bring on the semantic paradoxes. That’s everyone’s problem. Let’s hope, but without too much confidence, that it’s orthogonal to my disagreement with Putnam over further constraints being ‘just more theory’ or not.) Call an interpretation (semantically) immodest iff it makes this chapter true, and thereby says of itself that all constraints on reference set forth in that chapter are satisfied – plain constraints or fancy ones, whichever. My point: if an interpretation is unintended, then even if it’s immodest, that doesn’t mean that it satisfies the constraints. It says it does, or anyway it says the right words, but who knows what it might mean by them? 1   ‘ “Just More Theory”: A Manoeuvre in Putnam’s Model-Theoretic Argument for Antirealism’ (Taylor 1991).

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Your point: however, if it is intended, then we can take it at its word when it tells us whether it satisfies the constraints. Then if it’s immodest, it tells us truly that it satisfies the constraints, and thereby tells us why it’s intended. If an interpretation were modest, it couldn’t be intended. For if it were intended, it would tell us truly that it fails to satisfy the constraints it has to satisfy in order to be intended. If some models of ideal theory were modest, that would be disaster for Putnam’s idea that all models of ideal theory are intended – very bad news for him! Your main point is that this won’t happen. There’s no refutation of Putnam to be found in this direction. And I agree. Myself, I think the conclusion that ideal theory can’t be false in its intended interpretation(s), and the conclusion that intended interpretations differ from one another by wildly miscellaneous permutations, are each of them reductios as decisive as anyone should need. But if Putnam is content to accept those conclusions, I have nothing worse to bring against him. But remember who started this in the first place. He said my position was incoherent. And my position is that not all the models of ideal theory are intended; at best few are; maybe none are. Further, the reason some or all of them are unintended is that they fail to satisfy the constraints. Which constraints – since I suppose them to be discoverable – are set forth in the chapter on semantics in ideal theory, taken on an intended interpretation. The fact that all models of ideal theory are immodest no more challenges my conviction that most or all of them are unintended than the fact that all the used-car salesmen congratulate themselves on their uprightness challenges my conviction that most or all of them are hypocrites. In hindsight, I think I said something a bit like this in ‘Putnam’s Paradox’, p.226. ‘The Challenger is playing by the rules, and the Respondent cannot win. And yet the Respondent may indeed have given a correct account of the constraint that makes determinate reference possible, couched in language that does indeed have determinate reference in virtue of the very constraint that it describes!’ – But I think the foregoing account of the matter, based on your paper and our discussion, is much clearer. --Minor comment, I think the beginning of your §5 (bottom of p7) is misleading both about my account of Putnam’s move and about what your account is going to turn out to be. At this point you seem to presuppose that 𝒯 did not have a chapter on semantics, ℒ did not have a semantic vocabulary, and hence ℳ ‘can hardly make C-theory come true’. But I think we agree that if an allegedly ideal theory doesn’t include the semantic chapter, the thing for Putnam to do is throw it away and start over with the genuine ideal theory. It’s not a matter of adding C-theory to ideal

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303.  To W.V. Quine, 21 September 1989

603

t­ heory; rather, it’s a matter of ideal theory turning out to have included C-theory all along. (‘Adding C-theory to the rest of total theory’ was what I said.) That’s what I had in mind; and you too, since the ℳ of later pages comes by cutting back ℳ+, and needn’t have anything to do with the ℳ of the false start when ‘ideal’ theory has the semantic chapter left out. So this bit could do with a little rewriting, I think. But please don’t delay the submission of the paper – it deserves attention. Yours, David

303.  To W.V. Quine, 21 September 1989 [Princeton, NJ] Dear Van, Thank you for your letter of 27 August. I understand better what problem you have in mind, but I don’t agree that it’s a problem. Take the case of arithmetic as an example. We have set theory as a framework for arithmetic; let’s take for granted both that it’s unequivocally meaningful and that it’s true. We can say what it means for a relation – let it be a class of Kuratowski pairs – to be a succession relation. The Ramsey sentence for arithmetic says that there exists at least one succession relation. In fact we know that there are many succession relations, and they are apt to be mutually exclusive. ‘Structuralist’ proposes to translate any arithmetical sentence . . . succeeds . . . succeeds . . . succeeds . . . as For every succession relation S, . . . S . . . S . . . S . . . (Or maybe he’d like to conjoin the Ramsey sentence to each translation, but let’s keep it simple.) Your complaint: for no x and y does x stand to y in every succession relation. So Structuralist can’t do anything that corresponds to the ascribing of one particular succession relation to one particular pair of things. Say I: right, he can’t, and why should he want to? The closest he comes to ascribing succession is to assert such sentences as

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This he can do. First he expands into primitive notation with the aid of nested def­ in­ite descriptions. For ‘three’ he puts ‘that which succeeds that which succeeds that which succeeds that which something succeeds and which succeeds nothing’ and for ‘two’ he puts ‘that which succeeds that which succeeds that which something succeeds and which succeeds nothing’; and now he has a sentence with ten occurrences of ‘succeeds’; he replaces these occurrences with ten occurrences of the variable S and he prefixes the restricted quantifier ‘for every succession relation S’; and that’s his translation; and it’s true. We might lazily say that he has managed to ascribe succession to three and two. But that’s a bad way to put it. It’s not that there’s a particular pair of things to which he has ascribed all the succession relations, all at once; because which pair is the pair in question varies from one succession relation to ­another. Yours,

304.  To Murray MacBeath, 22 September 1989 [Princeton, NJ] Dear Murray MacBeath, Thank you very much for the paper on communication and time reversal.1 I hadn’t seen it, and I’m very glad I have now. It’s fun, ingenious, and completely convincing. Before reading it, I too would have doubted that communication was pos­ sible, though perhaps with less confidence than Lucas.2 No comments, I’m afraid, because there’s nothing there to dispute. The same goes for ‘. . . Who’s Father?’.3 I’m very glad you brought it to my attention. There I do have one comment. You ask (page 417) why I said ‘perhaps there must be loops if there is reversal’. What I had in mind is that perhaps, at least in a world like ours, there’s some causal influence to any point from any point on the surface of its past light cone. (The net electromagnetic force on me is a vector sum of contributions from sources all over my past cone.) Now let there be a long thin strip of reversal with two points in it, x being the later/EARLIER one and y being the LATER/earlier one. (They’d better both be on the edge of the strip of reversal. And   ‘Communication and Time Reversal’ (Macbeath 1983).   A Treatise on Time and Space (Lucas 1973, 47).    3  ‘Who Was Dr. Who’s Father?’ (Macbeath 1982).

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305.  To Hartry Field, 5 October 1989

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they’d better be both on the same edge, say the eastern edge.) Take a point z, outside the strip, on the intersection of x’s past cone and y’s future cone. Then what happens at x depends at least somewhat on what happens at z, what happens at z depends at least somewhat on what happens at y, what happens at y depends at least somewhat on what happens at x. A loop. However (1) another possible world might have more causal insulation than this one, and (2) if the reversed region were a different shape there might not be anywhere to put the point z, and mainly (3) a looped causal chain of events is something more than just a loop of some sort of causal dependence from point to point. Yours, David Lewis

305.  To Hartry Field, 5 October 1989 [Princeton, NJ] Dear Hartry, For quite a while I’ve meant to write you a reply to Section 2 of ‘Realism, Mathematics and Modality’1 – Lewis versus the epistemological challenge to math­ em­at­ic­al realism. My excuse that it would be better to send you a completed draft of Parts of Classes first went away a few months ago; your impending visit has prodded me to actually do the job. Maybe we can talk about this when you’re here, if you like – and if there’s a possible time, which there may not be. Your point one: statements partly about mathematics. Agreed. I meant to be talking about the purely mathematical part of our knowledge. I accept the ‘obvious strategy’ of splitting up mixtures. As to the difficulty of doing the splitting: I leave it to you to do the job – more power to you! – and I don’t say it can’t be done. I accept classical mathematics as literally true not because of its alleged indispensability to science, but out of theoretical conservatism (see PoC draft, Section 2.8). Your point two: in what sense necessary? – Absolutely necessary, necessary simpliciter; i.e. true at all worlds, with no accessibility restriction. But if you don’t believe in the many worlds, as I dare say you don’t, is there any neutral way to identify the sense I have in mind? Maybe not. Anyway I don’t know how to. That there’s a 1   ‘Realism, Mathematics and Modality’ (Field 1988). A revised version of this paper was published in Realism, Mathematics and Modality (Field 1989, ch. 7).

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sharp delineation of absolute possibility and necessity (unlike the fuzzy delineation of logical ‘possibility’, which depends on which vocabulary gets classified as logical, and unlike the fuzzy delineations of various kinds of restricted possibility) is a consequence of the many-worlds theory of possibility, not an independently plausible motivation for it. For me, absolute possibility is not a restriction of logical ‘possibility’. There do not exist any impossible, but ‘logically possible’, worlds inhabited by married bachelors, numbers without successors, sets without singletons, unfundiert sets, etc.; so the definition of absolute possibility needs no restriction to rule out such worlds. It’s otherwise for an ersatzer: he does need to restrict to get absolute possibility, since there do indeed exist ersatz impossible but ‘logically possible’ worlds (= purported world-stories, such as models or their theories) with married bachelors etc. Yes: if I believed in theology, I’d say many of the same things about it that I do about math. But I don’t, so I don’t. The relevant difference, say I, is that the­ ology is false and math is true. Justify that? What do you think I am, some kind of foundationalist? Your point three: counter-mathematical conditionals. They can be intelligible in the Mackie way, as elliptical arguments with contextual clues to how they’re to be filled out, though (like Mackie) I’d make that a matter of assertability rather than truth. That covers your example: what if the axiom of choice were false? However that is not the right sort of example. It isn’t a supposition that the mathematical objects are missing or different. For I take it the axiom of choice has nothing especially to do with the mathematical objects, though it applies to them along with all else. It’s a framework principle (PoC, Section 3.3); it can be stated as a schema using plural quantification, and a case of it can be stated non-schematically using plurals and mereology together. Since the question is about knowledge of the existence and nature of mathematical objects, the counterfactual supposition ought to be something like: what if there were no classes? Or none but hereditarily finite ones? Or none past rank omega-plus-17? Or what if there were unfundiert loops or descending chains? And here I stand by what I said: there’s nothing sensible we can say about how things would be different under these suppositions. Anyway, not about how the physical world would be different, or how our mathematical beliefs would be different. If we are Platonists, will we want to say that if the axiom of power set, or Fundierung, or . . . were false, then mathematicians would believe it false? Not me! (Or rather, I’ll want to say it only if I feel like asserting any old truth however out of place in the conversation. Of course I do think that any old counterfactual with an impossible antecedent is true.) Your point four: not putting the challenge in modal or counterfactual terms. OK, let’s talk about explaining the actual correlation between what’s true about

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305.  To Hartry Field, 5 October 1989

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mathematics and what we believe. I say that a full causal explanation of why we’re right consists of (1) a full causal explanation of why we believe only mathematical statements with so-and-so property, plus (2) the fact that all mathematical statements with so-and-so property are necessarily true. The causal explanation (1) can presumably be had, though I can’t produce it. It will be a biological and psy­cho­logic­al and sociological affair, and truth of mathematical statements needn’t enter it. ‘So-and-so property’, in an age of axiomatization, can be the property of either being one of a certain short list of axioms or else being deducible in certain ways from those axioms. And there’s no reason why (1) has to cover all the axioms and rules in one fell swoop instead of piecemeal. Compare explaining a chance meeting. Why did I happen to meet Frank Jackson in the Adelaide airport two months ago? Well, there’s (1) a causal ex­plan­ ation of why I was there then; and there’s (2) a causal explanation of why Frank was there then; and those two separate explanations between them add up to the full and correct explanation of why we were both there then, and hence met. That’s all there is to it. And had it somehow been a necessary truth that Frank was there then, no causal explanation of why he was there then would have been possible or would have been required; then part (1), plus the necessity of his being there, would have been the full and correct explanation of why we met. You might want an explanation of our meeting to be robust, in the sense that it would have explained our meeting even if the circumstances had been somewhat different. It could have been robust, if we’d met by prearrangement. But as it was, the meeting was fortuitous; we wouldn’t have met if circumstances had been somewhat different; so a robust explanation of our meeting couldn’t be right. Likewise you might like an explanation of the actual correlation between what we believe about mathematics and what’s true to be robust, in the sense that it would still have applied even if our beliefs and the truth had been somewhat different. On one side, that’s a way back toward those fishy counterfactuals about what we’d have believed if, per impossibile, the mathematical truth had been different. And as for the other side, an explanation that would still have applied if our beliefs had been somewhat different, I say what I said before: robustness is not required for correct explanation, and sometimes an explanation can be correct only if it isn’t robust. I don’t know how fortuitous the meeting may be between our mathematical beliefs and the mathematical truths. That is, I don’t know how narrowly we escaped having different mathematical beliefs and including some false ones. But even if it is fortuitous, a fortuitous meeting still can be correctly explained. You say that all you want is explanation. I say you have it, or rather you would have it if you found out the naturalistic explanation of why we believe what we do, and also accepted the necessary truth of the mathematics. It wouldn’t be an

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­ex­plan­ation that justifies us in mathematical belief, of course. That wasn’t in the bargain. What do you think I am . . .? One comment at a different point (page 241): the equal goodness of conflicting systems of mathematics. I don’t think you should say this; or anyway not with respect to the examples of choice versus its negation, or the continuum hypothesis versus its negation. For I think you should think that these alternative assertions are not alternative fictions about the goings-on in Platonic heaven; rather, they are open questions (well, not really so very open in the case of choice!) formulated in the topic-neutral, ontologically innocent framework of plural quantification and mere­ ology. (PoC Section 3.3; I dare say the same goes for the continuum hypothesis as for choice, though I don’t discuss it.) To get a better example, you could take assertion versus denial of some strong axiom of infinity – even if the axiom can be formulated in framework language, the only way it can come true is thanks to the sets, and hence you’d regard the assertion, if not its denial, as a fiction. In view of the categoricity of mereologized arithmetic (PoC Section 4.8) any other good example needs to involve a system that rejects some bit of standard iterative set theory – conflicting systems of fundiert versus unfundiert set theory, for instance. See you next week! I’m looking forward to it. Yours, c: Burgess

306.  To W.V. Quine, 10 November 1989 [Princeton, NJ] Dear Van, Section 2.6 of my June draft of Parts of Classes ended with the conclusion that the project of ‘Ramsifying out the singleton function’ fails because we can’t at that stage of the game quantify over relations. If we try it by saying ‘there are some pairs’ we need a prior notion of ordered pair; but we can’t at that stage of the game use a set-theoretical definition of pairing, and primitive pairing would be much of a muchness with the primitive singleton function that we were trying to do away with. As you know, that conclusion was wrong. Given plural quantification and mereology, Hazen has shown how we can, in effect, quantify over ordered ’tuples of

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306.  To W.V. Quine, 10 November 1989

609

atoms; and you have finished the job by showing how to get from there to ordered ’tuples of fusions of atoms. So we can say, in effect, that there are some ordered fusion-atom pairs that satisfy the appropriate conditions for a singleton function. Independently, and near enough simultaneously, John Burgess found a quite different way to accomplish the same thing. I’d like to include these new developments in Parts of Classes. Here is how I’d like to do it, if you and the others consent. In the first place, Section 2.6 should end not with the statement that there’s no satisfactory way to introduce pairing, but rather with the statement that introducing pairing is ‘unfinished business’. Then I’d like to add a co-authored appendix to the book, under the names (in alphabetical order) of Burgess, Hazen, Lewis, and Quine. I would like to write it myself, in the same style as the rest of the book, and submit it to the three of you for approval. The appendix would give the Burgess method of introducing pairing, then the Hazen-Quine method, then some brief discussion of what difference the possibility of introducing pairing makes to things said earlier. I have just signed a contract with Blackwell to publish Parts of Classes, and I have given them a manuscript. (Not including appendix or adequate correction of 2.6.) The schedule is a bit tight: I’m to check the copy-edited manuscript in December or January and read proof in May or June, for a publication date in September 1990. I’ve talked to Stephan Chambers at Blackwell about the possibility of adding an appendix, and he says that it can be done if I’m quick about it, and if the co-authors can agree. He would prefer (but this is negotiable) an arrangement on which you and Hazen and Burgess each had a separate contract with Blackwell, receiving a fixed fee rather than a fraction of the royalties. He would rather like it if the rest of you were willing to let me take responsibility for checking edited manuscript and proof of the co-authored appendix, but he is very far from insisting on this. Chambers doesn’t know yet, by the way, that you are one of the proposed coauthors. Hazen told me that ‘a correspondent’ had suggested the extension to ‘tuples of fusions, and I guessed wrong who this correspondent was. Burgess and Hazen consent in an unspecific way to the co-authored appendix, though we haven’t yet talked about fees or royalties, whether they want to check the proof, and so on. Whether I can write something they are happy to put their names to remains to be seen. I’d have to be very careful not to say as spokesman for the four some of the things I myself would say. Especially things about the ontological innocence of plural quantification and mereology: Hazen, at least, dissents vigorously. Would you be willing to join me in such a plan? Or in a plan somewhat resembling it? Yours, David Lewis

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307.  To Allen P. Hazen, 20 November 1989 [Princeton, NJ] Dear Allen, I heard from Bruce  L.1 that it was now official that Len2 was taking early retirement. By the way, could you please tell Bruce not to order either of the two new D.M. Armstrong books for the Boyce Gibson – they’ll both be in the carton from me.3 Right, I’d taken the point that a linear ordering of atoms was all you needed. I’ll write the appendix accordingly. But I wonder if there’s any more obvious reason to think there’s a linear ordering than there is to think there’s a well-ordering. Burgess’s method doesn’t handle gunk as it stands, but is rather easily extended so it does. The best I’ve been able to think of for the Hazen-Quine method is to splice a biggish chunk of the Burgess method into it – which may be something like what happens in your letter, which I haven’t yet digested fully. No, I wouldn’t like to posit atoms as limits of all ultrafilters of Oobleck. Anyway, not as an a priori, certain matter. Atomicity is nice, the method of wishful thinking (aka the pragmatic method) is a legitimate method of gaining knowledge, it’s reasonable to believe in spacetime points – but not to believe in them with the utmost confidence. You and Burgess have agreed in principle to letting me write the appendix to appear under all four names. Quine has not yet answered my letter. I’d better get moving on writing the thing! Practical question: you must, of course, give your approval to what’s to appear in your name. But would you be willing to authorize me to act for you in (1) making changes at the request of other co-authors that don’t affect the description of your work, (2) checking copy-edited manuscript to approve or disprove editorial alterations, (3) checking proof, and (4) indexing? I’ve changed Section 2.6 a bit. When the Ramsey sentence of mereologized arithmetic is written, then axioms may include ‘unofficial’ axioms to the effect that no singleton is part of any cat, or whatnot. So prior to the Ramsification, there’s supposed to be a division between individual atoms and atoms that end up being singletons. A possible source of uncertainty, controversy, ideological burden – granted. Necessary for categoricity of MA, though of course that might be relaxed. Yours,   Bruce Langtry.   Leonard Goddard, who was Boyce Gibson Professor of Philosophy at the University of Melbourne from 1976 to 1989. 3   (Armstrong 1989a, 1989b). 1 2

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308.  To George Boolos, 1 December 1989

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308.  To George Boolos, 1 December 1989 [Princeton, NJ] Dear George, I wrote to Quine pointing out that his addition to what Hazen had done, or alternatively Burgess’s method, makes it possible to Ramsify the singleton function, given the framework of mereology and plurals. I invited him to sign on as a co-author of an appendix to Parts of Classes that would explain this. You’ll like his reply – I’m delighted with your news . . . Mereology and plurals prove to be a for­mid­ able battery. We are the new and true Pluralists. By all means write the appendix and count me in.1 We? How much do you think he’s granting us? It would be at least somewhat peculiar to call yourself a ‘new and true Pluralist’ without granting ontological innocence of plurals. If he does grant innocence, I reckon that’s a change of position. It seems to me that his position on plurals, on the strength of previous writings, ought to be that ontological commitment is defined only with respect to a translation into first order; if you do translate then plural quantification isn’t innocent because it’s guilty, if you don’t translate then it isn’t innocent because its ontological commitment is un­defined. --Angelelli (Texas) brought it to my attention that Zermelo uses ‘Teil’ or sometimes ‘echter Teil’ to mean ‘nonempty proper subclass’, and says straightway that singletons have no parts: van Heijenoort, page 202.2 Actually, ‘Teil’ for (proper) subset goes back at least to Cantor. ‘Teilmenge’ is now the standard word for subset, though ‘Untermenge’ also exists. I’m not sure how interesting this is. Is it really evidence that others have found my thesis intuitively right? Is it just a technical usage of whatever near-enough word was handy to grab? Is it a hangover from times before anyone was very clear at all about membership, part-whole, and set inclusion? Yours,

1   Letter from W.V. Quine to David Lewis, 16 November 1989. However, in a letter dated 17 January 1990 Quine asks Lewis to drop him as a co-author of the Appendix to Parts of Classes. 2   From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 (van Heijenoort 1967).

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309.  To John Etchemendy, 15 December 1989 [Princeton, NJ] Dear John, Thank you very much for the preprint copy of your book on logical consequence.1 I’ve just finished reading it. I hereby applaud both doctrine and presentation. No criticisms at all, but I do have three comments. (1) When I took my first logic course in 1959 – a peculiarly philosophical undergraduate seminar taught by Michael Scriven – I remember being taught that there were three varieties of implication: material, formal, and strict. Material and strict I have heard of ever since, but formal? Who he? Somebody early in this century, maybe Russell, maybe not, tried responding to the ‘paradoxes of material implication’ just by slapping on universal quantifiers. The idea was to analyse Leslie is a bachelor implies Leslie is a man for instance, as the ‘formal implication’ All x (x is a bachelor materially implies x is a man). (Sic, don’t ask for quotation marks; ‘implies’ and ‘materially implies’ were meant to be object-language connectives.) This misguided notion must have disappeared after coming under well-deserved criticism – so I thought until I read your book. (2) My favourite way of thinking of objectual quantification helps make it easy to see Bolzano and Tarski as much alike. The truth clause for the quantifier is ‘All x . . .x. . .’ is trueL iff, for all o, ‘…o. . .’ is trueL+. (Or maybe it’s all o within some implicit restriction.) This looks like flagrant usemention confusion, right? But it isn’t; that ‘+’ at the end saves it. L+ is the Lagadonian extension of L: it has the syntax and vocabulary of L, but in addition each thing (or each within some restriction) serves as a name of itself. L+ is not a very handy language to speak or write, as Gulliver said, but it’s a fine thing to allude to in writing clauses for the quantifiers of L.  Lagadonian extension can go further: for instance each set may serve as a predicate applying to all and only its members, each property may serve as a predicate applying to all and only its instances, . . . . Objectual quantification is Lagadonian substitutional quantification. (3) Somebody might say, and it’s a particular somebody whom I have in mind: look, let the necessity and the a priori certainty of logical truth go hang. Let ‘logical truth’ be just a classification of truths by subject matter, on a par with ‘chemical   The Concept of Logical Consequence (Etchemendy 1990).

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309.  To John Etchemendy, 15 December 1989

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truth’, ‘historical truth’, . . . . Maybe we can say in general that a ---ical truth is a truth that is expressed using just the ---ical vocabulary. (Or better, a truth that is expressed by using just the ---ical vocabulary essentially, as when we start with a ---ically true universal generalisation and introduce non---ical vocabulary into it by in­stan­ti­ation.) Well then, is it so bad that ‘there are more than 17 things’ should come out as logic­ al­ly true (if the absolutely unrestricted quantifier is taken to be logical vocabulary)? It is a truth that can be expressed using just the logical vocabulary. And is it so bad that ‘there are at most 17 things’ would have come out logically true if (speaking unrestrictedly) there had been at most 17 things? Compare megethological truth. Megethology is the study of how many things there are in all of Reality. Elementary megethology limits itself to things that can be said using the resources of elementary logic. The elementary megethological vocabulary is exactly the same as the customary logical vocabulary. It’s fine and dandy to say that ‘there are more than 17 things’ is a megethological truth; and that ‘there are at most 17 things’ would have been a megethological truth, if (speaking unrestrictedly) there had been at most 17 things. ‘Megethological truth’ really is a subject matter classification. Now you should reply that although ‘logical truth’ might have been meant as a mere subject matter classification on a par with ‘chemical truth’, ‘(elementary) megethological truth’ etc., obviously that’s not how it really is meant. There’s no denying that ‘logical truth’ does carry a connotation of necessity and a priori certainty. And with that, of course, I agree. Now think of a revisionist: someone who much mistrusts the notions of necessity and a priori certainty, someone who is not above a bit of terminological piracy and goes in for grabbing pre-existing terms and redefining them to make them respectable by his own lights. Such a one might with his eyes open see fit to relaunch ‘logical truth’ as a mere subject matter classification. And that, I suggest, is Quine’s part in your story. I’ve known for some time that I have a problem of the sort your book is about. As you know, I’m interested in truths that can be expressed using what I call the ‘framework’ of Parts of Classes, Chapter 3: the resources of plural quantification and mereology (and it’s worth adding that the quantifiers can be absolutely unrestricted). Some of these truths I call ‘principles’: for instance the transitivity of the part-whole relation; for instance the axioms of choice and replacement, which turn out to be expressible in the framework, without recourse to set theory. (Replacement is a schema; or it might be expressed as a sentence by throwing in substitutional quantification, something I’m not averse to doing.) Only terminological conservatism stops me from wanting to call these principles ‘logical’. Other truths expressible in the framework – if indeed they are true – I call ‘hypotheses’ (or even ‘speculations’). These mainly belong to non-elementary megethology. The framework has the resources to express not only tame hypotheses like

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‘There are more than 17 things’, ‘There are infinitely many things’, ‘There are uncountably many atoms’, but also, for instance, ‘There are inaccessibly many atoms’, ‘There are measurable-cardinal many atoms’. Even if I were a bit of a revisionist (but not the sort who wants to junk the notions of necessity and a priori knowledge), no way would I want to call these megethological hypotheses and speculations ‘logical truths’. But what’s the difference between the ‘principles’ and the ‘hypotheses’ and ‘speculations’? They’re all alike expressible in the language of the framework alone. They’re all necessary if true at all, according to my views on modality. They’re all known a priori if known at all; anyway, there seems to be no way of checking up on them a posteriori. I don’t want to retreat to a psychological distinction: I just feel more sure of some than of others. Or a social distinction: some are more controversial than others. (That could change overnight.) I can’t really believe that there’s a primitive distinction. I can’t really believe there’s no real distinction. So what’s to say? It matters a lot. Because there’s one of these truths expressible in the framework language that I haven’t mentioned yet, and I don’t know whether it belongs with the ‘principles’ or the ‘hypotheses’. It’s the Ramsey sentence of Mereologized Arithmetic. Yes; it’s wrong what I said in PoC 2.6 and in the lectures about Ramsification being unworkable because there’s no notion of pairing available. Since a few months ago, there are two ways known of introducing ordered pairs within the resources of the framework (provided you have infinitely many atoms and not too much atomless gunk). One’s due to Burgess, the other’s due to Hazen and Quine. So the stuff I don’t understand the status of includes all of set-theoretical math, both the megethology part and the Ramsified Mereologized Arithmetic part. Not nice. Yours,

310.  To John Bigelow, 26 February 1990 [Princeton, NJ] Dear John, Thanks for ‘Sets are Universals’.1 I don’t think I’ve seen it, but maybe when I read it a bell will ring. Parts of Classes is in press; estimated publication date September 1990; Blackwell. In citing it, say in parentheses: with an appendix by John P. Burgess, A.P. Hazen, and David Lewis.   (Bigelow 1990a).

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311.  To D.M. Armstrong, 28 March 1990

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The appendix is the main change from the June 1989 draft, which I think you have. (It’s the one that’s stapled up like a little booklet.) The old section 2.6 asked whether you could eliminate the primitive member-singleton relation by Ramsi­ fication, and concluded that you couldn’t: the framework of plural quantification and mereology, before the advent of set theory, has no way to quantify over relations. Wrong. It can be done; Burgess found one way to do it, Hazen found another. The appendix says how. So a structuralist set theory is possible. I have mixed feelings about it – it is a reform of mathematics to make philosophy easier, and that I generally disapprove of – but probably I’m sufficiently bothered by primitive singleton to prefer to go structuralist. I’ll send you the appendix separately. Haecceities? OK. Presentism? !!?? Are you a slow learner? Don’t you discover, at every new moment, that there exists a time that you previously didn’t believe in? I’ll say the usual about the book: yes, do send it, I look forward to reading it – but I won’t necessarily comment.2 The editor of Dialogue invited me to reply to your paper on essences of worlds.3 I said I had nothing to add. It’s a nice piece. I’ll be at the Sydney and Massey conferences, and in Melbourne for most of the time in between. Steffi will probably be with me for the Sydney conference and two weeks after, partly driving and partly in Melbourne. Yours,

311.  To D.M. Armstrong, 28 March 1990 [Princeton, NJ] Dear David, I didn’t quite say that the Burgess/Hazen result was bad news for natural-class nominalism. What I said was that the Burgess/Hazen result makes it possible to Ramsify the singleton function and thus makes set-theoretical structuralism a ten­ able position; and set-theoretical structuralism is bad news for natural-class nom­in­ al­ism. But the B/H result doesn’t force us to become set-theoretical structuralists. It only opens the option. Despite the result, you can still think that we do have in mind some one definite singleton function. This is of course what you do think, on the basis of the theory of singletons as unithood facts; and it’s what I’m at least somewhat inclined to think, just on the basis of mathematical conservatism.   John Bigelow, Folk Time for Real People (draft manuscript).   ‘The World Essence’ (Bigelow 1990b).

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Set-theoretical structuralism is bad news for natural-class nominalism because it says that there is no one thing that is, unequivocally, the class with such-and-such members. Consider all the cats (all the cats, in all of space and time and, if I’m right, all the worlds). Consider some other things, equally many, that are as utterly miscellaneous as can be. We have many structurally suitable functions, singleton1, singleton2, . . . and if structuralism is true, no one of these has any privileged place as the one genuine, intended singleton function. Now we have a fusion F of atoms which is the fusion of the singletons1 of the cats, and hence is the class1 of cats; but this same F is also the fusion of the singletons2 of the utterly miscellaneous things, and hence is the class2 of the miscellaneous things. If structuralism is true, there’s no saying – except relative to a singleton function – whether F is the fairly natural class of cats or the unnatural class of the miscellaneous things. In itself, F is neither natural nor unnatural. That’s the bad news. I’ll get my (first and only) proofs of Parts of Classes in a few days, and return them early in May. So I can soon give you the page references you need for ‘What are Classes?’ But when I return the proofs, that’s my last chance to write the citation of ‘What are Classes?’ So I hope to know by early May where (and preferably when) it will appear. If that’s not known in time, then as second-best I’ll cite it as a paper presented at so-and-so conference in South America; in which case I need the name of the conference, place, and date.1 [. . .] I hope it works out that I can stay with you in the last week of June, but if Caroline and Francesco are in the house, I’ll be happy to stay at Palace Road (Why? What palace?) instead. No need to know in advance. See you then, in any case. Yours,

312.  To Steve Pyke, 27 July 1990 Melbourne, Australia Dear Steve Pyke, I am an old-fashioned analytic metaphysician, in pursuit of hypotheses about what things are the elements of being, and about how all else may be reduced to patterns of these elements. I am notorious for claiming that these elements must include 1   XII Congreso Interamericano de Filosofía, Buenos Aires, 26–30 July 1989. See ‘Classes Are States of Affairs’ (Armstrong 1991).

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313.  To John Burgess, 1 August 1990

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many that are merely possible, no part of this world that we ourselves live in, but none the worse for that. Apart from that, I am philosophically conservative: I think philosophy cannot credibly challenge either the positive convictions of common sense or the established theses of the natural sciences and mathematics.1 I hope this is what you needed? Best regards, David Lewis PS I found the ‘Firkin & Flounder’ – Thanks! But preferred the guest bitter to their own beer.

313.  To John Burgess, 1 August 1990 Melbourne, Australia Dear John, Let me tell you about some discussions I’ve been having with Allen Hazen and Jenny Davoren. (Jenny is a math-and-philosophy honours student here.) I’d be interested to know if you think the following is OK as far as it goes, and if you can see any way to take it further. We have that Ramsified 2nd-order-iterative set theory follows from 1 ) Principles of 2nd-order mereology, left informal, including versions of replacement and choice 2) Megethological hypotheses P) If something is small, its parts are few U) The fusion of a few small things is small I–) There are infinitely many atoms (this enables us to reduce polyadic 2ndorder quantification to monadic) I) There are some atoms that are infinitely many and nevertheless few. 3) The Ramsey sentence of mereologized arithmetic R) For any small thing x, there is a function S such that, taking the individuals to be the parts of x, S obeys the axioms of Functionality, Domain, Distinctness, and Induction. (You’ll see that I’m ignoring atomless gunk for convenience – assume everything is a fusion of atoms.)   This paragraph was published in (Pyke 1993), along with Pyke’s photo of David Lewis.

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We may wonder whether we really had to start with something as complicated as R.  No, we didn’t; the final section of the PoC appendix, based mainly on your ‘Ramsification Makes Foundation Redundant’ note, shows that R is equivalent to the seemingly weaker R–) There are a small thing x and a one-one function S such that all parts of x and all small things that don’t overlap x are in the domain of S, and such that the range of S consists of all atoms that are not part of x. We can go further (as I think your note did). Assume that the framework principles, together with I–, suffice to reproduce familiar results of cardinal arithmetic. We have that the atoms that aren’t part of x are equinumerous with all the atoms; and the small things that either are part of x or don’t overlap x are equinumerous with all the small things, so a fortiori the small things in the domain of S are equinumerous with all the small things. Let barelymany =df equinumerous withtheatoms. We have that R–, and hence R, are equivalent to

M) The small things are barely many.

M looks like another megethological hypothesis, a condition on the size of Reality. So the Ramsey sentence as an independent assumption has faded away: the foundations of set theory reduce to framework principles plus megethology. What’s more, M adds nothing to the megethology we already had to assume to get Unions and Power Sets. I– and P and U together imply M. We can say something a bit more definite. Consider P–) If something is small, its parts are at most barely many (that is, either barely many or few) which of course follows from P. Assume I–. Then CLAIM : M Û P - & U First, M ⇒ P– trivially. The small things that are part of a given small thing can’t be more numerous than all the small things. Second, M ⇒ U by the argument of fn 3, Ch 4, PoC.

(My worries about * go away once we have polyadic 2nd-order quantification so we can talk straightforwardly about equinumerosity.)1 Assume M; assume for reductio not U, some large thing ℓ is the fusion of a few small things. Imaging under the one-one 1   The asterisk in this parenthetical remark refers to the paragraph below beginning ‘Whenever ℓ is the limit of x . . .’ (p. 619).

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313.  To John Burgess, 1 August 1990

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function from the many atoms of ℓ to all atoms, we have that Reality likewise is the fusion of a few small things, s1, s2, . . . . But now we can encode anything, large or small, by a single atom. Given x, we have the few small intersections x ∩ s1, x ∩ s2, . . . . By M, we can encode each of these small things by an atom. So we encode x by a few atoms; hence by the small fusion of these atoms; hence by a single atom. So there are as many atoms as fusions of atoms. This completes the reductio. Finally, P– & U ⇒ M. The framework is supposed to give us any desired version of choice, so we have a well-ordering of all the atoms. Further, we have an initial wellordering of all the atoms: that is, one in which each atom is preceded by only a few others. Given a well-ordering, unless it’s already initial, take the first atom that is preceded by many others. Imaging under the one-one function from these many preceding atoms to all the atoms, we have a new well-ordering of all the atoms; and this new well-ordering, being isomorphic to a segment of the old one in which each atom is preceded by only a few others, is initial. Atom b bounds x iff every atom of x precedes b in our initial well-ordering. If any atom bounds x, there is a first atom that bounds x; call this the limit of x. Whenever x is small it is bounded: for any atom a of x, let sa be the fusion of a and all atoms that precede a; the sa’s are small and few; so by U their fusion s is small; so some atom b falls outside it; and b bounds x. So every small thing has a limit. Whenever ℓ is the limit of x, x is part of sℓ. By P–, since sℓ is small its parts are at most barely many. So each of barely many atoms is the limit of at most barely many small things. So, assuming again that framework principles, plus I–, reproduce car­ dinal arithmetic, we have at most barely many things with limits, hence at most barely many small things.2 And each of barely many atoms is small, so we have exactly barely many small things. QED --As a rabid anti-revisionist, of course I’m ready to assume P; so all I really need to know about P– is that it’s a consequence of P. Still, as a matter of idle curiosity, what would happen if we just assumed M, that is U and P–, without assuming P? What does that tell us about the size of Reality? We know how to say that some things are fewer than some others. Say that x jumps y iff the atoms of x are fewer than the atoms of y but the atoms of y are fewer than the parts of x. Say that x hits y iff the parts of x and the atoms of y are equinumerous. (From which it follows that the atoms of x are fewer than the atoms of y.) P says that Reality is unjumped and unhit, whereas P– says only that Reality is unjumped. So 2   In the left margin, Lewis wrote ‘* (see page 6)’. The ‘see page 6’ remark refers to the paragraph below starting ‘that we could use (along with a form of choice) . . .’ (p. 621).

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Philosophical Letters of David K. Lewis

if we assumed only M (that is, P– & U) and left P in abeyance, we’d be countenancing the possibility that Reality is of such a size as to be hit but not jumped. What do we know about such sizes? – Not much, it seems. Here I’m forced to shift gears, and assume that the sizes I’m interested in are cardinalities; that is, sizes of mere sets. So be it. So I’m asking: what do we know about regular cardinals (that’s U) that are hit but not jumped? Given GCH, the answer is easy: nothing is jumped, successor cardinals are hit, limit cardinals are neither hit nor jumped. Given GCH, P– adds nothing at all to U. But what if GCH is false? Let’s take consistency with first-order set theory, say ZFC (but should it be something stronger?) as our standard of epistemic possibility. There are many consistent hypotheses contrary to GCH, and fortunately this is a topic Jenny has some knowledge of. We wondered, in particular, whether it was consistent to suppose X) No regular cardinal is hit but unjumped

That would be interesting, because X & U & P– ⇒ P, so X & M ⇒ P, so X would make Power Sets redundant. (Not that I would propose that henceforth we should assume X and derive P!) Since a successor cardinal must be either hit or jumped by its predecessor, and is regular, X amounts to the conjunction X1) Every successor cardinal is jumped, and X2) No regular limit cardinal is hit but unjumped.

If only we had 2α = α++ for all α, we’d have X. As for X1, α would always jump α+. As for X2, if β hits λ and λ is a limit, β+ would jump λ; because we’d have β < β+ < λ = 2β = β++ < β+++ = 2β+. By Easton’s Theorem,3 it’s consistent that 2α = α++ for all regular α. That’s good enough for X2: if β hits λ, λ a limit, either β+ jumps λ and we’re done, or else β+ also hits λ. In the latter case – indeed, in both cases – β++ jumps λ. The argument is as before, except we have to note that β+ and β++, being successors, are regular. As for X1, we have several cases. If α is regular, whether successor or limit, α+ is jumped by α. If λ is a limit hit by some β, we saw how λ is jumped by β++; so λ+ is hit or jumped by β++; and in either case, λ+ is jumped by β+++. If λ is a limit jumped by some β, λ is jumped also by β+; so λ+ is hit or jumped by β+; and in either case λ+ is jumped by β++. So far so good. The remaining case is that λ is neither regular, nor hit, nor jumped: a singular

  ‘Powers of Regular Cardinals’ (Easton 1970).   

3

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313.  To John Burgess, 1 August 1990

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strong limit. Then λ+ is not jumped by anything below λ, and it is either hit or jumped by λ. How do we know that λ+ is jumped in this final case? It seems we know the opposite, at least for Easton models, such as the model that gave us 2α = α++ for regular α. Jenny reports something in Kunen, p. 267,4 which means that in Easton models, when λ is a singular strong limit, 2λ = λ+. So λ+ is an unjumped successor and X1 fails. Thus pursuit of the consistency of X via Easton’s Theorem looks to be a dead end. Jenny reports other things from Kunen, same place, that get into waters too deep for any of us. In these depths there lives a critter called 0#, who defies concise description.5 But anyhow Some successor of a singular strong limit is jumped ⇒ some uncountable set x of ordinals differs in cardinality from every constructible superset of x ⇒ 0# exists.

And with that we called it quits, for the time being. --I blithely assumed that ‘framework principles, plus I–, reproduce familiar results of cardinal arithmetic’. How can this be done? Of course the question is illdefined, since no official list of ‘framework principles’ has been offered. Of course it’s open to express the desired results in 2nd-order mereology and declare them ‘prin­ ciples’ forthwith. But it would be better if honest toil could derive them from premises much more obvious than themselves. Here’s the case Allen and I considered: whence can we derive the lemma L) There are many non-overlapping large things

that we could use (along with a form of choice) to make good the step marked * on page 3?6 Here’s a proof (due almost entirely to Allen). It assumes that we can develop a treatment of transfinite recursion, not to mention ordinary arithmetic, within the framework, using our initial well-ordering of atoms in the role of the ordinals – and what principles does that take? It uses U, which is OK in this application but seems as if it shouldn’t have been necessary. Of course it uses I–, which is to be expected. We have our initial well-ordering of all the atoms. Call an atom of Γ a successor or limit in Γ according as it does or doesn’t follow some other atom of Γ. (If we mean ‘in Reality’ we may skip the phrase.)   Set Theory: An Introduction to Independence Proofs (Kunen 1980).   See (Kunen 1980, 267–8). See also ‘The Bearing of Large Cardinals on Constructibility’ (Silver 1973). 6   Namely, the paragraph above beginning ‘Whenever ℓ is the limit of x . . .’ (p. 619). 4 5

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Case 1: all atoms are successors. Then treat the atoms as natural numbers. Our many large things can be the fusion of all powers of 2, the fusion of all powers of 3, . . . and so on through all the primes. Case 2: some atoms are limits. Then whenever x is large, some atoms are limits in x. Whenever x is large, x contains many atoms that are successors in x, and many that are limits in x. For if not, using U as in the second paragraph of page 3,7 we have an atom b of x that follows all the successors in x, or that follows all the limits in x. It is preceded by few atoms of x, so it is followed by many atoms of x. Among these followers is a first, which is a successor in x; among them also are limits in x; so b neither follows all the successors in x nor follows all the limits in x. Now define a transfinite sequence as follows G 0 = Reality

Γα + 1 = Fusion of all atoms that are limits in Γα except for the first atom of Γα ìï G  a if this is large G l = ía