Philosophy of Science Matters: The Philosophy of Peter Achinstein

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Philosophy of Science Matters

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Philosophy of Science Matters The Philosophy of Peter Achinstein Edited by Gregory J. Morgan

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1 Oxford University Press, Inc., publishes works that further Oxford University’s objective of excellence in research, scholarship, and education. Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With ofﬁces in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam

Copyright © 2011 by Oxford University Press Published by Oxford University Press, Inc. 198 Madison Avenue, New York, New York 10016 www.oup.com Oxford is a registered trademark of Oxford University Press 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, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Philosophy of science matters : the philosophy of Peter Achinstein / edited by Gregory J. Morgan p. cm. ISBN 978-0-19-973862-5 (hardcover : alk. paper) 1. Achinstein, Peter. 2. Science—Philosophy. I. Morgan, Gregory J. Q175.P5126 2011 501—dc22 2010035153

This book was set in Berling by SPi and printed and bound by Hamilton Printing Company.

1 3 5 7 9 8 6 4 2 Printed in the United States of America on acid-free paper

Contents

Preface, vii Contributors, ix 1

Ordinary Language and the Unordinary Philosophy of Peter Achinstein, 3 Steven Gimbel and Jeffrey Maynes

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Evidence, External Validity, and Explanatory Relevance, 15 Nancy Cartwright

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Maxwell, Matter, and Method: Maxwellian Methodology, Methodological Maxwellianism, and Methods of Historical and Philosophical Speculation, 29 Jordi Cat

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Achinstein’s Newtonian Empiricism, 44 Victor Di Fate

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Evidence and Objectivity in Achinstein’s Philosophy of Science, 59 Gerald Doppelt

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A Defense of Achinstein’s Pragmatism about Explanation, 72 Adam M. Goldstein

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On the Very Idea of a Theory of Evidence, 84 Philip Kitcher

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Mill on the Hypothetical Method: A Discussion of Achinstein’s Defense of Mill and Newton on Induction, 96 Frederick M. Kronz

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Waves, Particles, Independent Tests, and the Limits of Inductivism, 109 Larry Laudan

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What’s So Great about an Objective Concept of Evidence?, 124 Helen Longino

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The Objective Epistemic Probabilist and the Severe Tester, 135 Deborah G. Mayo

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Achinstein and Whewell on Theoretical Coherence, 151 Gregory J. Morgan

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Observationally Indistinguishable Spacetimes: A Challenge for Any Inductivist, 164 John D. Norton

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Making Contact with Molecules: On Perrin and Achinstein, 177 Stathis Psillos

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Achinstein and the Evidence for Evolution, 191 Richard A. Richards

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The Place of Artiﬁcial Selection in Charles Darwin’s Theory of Evolution through Natural Selection, 203 Michael Ruse

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Evidence and Justiﬁcation, 216 Kent Staley

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What Was Perrin’s Real Achievement?, 231 Bas C. van Fraassen

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Causes, Conditions, and the Pragmatics of Causal Explanation, 247 James Woodward

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Achinstein’s Replies, 258 Peter Achinstein

Index, 298

Preface

This book is a series of essays inspired by the work of Peter Achinstein, one of the most prominent philosophers of science of his generation, Jay and Jeanie Schottenstein University Professor at Yeshiva University, and long time professor at Johns Hopkins University. In addition to editing eight volumes, Achinstein has authored seven books: Concepts of Science: A Philosophical Analysis (1968); Law and Explanation: An Essay in the Philosophy of Science (Oxford University Press, 1971); The Nature of Explanation (Oxford University Press, 1983); The Concept of Evidence (Oxford University Press, 1983); Particles and Waves: Historical Essays in the Philosophy of Science (Oxford University Press, 1991); The Book of Evidence (Oxford University Press, 2003); and Evidence, Explanation, and Realism (Oxford University Press, 2010). Particles and Waves won the 1993 Lakatos Award, the highest honor for a book in philosophy of science. Surprisingly, the current volume is the ﬁrst book entirely devoted to Achinstein’s views and reactions to them. The book consists of nineteen short essays on various aspects of Achinstein’s corpus, followed by succinct replies by Peter Achinstein to each of the essays. Chapter 1, by Steven Gimbel and Jeffrey Maynes, provides a historical overview of Achinstein’s approach to philosophy of science; the essays that follow are organized alphabetically by author. They are weighted toward Achinstein’s most recent work on the notion of scientiﬁc evidence. Nancy Cartwright, Gerald Doppelt, Philip Kitcher, Helen Longino, Deborah Mayo, Richard Richards, and Kent Staley all consider how Achinstein’s conceptions of scientiﬁc evidence fare when applied to case studies or when compared with competing views of evidence. The essays of Victor Di Fate, Frederick Kronz, and John Norton look at the role of induction in scientiﬁc methodology, a topic not unrelated to a proper account of scientiﬁc evidence. James Woodward and Adam Goldstein consider questions related to Achinstein’s pragmatic theory of explanation. Gregory Morgan considers Achinstein’s interpretation of William Whewell, and Michael Ruse considers Achinstein’s early work on analogy in theoretical science. One distinctive aspect of Peter Achinstein’s approach to the philosophy of science is his use of the history of physics to

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illustrate and inspire philosophical views. Larry Laudan considersAchinstein’s use of the nineteenth-century wave–particle debate to assess the strengths of inductivism and hypothetico-deductivism. Stathis Psillos and Bas van Fraassen consider Jean Perrin’s relationship to the realism–antirealism debate and Achinstein’s use of Perrin’s reasoning to promote scientiﬁc realism. Jordi Cat considers Achinstein’s most recent article devoted to an interpretation of James Clerk Maxwell’s methodology. The title of the work is inspired by Achinstein’s attempt to create a philosophy of science that would be of help to working scientists. As reiterated by a number of the contributors, Achinstein begins The Book of Evidence with a story about a dean at Johns Hopkins who challenged Achinstein and perhaps other philosophers of science to produce philosophy of science that is of use to scientists. Whether Achinstein and the other authors have met this ideal I leave to the reader. At the very least, striving to meet this ideal is a useful heuristic in writing good philosophy of science. I thank Peter Ohlin of Oxford University Press, who supported this project and the parallel project to publish many of Achinstein’s papers in the book, Evidence, Explanation, and Realism (Oxford University Press, 2010). I am grateful for Petrina Guayasamin’s and Lucy Randall’s editorial and production expertise. My wife Stacey Welch deserves thanks for her emotional support and encouragement, which made organizing this collection possible. I also thank all the contributors, especially those who allowed me to abridge what were at ﬁrst much longer papers. While this volume is, among other things, a tribute to Peter Achinstein the scholar, allow me to end with some words about Peter Achinstein the mentor. It would not be an exaggeration to say that many of the contributors, myself included, would not have had the careers we have had or will have without our formative years as scholars working under and alongside Peter Achinstein and listening to his wise counsel. He has perfected the ﬁne balance between stinging criticism of poor argumentation and cheerleading the pursuit of academic excellence, a balance that makes him an exceptional mentor and advisor. Happy 75th birthday Peter, friend, mentor, and exemplar of historically informed, clear, and insightful philosophy of science. Gregory J. Morgan Hoboken, New Jersey, July 2010

Contributors

Peter Achinstein is Jay and Jeanie Schottenstein University Professor of Philosophy at Yeshiva University and Professor of Philosophy at Johns Hopkins University. He is the author of Concepts of Science: A Philosophical Analysis (1968); Law and Explanation: An Essay in the Philosophy of Science (Oxford University Press, 1971); The Nature of Explanation (Oxford University Press, 1983); The Concept of Evidence (Oxford University Press, 1983); Particles and Waves: Historical Essays in the Philosophy of Science (Oxford University Press, 1991); The Book of Evidence (Oxford University Press, 2001) and Evidence, Explanation, and Realism (Oxford University Press, 2010). He won the Lakatos Award in 1993. Nancy Cartwright is Professor of Philosophy at the London School of Economics and the University of California at San Diego, and a recipient of a MacArthur Fellowship. Cartwright is serving as the president of the Philosophy of Science Association for the years 2009–10. She has published several books including How the Laws of Physics Lie (Oxford University Press, 1983); Nature’s Capacities and Their Measurement (Oxford University Press, 1989); and Hunting Causes and Using Them: Approaches in Philosophy and Economics (2007). Jordi Cat is Associate Professor of History and Philosophy of Science at Indiana University. His research interests are primarily in history and philosophy of science, in particular the history and philosophy of physics and logical positivism. Among various topics in these ﬁelds, he is especially interested in models, scientiﬁc method, classical and quantum ﬁeld theories, and unity of science. He has published Otto Neurath: Philosophy between Science and Politics (1995) with Nancy Cartwright, Lola Fleck, and Thomas Uebel, and Master and Designer of Fields: James Clerk Maxwell and Constructive, Connective, and Concrete Natural Philosophy (Oxford University Press, 2010). Victor Joseph Di Fate is currently a student of Peter Achinstein’s at Johns Hopkins University. He works in history and philosophy of science, with a special emphasis on the history of scientiﬁc method.

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Gerald Doppelt is Professor of Philosophy and Science Studies at the University of California at San Diego and a University Academic Senate Distinguished Teacher. His research includes several publications in the philosophy of science on issues such as the nature of evidence, scientiﬁc realism, scientiﬁc change and progress, Kuhn and logical empiricism, values in science, and conceptions of scientiﬁc rationality. His work in political philosophy centers on John Rawls, liberalism, theories of justice, multiculturalism, feminism, and Marxian perspectives. Frederick Kronz is Director of the Science, Technology, and Society (STS) Program at the National Science Foundation (NSF). He was formerly Professor of Philosophy at the University of Texas at Austin and specializes in philosophy of physics. He has published in Philosophy of Science, Physical Letters A, and Synthese among other journals. Steven Gimbel is Associate Professor of Philosophy at Gettysburg College. His books include Exploring the Scientiﬁc Method: Cases and Questions (2011) and Defending Einstein: Hans Reichenbach’s Writings on Space, Time, and Motion (2006). His articles have appeared in Philosophy of Science, The British Journal for the Philosophy of Science, and Studies in the History and Philosophy of Modern Physics. Adam M. Goldstein is Assistant Professor of Philosophy at Iona College. His PhD thesis at Johns Hopkins, supervised by Peter Achinstein, concerns chance and explanation in evolutionary biology, a topic he continues to pursue. He is Associate Editor of the Darwin Manuscripts Project, where he is engineering a formal ontology of evolutionary processes, and he is Associate editor and Reviews editor at Evolution: Education and Outreach. Philip Kitcher is John Dewey Professor of Philosophy at Columbia University. He has written extensively on topics in the philosophy of science, the philosophy of biology, and the philosophy of mathematics. He is the author of Vaulting Ambition: Sociobiology and the Quest for Human Nature (1985); The Advancement of Science (Oxford University Press, 1993); and Science, Truth, and Democracy (Oxford University Press, 2001) among others. In addition, he has written books on Wagner’s Ring and Joyce’s Finnegans Wake. He won the Lakatos Award in 1987. Larry Laudan is Principal Investigator at the Instituto de Investigaciones Filosóﬁcas, Universidad Nacional Autónoma de México. He works in philosophy of science and legal epistemology. He has published many books including Progress and its Problems (1977); Beyond Positivism and Relativism (Westview Press, 1996); and Truth, Error and Criminal Law: An Essay in

Contributors

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Legal Epistemology (2006). He is former President of the Paciﬁc Division of the American Philosophical Association. Helen E. Longino is Professor of Philosophy and Chair of the Philosophy Department at Stanford University. She is currently completing a monograph analyzing the evidential structures and frameworks of inquiry of contemporary scientiﬁc approaches to the study of human behavior. She is the author of Science as Social Knowledge (1990) and The Fate of Knowledge (2002). Jeffrey Maynes teaches at McDaniel College in Westminster, Maryland, having been a student of Peter Achinstein’s at Johns Hopkins in the late 2000s. Specializing in the philosophy of language and linguistics, with an active research interest in ethics and moral psychology, his writings have appeared in Current Opinions in Psychiatry and Convergence Quarterly. Deborah Mayo is Professor of Philosophy at Virginia Tech and holds a visiting appointment at the Center for the Philosophy of Natural and Social Science at the London School of Economics. She is the author of Error and the Growth of Experimental Knowledge (1996), which won the Lakatos Award in 1998. The recent volume, Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science (co-edited with Aris Spanos), (2010), grows out of exchanges with philosophers of science on issues arising from that work. Gregory J. Morgan is Associate Professor of Philosophy at the Stevens Institute of Technology. He has published articles in Biology and Philosophy, The Journal of History of Biology, Journal of Molecular Biology, Trends in Biochemical Sciences, The British Journal for the Philosophy of Science, and Isis. He was co-winner of the 2009 Price-Webster Award from the History of Science Society. John D. Norton is a Professor in the Department of History and Philosophy of Science and Director of the Center for Philosophy of Science at the University of Pittsburgh. He works in philosophy of physics, with a special interest in Einstein, relativity, space and time, and general issues of induction and conﬁrmation. Stathis Psillos is Professor of Philosophy of Science and Metaphysics in the Department of Philosophy and History of Science at the University of Athens, Greece. He is the author of Knowing the Structure of Nature (Palgrave, 2009); Philosophy of Science A–Z (2007); Causation and Explanation (Acumen, 2002); and Scientiﬁc Realism: How Science Tracks Truth (1999). He is also the co-editor of The Routledge Companion to Philosophy of Science (2008). He is the co-editor of Metascience and has

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served as the President of the European Philosophy of Science Association (2007–09). Richard A. Richards is Associate Professor of Philosophy at the University of Alabama in Tuscaloosa. He has published on various topics in the history and philosophy of biology, from Darwin to phylogenetic inference, taxonomy and species, as well as on metaethics and aesthetics. In his book, The Species Problem (2010), he surveys the history of the species problem from Aristotle to modern systematics, and develops a solution based on the division of conceptual labor. Michael Ruse is the Lucyle T. Werkmeister Professor of Philosophy and Director of the Program in the History and Philosophy of Science at Florida State University. He is the author or editor of many books on the history and philosophy of science, especially evolutionary biology, including The Darwinian Revolution: Science Red in Tooth and Claw (2nd edition 1999); Monad to Man: The Concept of Progress in Evolutionary Biology (1996); and Can a Darwinian Be a Christian? The Relationship between Science and Religion (2001). Kent Staley is Associate Professor of Philosophy at Saint Louis University. His work centers on problems concerning experimental and statistical aspects of scientiﬁc inquiry and inference, particularly as these arise in physics. He is the author of The Evidence for the Top Quark: Objectivity and Bias in Collaborative Experimentation (2004). Bas C. van Fraassen is Emeritus Professor of Philosophy at Princeton University and Professor of Philosophy at San Francisco State University. He has been mainly concerned with what empiricism can be now. His research interests straddle philosophical logic and philosophy of science, with occasional forays into art, literature, and religion. His books include The Scientiﬁc Image (Oxford University Press, 1980); The Empirical Stance (2002); and Scientiﬁc Representation: Paradoxes of Perspective (Oxford University Press, 2008). He won the Lakatos Award in 1986. James Woodward is Distinguished Professor of History and Philosophy of Science at the University of Pittsburgh and J. O. and Juliette Koepﬂi Professor Emeritus of the Humanities at California Institute of Technology. He works on philosophical/normative issues in causation and explanation and on the empirical psychology of causal judgment and learning. He is the author of Making Things Happen (Oxford University Press, 2003). He won the Lakatos Award in 2005.

Philosophy of Science Matters

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1 Ordinary Language and the Unordinary Philosophy of Peter Achinstein Steven Gimbel and Jeffrey Maynes

1. INTRODUCTION In The Book of Evidence, Peter Achinstein quotes a former dean saying, “Peter, you have never made a contribution of interest to scientists” (Achinstein 2001, 3). Most would take offense; Peter wrote a book. The dean is right, he argues: philosophy of science ought to connect with the scientiﬁc discourse communities it covers. We can trace this concern to 1959, when Achinstein won a Harvard Traveling Fellowship. Since this was the heyday of ordinary language philosophy, he visited Oxford, shaping his approach to philosophy of science thereafter. Resolving the tension between positivist understandings of scientiﬁc reasoning and the ordinary language approach forms a central strand of his work.

2. ACHINSTEIN AT HARVARD Logical empiricism echoed through 1950s analytic philosophy, especially in philosophy of science. Well-schooled in the positivists’ formal tools and desire for rigor, Achinstein’s dissertation on Rudolf Carnap’s theory of probability emerged from studies with W. V. O. Quine, C. G. Hempel, Morton White, and Israel Schefﬂer, who “taught a very general philosophy of science course. We no longer teach it that way, philosophy of science with no science at all.”1 Philosophers of science ought to be concerned with rational reconstructions, axiomatic systems logically connected to observation reports through coordinating principles. Except for the truth of basic observation statements, everything that is needed is contained within the formal

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structure and relations of the axioms. This is why Schefﬂer could teach philosophy of science without science. Begin by making the basic concepts rigorous through explication. Achinstein describes the positivists’ methodology thus: It is the job of the philosopher to explicate concepts, that is, to replace them with ones that, although somewhat similar, are more precise, simpler, and more fruitful than those presently employed. (Achinstein 1969, 260)

Sets of necessary and sufﬁcient conditions are worked out with the truth of the observation reports being the sole empirical matter. Consider Carnap’s view of conﬁrmation. [I]nductive logic is like deductive logic in being concerned solely with the statements involved, not with the facts of nature. By a logical analysis of a stated hypothesis h and stated evidence e, we conclude that h is not logically implied but is, so to speak, partially implied by e to the degree of so-and-so much. At this point, we are justiﬁed, in my view, in assigning numerical value to the probability. If possible, we should like to construct a system of inductive logic of such a kind that for any pair of sentences, one asserting evidence e and the other stating a hypothesis h, we can assign a number giving the logical probability of h with respect to e. (Carnap 1966, 33)

This aprioricity is also displayed in Hempel’s deductive-nomological account of scientiﬁc explanation: The explanation of the occurrence of an event of some speciﬁc kind E at a certain place and time consists, as it is usually expressed, in indicating the causes or determining factors of E. Now the assertion that a set of events—say, of the kinds C1, C2,…, Cn—have caused the event to be explained, amounts to the statement that according to certain general laws, a set of events of the kinds mentioned is regularly accompanied by an event of kind E. Thus the scientiﬁc explanation of the event in question consists of

(1) A set of statements asserting the occurrence of certain events C1,…,Cn at certain times and places, (2) A set of universal hypotheses, such that a. The statements of both groups are reasonably well-conﬁrmed by empirical evidence, b. From the two groups of statements the sentence asserting the occurrence of event E can be logically deduced. (Hempel 1965, 233) The relation between explanans and explanandum is formally deﬁned. Like Schefﬂer, we do not need the science to do the philosophy.

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3. ACHINSTEIN AT OXFORD Concerns were raised about this approach by many, including ordinary language philosophers who objected to stripping away the context. So when Achinstein received a Harvard Traveling Fellowship, he left Cambridge (Massachusetts) for Oxford to explore alternatives to this approach. Upon arrival, Achinstein met with Gilbert Ryle to assign him a tutor. Since he was writing on induction, Achinstein requested Peter Strawson, whose ﬁrst book, Introduction to Logical Theory, ended with a chapter on the ill-groundedness of the search for a solution to Hume’s problem. Though they were supposed to meet only biweekly, the conversations were sufﬁciently enjoyable and productive that Strawson invited him back weekly, eventually inviting him for meals and picnics with his family. Strawson had just ﬁnished his second book, Individuals, on metaphysics, a topic of little interest to Achinstein, who worked to keep their discussions focused on Strawson’s views of language that challenged the Carnap he was reading. The formal logician now aims at an exact and highly systematic logic, comparable in these respects with mathematics. But he cannot give the exact and systematic logic of expressions of everyday speech; for these expressions have no exact and systematic logic. What he can, and does, do is devise a set of rules which satisﬁes his requirements, and, at the same time, while not doing full justice to the complexities of ordinary usage, and diverging from it in many ways does touch ordinary usage at some vital points. The formal logician, in relation to ordinary language, might be compared with a man ostensibly mapping a piece of country of which the main contours are highly irregular and shifting. But the man is passionately addicted to geometry, and insists on using in his drawings only geometrical ﬁgures for which rules of construction can be given; and on using as few of such rules as he can. Naturally his maps will never quite ﬁt. (Strawson 1952, 57–8)

Achinstein took full advantage of his time at Oxford attending a seminar co-taught by Ryle and the visiting Hempel, lectures with A. J. Ayer, and an ethics seminar with Richard Hare whose participants included the visiting Thomas Nagel. Especially inﬂuential was the course offered by J. L. Austin, who died of cancer that semester. I went to his seminar called “Excuses.” It was a graduate seminar and it was the most unique thing that I had ever seen at Oxford in philosophy. He would write down on the board three, four, or ﬁve excuses that people might give for things. This was supposed to be connected to a seminar in ethics. He would ask us to distinguish between these excuses. I remember

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one time he wrote, “mere accident,” “pure accident,” and “sheer accident” on the board. You know, “I may have done something wrong, but it was mere accident, pure accident, or sheer accident.” He put these things down and we were dumbfounded. What’s the difference and who cares? What does this have to do with philosophy? What Austin could do is to get us so engrossed in the question that we didn’t care if we didn’t care. We didn’t care whether it had some deeper implications in philosophy, it became a puzzle. And he conducted the class entirely Socratically. He went after a proposal on the ﬂoor as to what the difference is and we would all have to tell a story involving a situation in which you could say that it was mere accident, but not pure accident.2

That meaning involves context, that a full explication of a term might require the telling of a story involving a situation in which the term is employed, embedded itself in Achinstein’s work. Except for those with Ayer, the Oxford discussions remained a step removed from philosophy of science. For the positivists, understanding language was necessary for understanding science. But their project was foundering, so Achinstein considered how the insights and methods of ordinary language philosophy might augment what remained of its foundation. As Strawson asks in a different context, “How far is the symbolic apparatus of modern logic adequate for the expression of the form, or general logical powers, of these sentences?” (Strawson 1952, 217). Where does “philosophy of science without science” succeed and where is the contextualization of the ordinary language approach needed?

4. ACHINSTEIN ON EXPLANATION The inﬂuence of ordinary language philosophy on Achinstein is most explicit in The Nature of Explanation, where he argues that the sort of model of explanation envisioned by the positivists necessarily fails, proposing instead a pragmatic account inﬂuenced by Austin. The positivist-inspired approach requires two necessary conditions. The “No-Entailment-by Singular Sentences (or NES)” requirement requires “no singular sentence in the explanans (no sentence describing particular events), and no conjunction of such sentences, can entail the explanandum” (Achinstein 1983a, 159). Scientiﬁc explanations inextricably refer to general laws. Second, the “A Priori” requirement holds that “the only empirical consideration in determining whether the explanans correctly explains the explanandum is the truth of the explanans; all other considerations are a priori” (Achinstein 1983b, 162). Whether u explains Q is a matter of the logical properties and relations of and between u and Q once we know u to be the case.

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Achinstein argues that these requirements doom any account that tries to satisfy them. If we propose u as an explanation for Q that makes reference to purported laws of nature, then there must be empirical concerns beyond the truth of the explanans to determine whether we have a good explanation. It may be true that Jones ate a pound of arsenic at time t and that he died 24 hours later, but that does not explain his death if he was run over by a bus just after t. There are additional empirical concerns, including but not limited to intervening causes, that no a priori model of explanation can avoid. This can be circumvented if explanations are seen not as formal structures, but as “what Austin calls an illocutionary act. Like warning and promising, it is typically performed by uttering words in certain contexts with appropriate intentions” (Achinstein 1983a, 16; See also Austin 1962). Since a given utterance can do a number of things—one explains, apologizes, or gives an alibi with the same sentence—illocutionary acts are ordered pairs (x, y), where x is a proposition and y is a type of explaining act. If q is a phenomenon to be explained and Q is the request for an explanation, then speaker S explains q by uttering u if and only if we can represent u by the ordered pair (x, y) such that: (i) (ii) (iii) (iv) (v)

Q is a content-question; x is a complete content-giving proposition with respect to Q ; y = explaining q; (∃a)(∃u)(a is an act in which S explained q by uttering u); (a)(u)[a is an act in which S explained q by uttering u ⊃ (r) (r is associated with a ⊃ r = x)]. (I.e., x is the one and only proposition associated with every act in which S explained q by uttering something.) (Achinstein 1983a, 87)

We need not explore the details of Achinstein’s notions of a complete content-giving proposition for content-nouns to see that we have an ordinary language-inspired account of explanation. As Strawson argued generally, the reduction of the act of explaining to artiﬁcial logical structures fails to capture the actual act. We must account for the intentions of the speaker within the context as Austin does—scientists can offer very different but equally scientiﬁc explanations to different audiences, for example, school children, fellow specialists, or members of a wider scientiﬁc congress. Pragmatic elements ﬁnd their way into the philosophy of science.

5. ACHINSTEIN ON EVIDENCE Given that Achinstein’s account of explanation requires speaker’s intention and his account of evidence includes the likelihood of an

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explanatory connection as a necessary condition, one might expect his account of evidence to also contain pragmatic elements. But he contends that the operative notion of evidence in science, what Achinstein terms “veridical evidence,” is an objective notion independent of subjective beliefs or epistemic context. An evidence report e, given background information b, is veridical evidence that hypothesis h according to Achinstein if and only if (i) e, b, and h are true, (ii) e does not entail h, (iii) p(h/e,b) > 1/2, and (iv) p(there is an explanatory connection between h and e/e,b) > ½. This view synthesizes the positivist and ordinary language accounts. On the one hand, the high probability condition of Carnap is maintained, but is deemed insufﬁcient for reasons analogous to Achinstein’s argument against aprioricity in explanation. Just as cases like Jones eating arsenic before getting hit by a bus shows the need for empirical aspects beyond the truth of the explanans, so too examples of intervening causes show that we need to know more about the evidence statement than its truth and relation to the hypothesis in order to be able to assert an evidentiary relation between them. Michael Jordan eating Wheaties, for example, is not evidence that he will not get pregnant even if it is true that he eats his Wheaties and will not become impregnated afterward.3 But unlike the consideration of illocutionary acts in Achinstein’s account of explanation, the notion of explanation here is objective because an explanatory connection exists only if there is a correct explanation relating h and e—that is, if h correctly explains e, if e correctly explains h, or if some hypothesis correctly explains both h and e. The required correctness removes the appeal to speaker’s intention. So while the view is objective as the positivists wanted, it is not a priori as they required. We see this in the way we defend and attack evidence claims, which is not to point out logical relations, but rather to appeal to other empirical matters; for example, we might posit intervening causes to explain why other seeming counter-instances fail to undermine the relation. Where Achinstein’s account of explanation takes him to the ordinary language side of the debate, his view of evidence moves back toward, but not all the way to, the positivist approach; its Carnap-style explication does violate the aprioricity condition, but remains true to its spirit.

6. CONCEPT AND EVIDENCE The difference between Achinstein’s and the positivists’ approaches becomes clearer in his embrace of the dean’s challenge. His response is an explicative methodology seeking a middle path between Carnap and Austin.

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For Carnap, a successful explication satisﬁes four requirements: (1) similarity to the explicandum, (2) exactness, (3) fruitfulness, and (4) simplicity (Carnap 1950, 5). Carnap and Achinstein are similarly attentive to conditions (2)–(4), but there are interesting differences with respect to similarity. Carnap contends that similarity need only be the vaguest connection. Common use is often unacceptable in the more exacting scientiﬁc contexts and scientists must be free of the sloppy ambiguities of ordinary language. Carnap considers the zoological term “piscis” as an explication of the common notion of ﬁsh. The prescientiﬁc concept includes whales, which are no longer part of the scientiﬁc conception. We do not want to tie successful explication so close to usage that it keeps scientists from being able to employ the explicated notion as fruitfully as possible. The explications are normative, and explicated notions are not required to be coextensive or otherwise strongly tied to the vague and ambiguous explicans, lest we confuse the student for the master. But when we shift from scientists explicating scientiﬁc notions to philosophers explicating terms like “evidence,” the sloppiness is now in the scientists’ use, and the normativity lies in the hands of the philosopher. The explication of “evidence” need not be tied to scientists’ usage, but conform to philosophical fruitfulness, exactness, and simplicity. Epistemologists are in a position to tell scientists that they are wrong in taking evidence to mean what they think it means, just as scientists can tell the common person that whales and dolphins aren’t really ﬁsh. This power is certainly among the sources of the dean’s complaint. But the solution does not lie in adopting the ordinary language theorists’ approach. It may justly be urged that, properly speaking, what alone has meaning is a sentence. Of course, we can speak quite properly of, for example, “looking up the meaning of a word” in a dictionary. Nevertheless, it appears that the sense in which a word or phrase “has a meaning” is derivative from sense in which a sentence “has a meaning”: to say a word or phrase “has a meaning” is to say that there are sentences in which it occurs which “have meanings”: and to know the meaning which the word or phrase has, is to know the meanings of the sentences in which it occurs. (Austin 1961, 24)

For Austin, meaning is usage, and it makes no sense to tell the scientists that “evidence” ought to mean something other than what they mean by it Achinstein’s notion of evidence is a middle path between Carnap’s normativity and Austin’s “stressing that we must pay attention to the facts of actual language.” When we look at cases in which scientists’ writings have been taken as evidence for a controversial claim, especially cases in which they won the day, is there good reason from an ahistorical

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perspective to maintain that propositions taken by the scientists to be veridical evidence in fact are veridical evidence? We can answer the dean’s challenge by setting philosophers in a place different from the semantic trafﬁc cops of Carnap or the gloriﬁed lexicographers of Austin. Philosophers of science serve science as coroners, looking at the corpses of inferences past to see if the grounds upon which they were made are legitimate. There are the historical facts to be unearthed about why Jean Perrin held Brownian motion to be evidence for the existence of atoms, why Henry Brougham saw the reﬂection of colors to be evidence for the particle theory of light, and why Niels Bohr took the spectral lines of hydrogen to be evidence for his theory of the atom. This requires Austin’s sort of analysis. But then we can ask the normative question in hindsight: “Were they right?” For this we need something akin to Carnap’s approach. And that is precisely what we see in Achinstein’s writings of the past couple of decades and the notion of “concept” there employed: a serious commitment to the discourse of actual scientists coupled with the rigor and normativity of logical empiricism. But it is not only in the concept of concept that we ﬁnd a middle path; it is also in the use of evidence for his explication of evidence. When we look at the sort of philosophical evidence that Achinstein uses to support his account, particularly how the different ways he uses appeals to intuition, we see something that is not exactly in line with the positivists’ methodology, but something also ﬂavored by but distinct from the ordinary language approach. The notion of intuition employed here is not that of Kant or the usual pejorative sense one often hears in philosophy of science. Rather, we use the term “intuition” following recent work in epistemology to refer to the judgments elicited by thought experiments (see De Paul and Ramsey 1998). Membership in the class “intuition” does not confer special epistemic status to those judgments. Achinstein’s divergence from Carnap on the condition of similarity to the explicandum can be observed in two argumentative strategies employed in The Book of Evidence. The ﬁrst is his use of appeals to intuition and the second is his close analysis of what scientists actually take to be evidence. Together, these two sources of philosophical evidence constrain the concept of scientiﬁc evidence requiring it to satisfy the needs of scientists thus meeting the dean’s challenge. This challenge, however, does not merely require a greater degree of similarity or continuity between the concepts in use and the explications provided by philosophers. Rather, it requires that the explicated concept be useful to practicing scientists. Indeed, we ﬁnd that the usefulness condition is already included in Carnap’s notion of an explication under condition (3),

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fruitfulness. Achinstein ties this condition to the similarity condition; it is through a stronger similarity relation that fruitfulness is obtained. Explicated concepts that fail to meet the similarity condition will likely not sufﬁce to meet the fruitfulness condition. As such, he tests his and competing proposals against these two types of evidence: consistency with our intuitions about evidence and historical cases. Achinstein acknowledges that the dean is not only right that philosophical theories of evidence are ignored by scientists, but that they ought to be ignored, “because they propose concepts of evidence that are based on assumptions incompatible with ones scientists make when they speak of, and offer, evidence for hypotheses” (Achinstein 2001, 3). The ﬁrst of these assumptions is the weakness assumption, namely that something can qualify as evidence if it has any positive relevance for the hypothesis, for example, if it increases its probability or provides a positive instance of it. Against this assumption, Achinstein points out that when scientists talk about evidence, it is taken to be something that gives good reason to believe the hypothesis. The second incompatible assumption is the positivist claim that whether something counts as evidence is a strictly a priori matter. In order to challenge both of these assumptions, Achinstein points to historical cases, particularly to one involving the work of Heinrich Hertz and J. J. Thomson. Hertz devised an experiment to test for electric effects from cathode rays. The presence or absence of such electrical effects was an empirical prediction that differed between the theory that cathode rays are composed of electronically charged particles and the theory that they are electrically neutral waves of some sort. Hertz found no electric effects, and therefore concluded that cathode rays are not electrically charged. Thomson, however, found that with improvements to the experimental design that were unavailable to Hertz (for example, more complete evacuation of gas from a glass tube), the experiment did produce observations of electrical effects. In light of this episode in the history of science, Achinstein asks, were Hertz’s results evidence that cathode rays are not electrically charged? (Achinstein 2001, 224; Achinstein 1991, 325–28) Achinstein argues that to answer this question, we need to disambiguate four different concepts of evidence. On one notion of evidence (ES-evidence), Hertz did have evidence in favor of his hypothesis. Given his epistemic situation, Thomson’s improvements to the design of the experiment were unavailable. Thus, it seems he was justiﬁed in believing that his experiment produced evidence for his hypothesis. What this case shows, however, is that ES-evidence is not the type of evidence scientists care about. It is consistent with one set of usage patterns for the term “evidence,” but not with other ways of using the term, which are more closely tied to scientiﬁc interest in evidence (citing the Hertz–Thomson

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case as evidence). Rather, Thomson’s work showed that—earlier appearances to the contrary—Hertz’s experiment was not evidence for his hypothesis after all. Achinstein’s evidence for this claim is the behavior of scientists, pointing out that Thomson’s experiments are taken to have provided conclusive evidence that cathode rays are negatively charged, and that Hertz, in fact, did not have evidence to the contrary. This is because it turns out that Hertz’s experiment did not provide good reason to believe his hypothesis. Any deﬁnition of evidence that fails to account for this fact about scientiﬁc practice regarding evidence is guilty of the weakness assumption. Achinstein rejects the a priori assumption based on an examination of the Hertz–Thomson case as well. Thomson showed that Hertz did not provide (veridical) evidence to believe that cathode rays are electrically charged, and did so based on empirical facts, not on a priori grounds. It is only by discovering improvements to the methods Hertz employed that the question of evidence was settled. Therefore, we can reject analyses of the concept of evidence that diverge from the concept in use on either of these grounds. Scientiﬁc use of the concept of evidence is already fruitful, and if philosophers are going to improve the concept, they should retain the aspects of the present concept that scientists actually do ﬁnd useful. We discover what these aspects are by investigating the use of the concept in the “ordinary language” of the scientiﬁc community. Achinstein also uses appeals to intuition as evidence for and against proposed deﬁnitions of the concept of evidence itself. These intuitions serve to ground the philosophical explication in ordinary usage. For example, consider the counter-examples Achinstein offers to challenge the positive relevance and high probability deﬁnitions of evidence. Against the positive relevance deﬁnition, Achinstein considers whether the fact that Steve, an Olympic swimmer in ﬁne shape, is swimming laps constitutes evidence that he will drown. This purported evidence (that he is swimming laps) does make it marginally more likely that Steve will drown, satisfying the positive relevance deﬁnition. Yet, this is dismissed as “extremely implausible” (Achinstein 2001, 70) on the strength of the intuition that it is not actually evidence. Similarly, the Michael Jordan counter-example challenges the high probability deﬁnition. In that case, Achinstein concludes that “it seems counterintuitive to say that, given that [Michael Jordan] is a male basketball star, his eating Wheaties is evidence that this hypothesis is true” (71). These intuitions not only motivate dropping the positive relevance and high probability conceptions, but they are also constraints on positive proposals as well. In introducing the requirement that the p(h/e) > ½ for

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e to count as evidence, he notes that it is subject to the irrelevance counter-examples that caused problems for the high probability deﬁnition. To avoid this, he introduces the explanatory connection requirement, a move that is substantiated in part by its success explaining away this and related counter-examples. Much like the historical cases, the satisfaction of these counter-examples is a requirement for any adequate explication of the concept of evidence. On the Austinian program, one studies the intuitive responses (about what one would say) of “the folk,” the untrained, everyday users of the expressions or concepts under investigation. Austin argues that these intuitions encapsulate a body of knowledge developed through the crucible of centuries of experience. Indeed, there currently is a vibrant research program exploring these folk intuitions, and analyzing their relevance to philosophical investigation (see Knobe and Nichols 2008). It is hard to reconcile this, however, with Achinstein’s use of intuitions. Why should we care what ordinary users of the expression “evidence” would apply the term to? Surely there is a connection between the concept of evidence in science and in ordinary discourse, but Achinstein does not provide us with any reason to care about these folk intuitions. What he does provide us with, however, is reason to care about the intuitions of scientists. These appeals to intuition are not appeals to untrained folk intuition. Rather, they are appeals to the intuitions of those with sufﬁcient familiarity with the concept under investigation. On the Carnap model, these intuitions would be either irrelevant, or at the least considerably less relevant, to a philosophical investigation of evidence. For an ordinary language philosopher, however, limiting the intuitions to those of scientists (and scientiﬁcally trained philosophers) is an unwarranted restriction. As we have argued in this chapter, Achinstein brings these two approaches together, and no less so here. Like Carnap, the purpose of conceptual analysis is fundamentally explicative; it is concerned with improving one’s concept. Yet, to provide an improved concept that is still fruitful (that is, it meets the dean’s challenge), we must ground it in ordinary usage. The ordinary usage that is relevant is scientiﬁc discourse, where the concept of evidence already plays an important role. Thus, intuitions can help satisfy the ordinary usage requirement, while the restriction to the intuitions of scientists helps ensure that the explication will meet the needs of those scientists. Thus we can also see that appeals to intuition for Achinstein are not a matter of investigating the folk concept, or of the special insight of philosophical intuition. Like the historical cases he considers, they are tools used to pin down the central features of the ordinary usage of the concept of evidence, features that make this concept so useful to scientists.

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7. CONCLUSION Achinstein’s trip to Oxford in 1959 had lasting effects on his approach to philosophy of science. Philosophy of science had been built on the positivists’ view of language. When that view was challenged by the ordinary language philosophers, it had ramiﬁcations for the philosophy of science, ramiﬁcations that can be seen in Achinstein’s work on explanation and evidence. His views are a synthesis of the two, often using insights from one to augment and correct deﬁciencies in the other. This is clear in his notions of concept and the evidence that he selects for his explications in the service of answering the dean’s challenge. Philosophers, on Achinstein’s account, do maintain the normativity that the logical empiricists gave to them, but this power must be used in a way that does not alienate the explication from the history and practice of working scientists. REFERENCES Achinstein, P. 2001. The Book of Evidence. New York: Oxford University Press. ——— . 1995. Are Empirical Evidence Claims A Priori? British Journal for the Philosophy of Science 46 (4): 447–73. ——— . 1991. Particles and Waves. New York: Oxford University Press. ——— . 1983a. The Nature of Explanation. New York: Oxford University Press. ——— . 1983b. The Concept of Evidence. New York: Oxford University Press. ——— . 1969. Approaches to the Philosophy of Science. In The Legacy of Logical Positivism, ed. S. Barker and P. Achinstein. Baltimore, Md.: Johns Hopkins University Press. Austin, J. 1962. How to Do Things with Words. Cambridge, Mass.: Harvard University Press. ——— . 1961. Philosophical Papers. Oxford: Clarendon Press. Carnap, R. 1966. An Introduction to the Philosophy of Science. New York: Dover. ——— . 1950. Logical Foundations of Probability. Chicago: University of Chicago Press. DePaul, M. R. and W. Ramsey. 1998. Rethinking Intuition: The Psychology of Intuition and its Role in Philosophical Inquiry. Lanham, Md.: Rowman and Littleﬁeld. Hempel, C. 1965. Aspects of Scientiﬁc Explanation. New York: Free Press. Knobe, J. and S. Nichols. 2008. Experimental Philosophy. Oxford: Oxford University Press. Strawson, P. 1952. Introduction to Logical Theory. London: Methuen.

NOTES 1. Interview with Peter Achinstein, 9/28/2004. 2. Interview with Peter Achinstein, 9/28/2004. 3. See Achinstein 1995 for this and other examples.

2 Evidence, External Validity, and Explanatory Relevance Nancy Cartwright

1. INTRODUCTION When does one fact speak for another? That is the problem of evidential relevance. Peter Achinstein’s answer, in brief, is as follows: evidential relevance = explanatory relevance.1 My own recent work investigates evidence for effectiveness predictions, which are at the core of the currently heavily mandated evidence-based policy and practice (EBPP). I study predictions of the form “Policy treatment T implemented as, when, and how it would be implemented by us will result in targeted outcome O.” RCTs, or randomized controlled trials, for T and O are taken to be the gold standard for evidence for effectiveness predictions. I question not just whether they are gold-standard evidence, but more importantly, how can they be evidence at all? What makes them relevant to the truth of the prediction that T will work for us? I am going to follow Achinstein’s lead here and suppose that evidential relevance = explanatory relevance, where A is explanatorily relevant to B just in case A is an ineliminable part of a correct explanation of B, or the reverse, or A is indirectly relevant to B: there is some common fact that is an ineliminable part of correct explanations for A and B. I shall argue: 1. It’s not evidence for us without evidence that it’s evidence. 2. Evidential relevance is a conditional relation: E is evidence for H conditional on the non-shared factors that ﬁll out explanations for E and H. Finding these involves a horizontal search. 3. To get shared explanatory elements we need a vertical search, up and down the ladder of abstraction. If we haven’t climbed the right ladder in the right way, an RCT may not show what we think it does.

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It follows from my discussion that RCTs cannot play anything like the central evidential role for effectiveness predictions that they are standardly awarded in EBPP literature (Cartwright forthcoming; Cartwright and Munro 2010). I begin with some terminology, some assumptions, and some simplifying procedures. First, the fact that effectiveness predictions are predictions should not put us off an explanatory relevance account. Just suppose that the predictions are true. Then look for explanatory relevance. Second, I adopt the probabilistic theory of causality. I suppose that for each effect-type at a time t, Ot, and for each time t’ before t, there is a set of factors {C1t’, …,Cnt’}—the causes at t’ of O at t—whose values in combination ﬁx the objective chance at t’ that O takes value o for any o in its allowed range. A causal structure, CSt’(Ot), for Ot is such a set along with the related objective chances for all values of Ot for all combinations of allowed values, Ljt’, of the causes in the set: Prob(Ot = o/Ljt’). For simplicity I will usually suppress time and other indices and also restrict attention to two-valued variables. So a causal structure looks like this: CSt’(Ot) = <{C1t’, …,Cnt’}, {Prob(Ot/L1t’), . . . ,Prob(Ot/Lmt’)}>. Third, I follow the EBPP literature and concentrate on the effect size of T for O in a population: Prob(O/T) – Prob(O/-T). Fourth, I restrict attention to predictions about the effects of policies on populations and not on single units. Fifth, I consider only positive relevance since that ﬁts in a simple way within Achinstein’s explanatory account. Sixth, I concentrate on cases where E is indirectly relevant to H because these are the most complicated cases. Finally, for simplicity I assume that the evidence claims in question are well conﬁrmed—we can reasonably take them as true.

2. RELEVANCE IS CONDITIONAL ON UNSHARED FACTORS The relevance relation I focus on is objective: one fact (E) bears on the truth of another (H). This relation holds between facts because of the way nature and society operate; it does not depend on our knowledge of this operation. Corresponding epistemic notions—like our reasoned judgments about what is relevant to what—do depend on the state of our knowledge and a variety of other factors as well, such as time and resource constraints, or level and type of expertise. Objective relevance is important for policy deliberation predictions; gathering, discovering, and surveying facts are all costly. We’d

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like to conﬁne our attentions to facts that matter to the truth of the policy prediction. “Bears on the truth of” can seem hopelessly vague, so there are various well-known attempts to explicate it with more familiar notions. One takes relevance to be some kind of causal relation. That’s too narrow. So too are various kinds of probabilistic relations: there just aren’t enough of these in the world to account for all the obvious evidential relevance.2 Moreover, relying on probabilities puts the cart before the horse when it comes to the needs of estimating if a policy will work. Achinstein’s explanatory relevance, by contrast, ﬁts the bill nicely. Why should explanatory relevance be a good stand-in for the more abstract concept “bears on the truth of”? My answer is a mix of Achinstein’s views and my own. Just as the relevance relation aimed for is objective, so must the explanatory relation be in order to serve as a marker for relevance. “Explanation” as I use it, then, doesn’t mean something that has the right form and is proffered as an explanation; it means something that is an explanation. There will be many of these, some of them nested, which is why, as I argue in sections 4 and 5, we need good vertical searches to ﬁnd the widest scope of evidential relevance a result can have. Achinstein has been criticized for using explanatory relevance because this concept itself, it is argued, is in need of explication. I disagree that we need an explication for the task at hand.3 There are a host of different “thick” relations in nature we label “causal” (like pushing, feeding, lapping up, mailing…). So too are there a host of relations that we lump together under the label “explains” when explanation serves as a guide to “bears on the truth of.” The fact that we cannot give an interesting non-circular explication of “explains” as an objective relation does not mean that we cannot recognize it when we see it—Newton’s laws explain Kepler’s, and my taking an aspirin explains my headache getting better. Nor does it mean that we cannot take certain claims to be generally true of “explains”. There is good reason why the Achinstein slogan should work for EBPP. To start, a correct explanation is always evidentially relevant to its explanandum and vice versa. The ﬁrst follows trivially if one adopts a deductive nomological account of explanation since the explanans cannot hold without the explanandum doing so as well. However, even if one follows G. E. M. Anscombe in maintaining that an explanans can be enough—it can be as full an explanation as nature allows—without the explanandum obtaining (Anscombe 1993), nevertheless the occurrence of the explanans is undoubtedly evidentially relevant to the occurrence of the explanandum. The converse is trivial since “explanation” is meant to be “correct explanation.”

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Indirect evidence is harder. E is (indirectly) relevant to H if there is a correct explanation for H that shares a common element, X, with some correct explanation for E. X + XuE correctly explains E and X + XuH correctly explains H.4 E is evidence that X obtains. But X obtaining cannot be part of a correct explanation for H unless XuH obtains. If XuH is not the case, then X and XuH cannot be a correct explanation for H—it doesn’t matter how well-conﬁrmed X is. The relevance of E’s truth to the truth of H ﬂows through X and it can only do that given XuH. E’s truth is of no matter at all to H’s where XuH fails. Suppose your interest is in whether H is true. But you know that XuH is false.5 Would you pay to learn E? No. Or take a stock philosopher’s case: You are asked to predict the color of a bird in the river. Is the bevy of observed white swans relevant? It is if “all swans are white” is part of the explanation of both your bird’s color and that of the bird in the river. But if you are told that color and your bird is certainly not a swan, all those observations of swan color are worthless to you. So: When the topic is evidence for policy predictions, the relevant concept of relevance is a conditional one: the relevance of a fact E that would have a shared explanatory element with H were H to be true is conditional on the obtaining of the unshared portion of the explanation H would have. Moreover, the epistemic probability awarded to E being relevant should be no higher than the epistemic probability that appropriate unshared factors obtain.

3. EXTERNAL VALIDITY AND THE NEED FOR HORIZONTAL SEARCH An ideal RCT is a study in which the population in the study, φ, divides into two groups that are identical with respect to all features causally relevant to the targeted outcome, O, except for the policy treatment, T, and its downstream consequences. Suppose the probability of O is greater in the T group than in the –T group. Where can we go from there? Under the probabilistic theory of causality, the values of a full set of O’s causes ﬁx the objective chance that O takes any value in its range. That’s what prompts the attention to the conditional probabilities from the causal structure for φ, Prob(O/K&T) > P(O/K& –T), where K is an assignment of values to all the members of CSφ(D) with the exception of T and its downstream effects. Whether T has a positive effect size in φ depends on the relative weights in φ of subpopulations in which T acts positively and those in which it acts negatively.

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A study is said to be externally valid when “the conclusion established in the study holds elsewhere.” Consider an ideal RCT for T,O on a large study population φ that has a positive result: Study Conclusion (SC:) Prob(O/T) > Prob (O/–T) in φ.

The study has external validity for target population θ if Target Conclusion (TC): Prob(O/T) > Prob (O/–T) in θ.

(Recall, θ describes the target population, supposing the implementation that would in fact occur given the policy in question.) When is SC evidence for TC? Since neither SC explains TC nor the reverse, if SC is to be evidence for TC there must be some shared part in their separate explanations. The explanation for the successful RCT results in φ under the probabilistic theory of causality look like this for some speciﬁc causal structure, CS(O), and some speciﬁc set of causally homogeneous subpopulations from CS(O), K = {…,Kj,… }. Study Conclusion Explanation (SCE): SCE1: The causal structure for O of φ is CS(O). SCE2: For KJ in K , Prob(O/KJ & T) > Prob(O/KJ & –T) according to CS(O). SCE3: The possible negative effects of T on O in other subpopulations are not enough to outweigh this increase.6

The explanations for the predicted hypothesis TC are the same in form and must refer to the very same causal structure and the very same causally homogeneous subpopulations if there are to be shared factors: Target Conclusion Explanation (TCE): TCE1: The causal structure for O of θ is CS(O). TCE2: Some member(s), KJ, KJ’,… of K are subpopulation of θ. TCE3: For these KJ, Prob(O/KJ & T) > Prob(O/KJ & –T) according to CS(O). TCE4: The possible negative effects of T on O in other subpopulations of θ are not enough to outweigh the increase due to these.

Since most of the claims in both explanations are indexed to the population, the only shared element is the claim that CS(O) implies that Prob(O/KJ & T) > Prob(O/KJ & –T) for the KJ of TCE3. It is this—and only this—one shared explanatory element that makes the RCT result relevant to the policy prediction. But it is shared only supposing that TCE is a correct explanation for the prediction about θ. That is, the RCT is explanatorily relevant, and thus evidentially relevant, only relative to the truth of TCE1, 2, and 4. What then should be required for the RCT to be accepted as

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evidence? My dictum: it’s not evidence for us unless we have evidence that it’s evidence. That means having evidence for TCE1, 2, and 4. And what reasons do we have to accept these? To start, what supports TC1—that φ has the same causal structure for O as φ? Common causal structures are not all that typical. The refurbished Cuisinart Classic four-slice toaster that I almost bought for £41.46 has a different causal structure than does the Dualit three-slice stainless steel toaster at £158.03, which has a different structure again from the new Krups expert black and stainless steel toaster at £44.99. Perhaps you think—as many economists and medical RCT advocates seem to—that your two populations are more likely to share causal structure than are the toasters on offer in Oxford. That’s ﬁne. But for EBPP you should have good evidence-backed reasons for that. Supposing that the two populations do have a common causal structure, what assures that some of the very subpopulations KJ of φ in which Prob(O/KJ & T) > Prob(O/KJ & –T) are subpopulations of θ? The mix of causal factors that obtain shifts all the time, both across situations and across time. Worse, no matter what mix was there before, in implementing policy we all too often alter that mix. Consider the California class-size reduction program. Reduced class sizes did not improve educational outcomes because the program was rolled out over a short time; the need for teachers doubled within a year but the availability of trained teachers did not. Teaching quality went down, offsetting the good inﬂuence of class size.7 Finally, why suppose that were T to increase the probability of O in θ as predicted, that would be due to the positive effects in the shared subpopulations rather than in some subpopulations of θ not shared with φ? These questions need answers, and for EBPP, answers must be reasonably underpinned by empirical and theoretical support. One cannot just plop SC on the table and say that it is relevant to TC. Whether it is relevant depends on common explanatory factors, and presuming that common factors obtain requires good evidence. “It can’t count as evidence unless there’s evidence that it’s evidence.” Clearly this dictum can create a regress. That, however, is the human condition. We have to stop somewhere. But it should be somewhere reasonable and defensible. Consider CCTV cameras.8 Are they working? A glance at the monitor is generally enough to be reasonably certain, despite the fact that, in heist movies, elaborate techniques are undertaken to make the monitors lie. For relevance, too, we need reasonable and defensible stopping points for the chain of evidence that shows that evidence offerings are evidence. Consider for a moment not the relevance but the credibility of evidence offerings. Where detailed scientiﬁc argument and experiment are involved, this is going to be hard for policy

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analysts and practitioners to judge. That is why institutions like the Cochrane and Campbell Collaborations or the What Works Clearing House have been set up. If they give a study result high marks, it is generally reasonable for a practitioner to take that on faith.9 What then of the evidence for the relevance of SC for TC? Sometimes we can assemble some body of facts that are reasonably well attested and that provide good reasons in favor of claims like TCE1, 2, and 4. But it is hard to do this. And the very cases in which one most wants to perform an RCT are the cases where there will be least evidence that a positive RCT result for the policy treatment is evidence that the policy will work for us. RCTs are touted as the gold standard because only they “control for unknowns,” for the factors in the causal structure for O that we don’t know are there and hence can’t check explicitly are distributed the same in the two groups. RCTs come into their own when we suspect that a good many factors in the causal structure for the study population are unknown. But then how are we supposed to produce evidence that those very unknown factors are causal factors according to the causal structure for θ? And that θ has some of the same causally homogeneous subpopulations in which T is positive for O as φ does? Finally, how do we estimate that in other subpopulations of θ, T won’t have enough negative effects to decrease the chance of O there? The very same epistemic gaps that make the RCT the method of choice also make results practically useless for prediction. The problems discussed in this section demand horizontal search. T can increase the probability of O in some mixes of causal factors and not in others; it can even decrease the probability in some while increasing it in others. A positive RCT result is relevant to a policy prediction only relative to assumptions about the mixes of factors operating in the study population and in the target population. To be justiﬁed in taking the RCT as evidence, we need to gather information about what other factors operate with T in the two populations. That’s what I mean by a “horizontal search.” To increase the range of relevance of the RCT we also need a “vertical search,” which reviews causes across levels of abstraction.

4. EXTERNAL VALIDITY AND VERTICAL SEARCH The causes in a causal structure can be more or less abstract; structures involving factors at different levels of abstraction can all obtain at once. The statement, “The trajectories of bodies moving on a sphere subject only to inertia are great circles” is true; so too is the statement, “The tra-

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jectories of bodies moving on a sphere subject only to inertia are geodesics (i.e., the shortest distance between two points).” They are equally true because, on a sphere, a great circle is a geodesic.10 Generally, the higher the level of abstraction of a causal structure, the more widely it is shared across populations. For example, bodies on Euclidean planes subject only to inertia follow geodesics but not great circles. This matters for explanatory relevance. An easy way to get a grip on how it matters is to consider some examples. The ﬁrst is from climate-change modeling, where development economists argue that many of the policies that can help alleviate harmful effects of climate change are things that should be done in developing countries anyway. This is the case of the Bangladesh Integrated Nutrition program (BINP) for providing pregnant women with nutritional counseling, with the idea that poor nutrition is not only due to poverty but also to ignorance, for instance, the belief in “eating down” during pregnancy (White 2009). Of course knowledge by itself is not enough; resources are required too, so a supplementary feeding program augmented the counseling. This is the kind of factor that comes up in a horizontal search. An analysis by the World Bank’s Operations Evaluation Department found no signiﬁcant impact on infants’ nutritional status, despite the fact that the program had “worked” elsewhere. What went wrong? A number of reasons suggest that the results elsewhere were not evidentially relevant to the success of the policy in Bangladesh. They might have been. It is natural to expect that explanations for the results elsewhere and for Bangladesh success would share an important common element: a general principle. Principle 1: Better nutritional knowledge in mothers plus supplemental feeding improves the nutritional status of their children.

In fact the two populations did not share this principle. The ﬁrst reason for the lack of impact, it seems, is that there was “leakage”: in Bangladesh the food was often not used as a supplement but as a substitute, with the usual food allocation for that child passing to another member of the family (Save the Children 2003). The principle, “Better nutritional knowledge in mothers plus supplemental feeding improves children’s nutrition,” was true in the original successful cases but not in Bangladesh. A better candidate for a shared explanatory element is as follows. Principle 2: Better nutritional knowledge in mothers with sufﬁcient resources to use that knowledge improves children’s nutrition.

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This principle uses concepts at a higher level of abstraction. In the successful cases the more concrete description “food supplied by the supplementary feeding program” counted as an instance of the more abstract concept “sufﬁcient resources,” but not in Bangladesh. Not getting this straight is a failure of vertical search: A failure to identify the right level of abstraction to ﬁnd common explanatory elements. A second reason for the lack of positive impact is also a problem with vertical search. The program targeted the mothers of young children. But mothers are frequently not the decision makers, and rarely the sole decision makers, with respect to the health and nutrition of their children. For a start, women do not go to market in rural Bangladesh; it is men who do the shopping. And for women in joint households—meaning they live with their mother-inlaw—as a sizeable minority do, then the mother-in-law heads the women’s domain. Indeed, project participation rates are signiﬁcantly lower for women living with their mother-in-law in more conservative parts of the country. (White 2009, 6)

This suggests yet another vertical move to secure a shared principle: Principle 3: Better nutritional knowledge results in better nutrition for a child in those who: 1. Have sufﬁcient resources to use that knowledge to improve the child’s nutrition, 2. Control what food is procured with those resources, 3. Control how food gets dispensed, and 4. Hold the child’s interests as central in performing 2 and 3. Just as supplementary food did not count as sufﬁcient resources in the BINP, mothers in that program did not in general satisfy the more abstract descriptions in 2 and 3. The previous successes of the program are relevant to predictions about the BINP only relative to the vertical identiﬁcation of mothers with the abstract descriptions in 2, 3, and 4. But not all of these identiﬁcations hold, so the previous successes are not evidentially relevant. For an RCT to be relevant, and to be justiﬁably taken as such, we need good reasons to back up the claims that the characteristics referred to in study conclusions, which are often fairly concrete, are the same as the characteristics appearing in principles shared across study and target populations, which are often relatively abstract. Consider another possible example, this from UK child welfare policy. In many cases a child’s caregivers, though not legally compelled, are heavily encouraged, perhaps even badgered, into attending parenting classes. Consider in this context making fathers attend parenting classes.

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First, is “father” to be instantiated by “biological father” or, for example, “male partner of the mother who lives in the household with the child,” or maybe “male caregiver”? It may well be that the policy would be effective if the male caregivers or men living with the mothers are the target, but not biological fathers who are neither on site nor caregivers. If so, to focus on “being a father” would be to move to too high a level of abstraction since only the more speciﬁc feature, “male caregiver” or “male partner of mother who shares the child’s household,” enters into a reasonably reliable principle. Yet “compelling father” or “compelling male caregiver” can simultaneously be too concrete. Different cultures in the UK have widely different views about the roles fathers should play in parenting. Compelling fathers to attend classes can fall under the more abstract description, “ensuring caregivers are better informed about ways to help the child,” in which case it could be expected to be positively effective for improving the child’s welfare. But it may also instantiate the more abstract feature “public humiliation,” in which case it could act oppositely. And of course it can fall under both at once. In any case, if the two more abstract features pull in opposite directions, there will be no reliable principle to formulate at the more concrete level involving “fathers.” Nor is this pull in opposite directions an unrealistic hypothesis. We know from empirical research that there are varying outcomes associated with compelling or strongly encouraging parents to attend parenting classes and also that these are correlated with varying motivations (Barlow et al. 2006). Unfortunately we do not yet have sufﬁcient theoretical probing to explain the variation and the correlations.

5. TROUBLES WITH VERTICAL SEARCH To secure explanatory relevance in cases like the BINP, it is necessary ﬁrst to ﬁnd and defend a shared explanatory principle. This involves ﬁnding the right ladder of abstraction to climb and knowing just when to stop.11 But a principle can only be shared between study and target if it applies to both. So it is equally necessary to defend that what happens in the study and what is predicted to happen in the target instantiate the abstract concepts in the putatively shared principle. This is no easy matter since what an abstract property consists in, in the concrete, often differs dramatically from circumstance to circumstance. This problem arises regularly in economic climate mitigation and adaptation models (and many other economic models as well). Consider studies of how to change American insurance schemes to provide ﬁnancial incentives for those living in high-risk areas, like the chic Florida coast,

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to make their homes less prone to risk, for instance by changing the roof construction (cf. Kunreuther and Michel-Kerjan 2009, plus references therein). The models often rely on an assumption from game theory that rational agents act to maximize their expected utility. Here we have to worry about misplaced concretization of the abstract feature “utility.” The models typically take money to instantiate utility. But there is a good chance that the targeted agents—say rich owners of beach-front residences— will be more moved by the disruption to their domestic arrangements of having builders at work for months than by any contrary ﬁnancial incentive that could realistically get built into an insurance scheme. The same problem of context-dependence resurfaces when it comes to measurement, where we see a familiar trade-off: shared principles require higher levels of abstraction, whereas good measurement requires lower levels. For good comparable measurements, we want speciﬁc operational procedures that are carried out in the same way each time the measurement is performed. By contrast, the methods for measuring an abstract feature generally differ depending on what more concrete features the abstract feature consists in, which is not the same from case to case. We are pulled in two directions here. One is to plump for a false universal concretization in order to secure a universal measure. For instance, measure “educational value added” in new British inner-city academies by counting the number of GCSEs passed at a grade of C or better. Alternatively, devise a measurement deﬁnition that more correctly captures the abstract feature of interest across its various concrete instantiations. The danger then is that the deﬁnition will be so abstract that we don’t know what it consists in from situation to situation. For example, what constitutes human ﬂourishing differs dramatically according to individual circumstances and abilities, natural resources, availability of public goods, need, and the like. The capability approach of Amartya Sen (1985; 1999) proposes as a measure “the number of lives worth living open to the individual.” Some propose to measure the economic freedom that individuals enjoy by the size of their choice sets. Neither of these provides much of a clue about what we are actually to do to assign numbers or ranks to the individuals to be measured. For EBPP we look to science for advice. Unfortunately, when it comes to ﬁxing what constitutes abstract features in the concrete, science offers at best rules of thumb that are highly defeasible. In particular they are beset by what John Perry (2010) dubs “the failure of enrichment”: that A consists in M in circumstances C does not imply that A consists in M in circumstances C & C’ for every C’ consistent with C. The moral particularism literature is rife with examples where A is a moral feature.

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Stuart Hampshire, for instance, describes telling stories to philosophical audiences (Hampshire 2000). The stories involve a young intellectual French Fascist, a reader of Celine, held by the Free French, to whom Hampshire is sent by the British to interrogate. The French will execute the young man; but they tell Hampshire that he can certainly promise the prisoner—falsely—that he will not be executed in exchange for information. Is it acceptable, or even required, for Hampshire to lie to the young man? Hampshire tells the story differently on different occasions. Often the descriptions can be nested, the more detailed descriptions containing the previous, plus more. Depending on how Hampshire tells the story, the audience is in general agreement about what he should do, but the verdict changes as he shifts from level to level. Enrichment fails. Hampshire’s stories involve highly abstract features—morally acceptable, morally required. Perry’s own example involves speciﬁc motions that may or may not instantiate his eating a Brussels sprout at his Dewey lecture, depending on the level of detail of the description of the circumstances. So the abstract feature need not be very abstract at all for the failure of enrichment to appear. Where then can we ﬁnd help in science, either with the problem of settling on the right level of abstraction to ﬁnd shared explanatory principles, or of ascertaining what the abstract features in these principles consist in for both study and target populations? I don’t know an answer. But I am sure it takes both theory and local knowledge, neither of which are much in favor in EBPP communities. Without these, scientiﬁc studies like RCTs, which are so highly prized for the credibility they confer on their results, will not be explanatorily relevant to the predictions about what will work for us in practice and policy. And I am sure Achinstein is right for these kinds of cases: if explanatory relevance goes, so too goes evidential relevance. Then we have no scientiﬁc evidence to bring to bear, and evidence-based policy and practice is out the window.

ACNOWLEDGMENTS Research for this essay was supported by grants from the British Academy to study evidence for use; the LSE ESRC Centre for Climate Change, Economics, and Policy and the associated Grantham Centre; and a UK AHRC grant to study evidence related to child welfare policies. I am grateful to all three for ﬁnancial support and to collaborators on them for intellectual support. I am also grateful to Eileen Munro for help with the child welfare example and to Adam Spray and Ravit Alfandari for help in editing.

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REFERENCES Achinstein, P. 2004. A Challenge to Positive Relevance Theorists: Reply to Roush. Philosophy of Science 71 (4): 521–24. ——— . 2001. The Book of Evidence. New York: Oxford University Press. ——— . 1996. Swimming in Evidence: A Reply to Maher. Philosophy of Science 63 (2): 175–82. ——— . 1983. The Nature of Explanation. New York: Oxford University Press. ——— . 1981a. Can There Be a Model of Explanation? Theory and Decision 13: 201–27. ——— . 1981b. On Evidence: A Reply to Bar-Hillel and Margalit. Mind 90 (357): 108–12. ——— . 1978. Concepts of Evidence Mind 87 (345): 22–45. Anscombe, G. E. M. 1993. Causality and Determination. In Causation, ed. E. Sosa and M. Tooley. Oxford: Oxford University Press. Barlow, J., I. Johnson, D. Kendrick, L. Polnay, and S. Steward-Brown. 2006. Systematic Review of the Effectiveness of Parenting Programmes in Treating Abusive Parenting. Cochrane Database of Systematic Review 3: 1–20. Cartwright, N. Forthcoming. The Long Road from RCTs to Effectiveness. The Lancet. ——— . 2007. Hunting Causes and Using Them. Cambridge: Cambridge University Press. Cartwright, N., and E. Munro. 2010. The Limitations of Randomized Controlled Trials in Predicting Effectiveness. Journal of Evaluation in Clinical Practice 16 (2): 260–66. Hampshire, S. 2000. Justice Is Conﬂict. Princeton: Princeton University Press. Kunreuther, H., and E. Michel-Kerjan. 2009. At War with the Weather: Managing Large-Scale Risks in a New Era of Catastrophes. New York: MIT Press. Pawson, R., and N. Tilley. 1997. Realistic Evaluation. London: Sage. Perry, J. 2010. Dewey Lecture: Wretched Subterfuge. American Philosophical Association: Paciﬁc Division. Save the Children. 2003. Thin on the Ground. London: Save the Children. Sen, A. 1999. Development as Freedom. New York: Knopf. ——— . 1985. Commodities and Capabilities. Oxford: Oxford University Press. White, H. 2009. Theory-Based Impact Evaluation: Principles and Practice. New Delhi: The International Initiative for Impact Evaluation.

NOTES 1. The ideas of Peter Achinstein I draw on here are primarily from Achinstein 2001; 1983. But of course I also draw from his long series of works over three decades from Achinstein 1978 onwards. 2. For Achinstein’s views on why purely probabilistic characterizations of evidence do not work, see, inter alia, Achinstein 2004, 1996, 1981a. 3. For Achinstein’s views on this issue, see especially Achinstein 1981b. 4. Subscript “u” marks the unshared elements of the explanations. 5. I suppose here that X would not ﬁgure in any other correct explanation for H were H to obtain.

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6. One can express this more formally, but that seems needlessly complicated for our purposes. 7. Elsewhere I describe this case in terms of capacities. The same kinds of problems arise in both cases. 8. See Pawson and Tilley 1997 for a good use of the example of CCTV cameras in parking lots discouraging car theft to argue the need for what I here call “horizontal search,” and to show how understanding the mechanism at work can help with that. 9. I think, however, that negative judgments by these organizations are often made on bad premises. They tend to presume that trusting to pure method is always better than supposing substantive knowledge claims. That, for example, is why RCTs are the gold standard, and econometric modeling doesn’t get a look in. See Cartwright 2007 for more details. 10. Here I shall be relatively cavalier about the metaphysics of properties. I treat both abstract features and concrete ones as real, and I treat them as different features even if having one of these (the more concrete feature) is what constitutes having the more abstract one on any occasion. I take it that claims like this can be rendered appropriately, though probably differently, in different metaphysical accounts of properties. 11. Stopping matters. Increased abstraction generally goes along with increased generality. So the more abstract the principles you embrace, the more so-far-unexplored concrete predictions you are committed to. My own advice has always been: don’t commit to anything more than you need. That is why I have always urged sticking to the numerous more concrete, detailed laws that explain—and explain in proper detail—the various natural and experimental results we observe rather than committing to the super-abstract laws of high theory.

3 Maxwell, Matter, and Method: Maxwellian Methodology, Methodological Maxwellianism, and Methods of Historical and Philosophical Speculation Jordi Cat

1. INTRODUCTION Europe’s history may be expressed by the history of representations of Greece. Similarly, the history of philosophy of science may be tracked by the history of representations of scientists such as James Clerk Maxwell. In this, the “many-Maxwells interpretation,” Peter Achinstein stands in the company of distinguished others. In this essay, I examine Achinstein’s historical and philosophical speculations about Maxwell’s natural philosophy, and those speculations’ role as evidence for Achinstein’s more general philosophical speculations. Achinstein seeks the authority of Maxwell, as a theoretical physicist; as an author of a kinetic theory of gases and the theory of electromagnetism, committed to the existence of molecules; as a contributor of theoretical derivations valued regardless of their experimental, meta-theoretical, or philosophical signiﬁcance; as an author of methodological models; and as a proponent and practitioner of a “method of physical speculation.” As a meta-methodological expression of Maxwell’s method of physical speculation, one may call Achinstein’s methodological move a method of philosophical speculation. At the methodological and meta-methodological level, scientiﬁc realism requires an adequate empirical basis, or pool of instances of scientiﬁc practice. Here is where the historical record plays the key role in Achinstein’s approach. I call this position methodological historicism. It requires a philosophical understanding of scientiﬁc concepts, restricted to the application of abstract deﬁnitions to actual historical scientiﬁc

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cases. This application is constrained by the scientists’ explicit beliefs and conceptions. One constraint is guidance from the scientists’ particular deﬁnitions. The move sets two clear methodological demands: the correct attribution of the meta-scientiﬁc or philosophical concept to the scientist, instantiated in his abstract commentary; and further instantiation of the conception, articulated by the scientist or someone else, in his or another’s practice (Achinstein 2010). I argue, or at least suggest, that: (1) Achinstein’s method and his conclusions depend on his speculative representation of Maxwell’s work; (2) they depend on a particular correspondence between his general philosophical concepts of evidence, explanation, understanding, and realism and those of Maxwell; (3) Achinstein’s Maxwell can be substituted with another speculation that, in his language and Maxwell’s, appears more warranted; and (4) the new Maxwell teaches new lessons.

2. MOLECULAR UNDERSTANDING For Achinstein, the kinetic theory of gases of 1860 is not a physical analogy, but an “identical property analogy,” an explanation, a realistic explanatory speculative hypothesis, based on the laws of the system of unobservable particles and the identity of the properties of the two systems (Achinstein 1991, 220–1). Achinstein sees here a meta-methodological path to realism. He speculates on the workings of another method, neither analogy nor mere hypothesis, which Maxwell named in a discussion of molecular theories only in 1875 (Niven 1890, vol. 2, 429). This is the so-called method of physical speculation. Equations and identity statements, however, do not constitute reliable indicators of a commitment to physical identities or explanatory causal relations. Maxwell used them in 1855 as metaphorical statements, to represent physical analogies in his electromagnetic model. After referring to “the analogy in ﬂuid motion,” he immediately stated that “lines of force are the unit tubes of ﬂuid motion,” and that (the electrical potential) V = –p (ﬂuid pressure) (Niven 1890, vol. 1, 177; Cat 2001). In the case of the 1860 molecular theory of gases, Maxwell declared explicitly his aim to establish “an important physical analogy” (Niven 1890, vol. 1, 378); physical analogies illustrate theories, rendering them and the phenomena to be explained “intelligible.” His intention and accomplishment were stamped in the paper’s title, “Illustrations of the Dynamical Theory of Gases.” Contrast this title with the more conﬁdent title of the subsequent paper of 1866, “The Dynamical Theory of Gases” (Niven 1890). The contrast appears intercalated chronologically, and conceptually linked, with a

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similar one in the context of electromagnetism. Maxwell’s project evolved from the physical analogies of “On Faraday’s Lines of Force” (1855–56) to the more assertive “On Physical Lines of Force” (1861–62) and “A Dynamical Theory of the Electromagnetic Field” (1864). Finally, in 1875 we ﬁnd a reference to the “method of physical speculation” (Niven 1890, vol. 2, 420) and in 1876 to “the true method of physical reasoning” (Niven 1890, vol. 2, 309).

3. AGAINST METHOD: WHERE AND WHAT IS THE METHOD OF PHYSICAL SPECULATION? In pursuit of a theory-oriented argument for realism, Achinstein wishes to explain some of Maxwell’s scientiﬁc work in terms of the method called physical speculation. Achinstein contrasts it with the hypothetico-deductive method, which is linked to the role of observation. A hypothesis gets its credibility from the conﬁrmation of the observational inferences— predictions and explanations—it makes; it loses credibility to the extent that it shares credibility with equally successful competing hypotheses. Instead, he attributes to Maxwell the use of the method of speculation “to develop and defend a theory (or at least the set of its central and distinctive assumptions) to be true, without being able to experimentally prove that it is true” (Achinstein 2009, 35). What is this method? In Particles and Waves, Achinstein characterizes the method in terms of an emphasis on theoretical derivations and a condition of independent warrant (Achinstein 1991, 223–4). Recently, for example in “What to Do If You Want to Defend a Theory You Cannot Prove: A Method of ‘Physical Speculation,’” he has expanded his reconstruction to an additional aim, to answer questions about the relevant unobservables with precision and completeness sans epistemic warrant. What constitutes the method per se has expanded to four components: independent warrant, derivations and explanations of known phenomena, theoretical development, and unsolved problems (Achinstein 2009, 40–6). Achinstein addresses the ﬁrst component, independent warrant, with three examples and sorts of independent warrant that play the role that observation and experiment play in the inductive methods: (1) experimental results and observations from another domain of phenomena and related to another theory that nevertheless bear an analogical or causal inductive relation to the primary domain; (2) a methodological defense of the fundamental character and simplicity of the principles applied in the theory of the unobservables; (3) an inductive defense of the same principles based on their success in another domain (Achinstein 2009, 41–2). They

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provide epistemic warrant for the molecular theory of gases, independent of any predictive and explanatory role. The ﬁrst example seems inadequate. The evidence cited by Maxwell, dating from 1819, plays its role of evidence in the hypothetico-deductive form (Niven 1890, vol. 2, 457). The second and third examples involve prior defense, empirical success, and methodological values. The case of dynamical explanation plays a top-down role in its eligibility to contribute to the construction of models. But that is not the ultimate source of warrant. Either way, this is a feature of hypothesis-construction common in the application of the hypothetico-deductive method. Methodological values are important, and Achinstein cites simplicity and completeness of dynamical explanation. Unity, precision and generality, intelligibility, and explanation itself are related values (see below). The constraining and constructing role of determination by fundamental ideas and mathematical and dynamical reasoning are central to Maxwell’s perspectivalism, and his scientiﬁc “point of view.” In his preface to Matter and Motion, Maxwell introduces physical science as having entered “the next stage of progress,” which he characterizes in dynamical “fundamental ideas” and “strict reasoning”: “the energy of a material system is conceived as determined by the conﬁguration and motion of that system, and in which the ideas of conﬁguration, motion, and force are generalized to the utmost extent warranted by their physical deﬁnitions” (Maxwell 1952, Preface). The second component of the method is the derivation and explanation of known phenomena. But that is also a standard feature of some uses of the hypothetico-deductive method. None of the aforementioned values, constraints, or aims constitute a condition of independent epistemic warrant, or operate or are formulated as such, especially in any uniﬁed and systematic, that is, methodological way. There is no gain in setting it apart as a distinguishing component of some other hypothetical methodological cluster. The third component, theoretical development, goes to the heart of Achinstein’s program. He rightly points out, here (Achinstein 2009) and in more detail in Particles and Waves, that part of Maxwell’s work in kinetic theory of gases takes the form of theoretical derivations that have little direct empirical grounding or seek any empirical insight and prediction. Surely, he concludes, this fact about scientiﬁc practice invites a broader perspective, away from observation-constrained methodologies, one that values the derivation of information of unobservables making room for realism. All of this will require independent forms of warrant. That by itself is no warrant for Maxwell’s dynamical models, or for realism. As in other applications of the method of analogies, the deriva-

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tion of theoretical developments and results, including the laws of electromagnetism, do not dictate a realist position. They compel a realist position no more or less than the values of unity of the construction of intelligible models or conceptions do. Even recent accounts of understanding that are closer to Achinstein’s than to Maxwell’s in the centrality of explanation do not require, in fact shun, realism (see de Regt, Leonelli, and Eigner 2009). Achinstein’s emphasis on theoretical derivation in kinetic theory helps weaken any overly empiricist picture of Maxwell’s science. It is consistent with his application of the newly minted energy principle and his defense of the project of kinetic theory in the light of famous greatest difﬁculties. This, however, needs to be integrated alongside his commitment to experimentalism and the modiﬁcation of models in response to experimental results as well as his conceptualist positions and philosophical speculations (Cat 2011). The fourth and ﬁnal component, problem-solving, is central to Maxwell’s creative but humble, instrumental, and cautious attitude toward the construction of science. Yet it does not by itself warrant any speculation about the operation of methods that certify a position not expressed, or expressed as linked to the hypothetical method itself. If there is any independent, scientiﬁc warrant for Achinstein’s method of speculation, it is not in Maxwell. This is a problem that afﬂicts the very structure of the method presented in Achinstein’s speculation. Its disunity and unsystematicity suggest that Maxwell himself defended it as a point of view, rather than as a method. But this cannot be good enough for Achinstein’s realist project. Achinstein needs to lend credence to this Maxwellian methodological unobservable from within the Maxwellian context in order to support his meta-methodological philosophical program. A much earlier and alternative discussion of the method of physical speculation was put forward ﬁrst by Jon Dorling (1970). Dorling’s version is to consider Maxwell’s method of physical hypothesis as a localized argument rather than a general method. Dorling’s characterization of the form of the argument is this: a deductive inference from a phenomenon q and a general theoretical assumption o to a hypothesis p that is meant to explain the phenomenon q, which o alone cannot explain (Dorling 1970, 238–9).What this reconstruction shares with Achinstein’s is the emphasis on the requirement that the assumption o be independently warranted. Curiously, for Dorling, this is an argument for non-speculative theory construction.1 More relevant to Achinstein’s meta-methodological purposes is the question, how local is too local?

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4. THE TWO FACES OF GENERALITY OF REPRESENTATION: FROM EXPLANATION TO WARRANT. (1) The path of the method of hypothesis In Maxwell’s research, a series of reciprocal inputs of general principles and particular conceptual and material models take place in different domains of inquiry. The complex process seems to have generated an effect of methodological consilience of induction for a generalized project of molecular science. Molecular science is molecular modeling. By the early 1870s Maxwell was fully steeped in “modern molecular science” (Niven 1890, vol. 2, 451). Molecular science is concerned with how to characterize and individuate a molecular part of a system and its connection with others in order to explain phenomena. Simultaneously, he held high the aims of completeness and dynamical explanation and provided dynamical theories of electromagnetism and dynamical theories of gases. From the new perspective, Maxwell declares in Matter and Motion that Newton’s presumably inductive, empirical method was inadequate for the pursuit of molecular science as described above and writes instead of the “methods of molecular investigations.” In contrast with Achinstein’s account, the two key ideas are these: the methods of molecular investigation serve the purpose of pursuing molecular science, not a philosophy of realism; and, the method of investigation, Maxwell notes approvingly, has been “the method of hypothesis”! Finally, the method of hypothesis involves “comparison of the results of the hypothesis with the observed facts” (Maxwell 1952, 122). What hypothesis? The differences in results among the areas of elastic theory, electromagnetic theory, and the theory of gases show that dynamical theories didn’t always take the eventual form of molecular models or hypotheses. Molecular hypotheses suffered different fates on different fronts, as he explains in the article “Atom” (Niven 1890, vol. 2, 445–84). Maxwell’s enduring methodological concern with the construction and justiﬁcation of hypotheses applied to the new framework in the 1870s by appeal to his other equally enduring concerns with determination and generality. This is the methodological development in the 1870s behind Maxwell’s talk of “method of hypothesis” (Maxwell 1952, 122), “method of physical speculation” (Niven 1890, vol. 2, 420), and “true method of physical reasoning” (Niven 1890, vol. 2, 309). The key methodological parameters to track are: hypothesis, phenomena, determination, explanation, and generality. Maxwell’s methodology in his early papers follow the problem-solving format of Euclid’s Elements of Geometry (Heath 2002), his longtime companion from school and college, and the exercises in preparation for

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the Honors Tripos examinations.2 The format required him to determine, or ﬁnd, solutions of equations or values of quantities, with an operative notion of generality of principles, laws, axioms, or assumptions based on the application to a plurality of particular cases. Only two epistemologically signiﬁcant considerations appear to have been published. In a short 1853 paper, he mentions aiming at a Herschelstyle “general explanation of the true cause of the phenomenon” (Niven 1890, vol. 1, 115). In another undergraduate paper, Maxwell places his research ﬁrmly after the model of the application of the calculus by his teacher Stokes and his distant mentor Kelvin. The goal remains “the formation and application of general equations,” which in Edinburgh-style fashion he motivates historically. French mathematicians’ work in elastic theory, Maxwell notes, is based on axioms themselves resting on molecular hypotheses. But the molecular hypotheses led to “conclusions which were shewn to be erroneous by the observations of experimental philosophers” (Niven 1890, vol. 1, 30). Maxwell’s alternative was to derive empirically superior equations from axioms that “are the results of experiments” (31). Both hypotheses and general equations are independently warranted: the former more speculatively in the wake of the Newtonian success and Laplacean style; the latter, on assumptions idealized from experiment (like modeling, never a straightforward logical argument). The crux of the methodological matter lies in the role of the confrontation with experimental results. Maxwell is applying a version of the hypothetico-deductive method, one that values the correct explanation by mathematical determination of experimental data or phenomena. Generality is a value: Maxwell’s explanation is empirically more general. A similar framework resurfaces in Maxwell’s ﬁrst formulation of the dynamical theory of gases, or, rather, of its dynamical illustration that would “lead to a more accurate knowledge of the properties of matter.” He is not dismissing hypotheses beforehand. Maxwell is explicit about his methodological criterion: “If experiments on gases are inconsistent with the hypothesis of these propositions, then our theory, though consistent with itself, is proved to be incapable of explaining the phenomena of gases.” Testing its explanatory value, or warrant, requires us “to follow out the consequences of the hypothesis,” to work out theoretical derivations or determinations (Niven 1890, vol. 1, 378). Maxwell deﬁnes the method of hypothesis relative to an established domain of phenomena. It emphasizes general explanatory success and empirical refutation. In Maxwell’s attempt at a formulation of a complete molecular theory of electromagnetism in 1861, he insists on a similar methodological approach to hypotheses: “I propose now to examine magnetic phenomena from a mechanical point of view” (Niven 1890, vol. 1, 452) Within this framework

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Maxwell constructs his model as such, “an imaginary system of molecular vortices,” and presents its role as the source of mathematical—dynamical— coherence, as part of intelligibility, and as a “comparison between its necessary results and known facts” (488). Maxwell acknowledges the plurality of competing types of hypotheses as a historical fact and also makes explicit its methodological signiﬁcance, the evaluation of the empirical warrant of explanations, not just hypotheses, from the inductive point of view, the hypothetico-deductive mode of justiﬁcation, and with respect to Whewell’s additional consideration of consilience of induction: The facts of electro-magnetism are so complicated and various, that the explanation of any number of them by several different hypotheses must be interesting, not only to physicists, but to all who desire to understand how much evidence the explanation of phenomena lends to the credibility of a theory, or how far we ought to regard a coincidence in mathematical expression of two sets of phenomena as indication that these phenomena are of the same kind. (Niven 1890, vol. 1, 488)

When he next switches to the molecular dynamical theory of gases, the goal of a general explanation of phenomena and empirical properties remains the central aim. The value of the molecular theory lies in providing the ability “to explain a great variety of phenomena by dynamical theory which have not been hitherto explained otherwise” (Niven 1890, vol. 2, 27). In 1871, Maxwell returned to a central trope of his earlier methodological academic speeches that overlapped with his research: the formal determination of precise quantities and its methodological relevance to empirical grounding. The growth of physical science, writes Maxwell, consists ﬁrst in the “discovery of a system of quantities on which its phenomena may be conceived to depend” and the “mathematical form of the relation between the quantities.” Next comes “the veriﬁcation of the laws” through measurement in experimental conditions (Niven 1890, vol. 2, 257). Maxwell insists on the conceptual value of the construction of hypotheses and the value of theoretical development even in the most experimental of contexts. His obituary of Faraday, the foremost experimental philosopher of his time, adopts the same methodological viewpoint (with a Whewellian twist): For the advancement of the exact sciences depend upon the discovery and development of appropriate and exact ideas, by means of which we may form a mental representation of the facts, sufﬁciently general, on the other hand, to stand for any particular case, and sufﬁciently exact, on the other, to warrant the deductions we may draw from them by the application of mathematical reasoning. (Niven 1890, vol. 2, 360)

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Intelligibility and testability are not replaced by exclusive strategies for realism. Maxwell points out, in a hint of idealist metaphysics, the Whewellian value of the fundamental ideas to be “modes of thought by which the process of our minds is brought into the most complete harmony with the process of nature” (325).

(2) Drama of indetermination Maxwell refers to the method of physical speculation in a lecture in 1875 to members of the Chemical Society (Niven 1890, vol. 2, 418). To establish the relevance of physics to chemistry, Maxwell sets out to introduce the fundamental ideas for his proposal. He starts with explanation: When any phenomenon can be described as an example of some general principle which is applicable to other phenomena, that phenomenon is said to be explained. Explanations, however, are of very various orders, according to the degree of generality of the principle which is made use of. (Ibid.)

Dynamical explanation in terms of change in the conﬁguration and motion of a material system is complete and ﬁnal. Unlike in the domain of astronomy or electricity, the complete dynamical explanation of chemical phenomena requires unobservable hypotheses. Maxwell introduces the hypothetico-deductive method thus: “that of forming an hypothesis, and calculating what would happen if the hypothesis were true. If these results agree with the actual phenomena, the hypothesis is said to be veriﬁed . . .” And here for the ﬁrst time Maxwell adds the qualiﬁcation, “so long, at least, as some one else does not invent another hypothesis which agrees still better with the phenomena” (Nivens 1890, vol. 2, 419). He spells out the logical form of the problem in Matter and Motion within a Lagrangian context attached to the method of hypothesis as the method of molecular science: If, on the other hand, we frame the hypothesis that the conﬁguration, motion, or action of the material system is of a certain deﬁnite kind, and if the results of this hypothesis agree with the phenomenon, then, unless we can prove that no other hypothesis would account for the phenomena, we must still admit the possibility of our hypothesis being a wrong one. (Maxwell 1952, 122, my emphasis)

What Maxwell is decrying, if rather unreasonably, is the fallibility of hypotheses. From a logical point of view, he is not rejecting the method of hypothesis so much as the logical form of the deﬁnite and particular hypothesis as the relevant candidate for veriﬁed general explanation. Phenomena underdetermine the truth of speciﬁc molecular hypotheses.

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The semantic and logical problem of deﬁniteness and determination was an old anxiety of growing presence in his work with interpretive and epistemic implications (Cat 2011). The value and applicability of mathematical language depend on precise form based on determinate relations. Even so, its application to counting and measurement requires conventional units or standards. The advancement of knowledge during his student years had the canonical form of determining solutions to problems, which meant the determination of forms of functions or values of variables. Many words and ideas were fraught with indeﬁniteness and had little methodological value. A standard problem in the application of analysis he learned from his tutor and from his tutor’s earlier student Kelvin was the problem in potential theory that the differential equations left the value of the potential indeterminate. This fact was compatible with the instrumental interpretation of the gravitational potential, underdetermined by the value of force at any point. But it had more serious implications for the physical interpretation of electrical and magnetic potential functions, and their physical analogy with temperature (Cat 2001; 2011). In color theory, Maxwell encountered as a consequence of applying mathematical relations between colors that “there are an inﬁnite number of pairs of complementary colours in the spectrum” (Niven 1890, vol. 1, 414). In the molecular theory of gases, Maxwell had to face the representation of the dynamics of “an indeﬁnite number” of particles (377). Failure of determination became more radical when indeterminism took the form of the methods of probability and statistics and Maxwell faced the prospect of relinquishing the speciﬁc dynamical determination of the state of each molecule—called the “historical method”—and as a result replacing the complete dynamical explanation for a population of molecules, with the “statistical method” (Niven 1890 vol. 2, 372). For our purposes, the most dramatic challenge comes from the failure to construct a complete and consistent molecular model of the electromagnetic ether, with a speciﬁc hypothesis about the hidden connecting mechanisms. In 1867 Kelvin and Tait set out to establish the science of dynamics on the foundations set by the new general energy principles and methods (Cayley 1857; Thomson and Tait 1867). From this standpoint, Maxwell could admit in 1873 in the Treatise on Electricity and Magnetism to another mathematical and logical failure of determination that correlated with a failure of physical signiﬁcance and failure of epistemic warrant: The attempt which I then made to imagine a working model of this mechanism must be taken for no more than it really is, a demonstration that mechanism may be imagine capable of producing a connexion mechanically

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equivalent to the actual connexion of parts of the electromagnetic ﬁeld. The problem of determining the mechanism required to establish a given species of connexion between the motions of the parts of a system always admits of an inﬁnite number of solutions. (Maxwell 1955, vol. 2, 470, my emphasis)

From this epistemic standpoint, the cognitive agents applying the hypothetico-deductive method to concrete hypotheses are “speculators.” The cognitive attachment to the intelligibility provided by particular concrete models or hypotheses is what led “the speculators” to “leave their ideas vague and therefore useless” (Nivens 1890, vol. 2, 419). Maxwell’s solution to the physical speculators’ problem is to follow the Continental mathematicians such as Lagrange and his new general method of dynamics, which Kelvin and Tait reformulated in terms of the “method of ignoration” of speciﬁc details for the construction of the right coordinates to turn the tables on indeterminacy, ignorance, arbitrariness, and ambiguity. The solution is to apply the method of hypothesis to a new logical species of hypothesis, as general as can be, to aim at the most empirically “warrantable” one. This is the so-called method of physical speculation: [Mathematicians] had developed with the utmost generality the dynamical theory of a material system. Of all hypotheses as to the constitution of bodies, that is surely the most warrantable which assumes no more than that they are material systems, and propose to deduce from the observed phenomena just as much information about the conditions and connections of the material system as these phenomena legitimately furnish. When examples of this method of physical speculation have been properly set forth and explained, we shall hear fewer complaints of the looseness of the reasoning of men of science, and the method of inductive philosophy will no longer be derided as mere guess-work. (Niven 1890, vol. 2, 420, my emphasis)

In particular, For whatever may be our ultimate conclusions as to molecules and atoms, we have experimental proof that bodies may be divided into parts so small that we cannot perceive them. (Ibid., my emphasis)

The most plausible methodological conclusion is this: the only recognizable formulation and application of the method of physical speculation is not a logical alternative to the method of hypothesis per se; it is not an exclusively theoretical method; and it is not a non-inductive method for the defense of realism about the speciﬁc models or hypotheses about unobservables. Maxwell’s solution to the physical speculators’ problem was to impose the viewpoint of generality of representation. With all its associated values of construction and guidance, it is an inductive method

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linked to empirical warrant. The method of physical speculation, I propose, is the method of generalized hypothesis. Maxwell writes in the same terms about the method of hypothesis in Matter and Method in the same context of dynamical explanation: The success of this method depends on the generality of the hypothesis to begin with. If our hypothesis is the extremely general one that the phenomena to be investigated depend on the conﬁguration and motion of a material system, then if we are able to deduce any available results from such a hypothesis, we may safely apply them to the phenomena before us. (Maxwell 1952, 122, my emphasis)

He concludes: “It is therefore of the greatest importance in all physical inquiries that we should be thoroughly acquainted with the most general properties of material systems” (ibid., my emphasis). Unlike the other two formulations and interpretations of the method of physical speculation, namely Achinstein’s overly disuniﬁed and distorted one and Dorling’s overly localized one, my more modest proposal is grounded on a more general pattern of conceptual considerations and a broader view of the many different speciﬁc yet connected contexts underlying it. Its plausibility is increased further by the fact of removing two puzzles raised by the others. It is consistent with Maxwell’s presentation of “the true method of physical reasoning” in 1876, between the year of coining “the method of physical speculation” and the year of an analogous discussion in Matter and Method. The true method of physical reasoning is the method of physical speculation. There is only the method of generalized hypothesis: The true method of physical reasoning is to begin with the phenomena and to deduce the forces from them by a direct application of the equations of motion. The difficulty of doing so has hitherto been that we arrive, at least during the first stages of the investigation, at results which are so indefinite that we have no terms sufficiently general to express them without introducing some notion not strictly deducible from our premises. It is therefore very desirable that men of science should invent some method of statement by which ideas, precise so far as they go, may be conveyed to the mind, and yet sufficiently general to avoid the introduction of unwarrantable details. (Niven 1890, vol. 2, 309)

This also explains the apparent tension between the dynamics of gases and the dynamics of ﬁelds: that is, the inconsistency in the qualiﬁcation of dynamical theory applied at the same time to a molecular theory of gases and a ﬁeld theory of electromagnetism that avoids representing the hidden connections that escape it. Already in the ﬁrst formulation of 1864, Maxwell writes that the descriptions in the model of the speciﬁc mechanisms in the ether “are to be considered as illustrative, not as explanatory,”

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whereas, at the general level, “speaking of the Energy of the ﬁeld, however, I wish to be understood literally” (Niven 1890, vol. 1, 564). As the method of physical speculation, the true method of physical reasoning gets its methodological signiﬁcance as an episode in the history of the methodological virtue of generality. Maxwell’s initial dictum that physical theory is devoted to the pursuit of generality and precision (Niven 1890, vol. 1, 159; vol. 2, 360) was explicated in terms of the methodological aims of generality of explanation and generality of reasoning (vol. 1, 188, 272, 488; vol. 2, 419). The empirical injunction mandated exploring limiting cases and the limits of applicability of mathematical (physical) laws (vol. 2, 418–20). Generality of scope is valuable within a larger domain of thought. One might speak not just of an internal history of generality, but an external, broader culture of generality that calls for more detailed study. Two elements of that culture or context are British logic and algebra in the 1830s and 1840s. Through the metaphysics lectures of his teacher in Edinburgh, the Kantian-Aristotelian William Hamilton, Maxwell became aware of the logical and epistemological value of generality. He would revisit the matter in his readings on scientiﬁc reasoning by Cambridge-trained Herschel and De Morgan (on logic of probability, belief, and evidence) and, at Cambridge, in readings by Whewell and Mill. Also in Edinburgh, concerns with the role of generality became attached to developments in mathematics, that is, George Peacock’s new algebra at Cambridge based on generalization of form, symmetry and invariance (Peacock 1830, Preface, ix and 68), reported by his student and Maxwell’s teacher Philip Kelland (1839).3 Maxwell’s fascination with formal and physical analogy was partially in the spirit of the cognitive place of relations (learned from the idealist philosophy of Edinburgh’s William Hamilton). It implied the methodological use of invariance and symmetry, even in the manipulation of ordinary language, and also in puns (Harman 1995, 376). The pursuit of generalization and symmetry was accomplished precisely by adopting a strategy of concreting the abstract, by establishing abstract–concrete relations to serve a number of different heuristic and cognitive purposes, from keeping off speciﬁc unobservable microstructures from representation of phenomena to the “ﬁxing” of abstract concepts. He also turned to methodological matters of evidence. In a letter of the summer of 1850, in hiatus between Edinburgh and Cambridge, Maxwell borrowed De Morgan’s vocabulary in his Formal Logic: Or, the Calculus of Inference, Necessary and Probable (1847) to write as follows: When the probability (there is no better word found) in a man’s mind of a certain proposition being true is greater than that of its being false, he believes

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it with a proportion of faith corresponding to the probability, and this probability may be increased or diminished by new facts. This is faith in general. When a man thinks he has enough of evidence for some notion of his he sometimes refuses to listen to any additional evidence pro or con, saying, “It is a settled question, probatis probata; it needs no evidence; it is certain.” This is knowledge as distinguished from faith. (Campbell and Garnett 1882, 144–5)

Then came the shift. In the 1860s and 1870s generality became entrenched in physics in connection with the unifying spirit embodied in the quantitative principle of conservation energy applied by Helmholtz, Kelvin, and Tait, imagined qualitatively by Faraday to make sense of all the phenomena of interrelation of distinct forces. Cayley contributed to this process the Continental methods of generalized or connected systems with generalized coordinates. This is the period when Maxwell also started writing about material “systems” rather than “bodies,” and he ended up writing about “degrees of freedom.” The commitment to generality of representation extended to the earlier cognitive rhetoric of science, bridging the illustrative gulf between the abstract and the concrete. In the new dynamics of connected systems, mechanical terms are employed “in a sense, which, though perfectly analogous to the elementary sense, is wider and more general.” And he added: “These generalized forms of elementary ideas may be called metaphorical terms in the sense in which every abstract term is metaphorical” (Niven 1890, vol. 2, 227). The new emphasis on probabilistic methods and interpretations, both in the kinetic theory of gases and in thermodynamics (as can be seen illustrated by the famous Maxwell’s demon thought experiment) also contributed to this micro-history of generality. Maxwell had new recourse to his earlier epistemic considerations related to De Morgan’s views and associated “extremely general” with high probability of being right. All this additional historical detail suggests, with robustness of circumstantial evidence, a different methodological pattern, both later and smaller. The method of physical speculation is the method of generalized hypothesis. What realism is left beyond the intelligibility of hypotheses is what may be called a generalized realism, realism about general speculations qua general, that is, speculations based on the further assumption of some particular— but as yet unknown, indeterminate, or more uncertain—representation.

ACKNOWLEDGMENTS Thom Gennaro and Pat McNeela helped shorten this essay to one third of its original length.

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REFERENCES Achinstein, P. 2010. Evidence, Explanation, and Realism. New York: Oxford University Press. ——— . 2009. What to Do If You Want to Defend a Theory You Cannot Prove: A Method of “Physical Speculation.” Journal of Philosophy 107 (1): 35–56. ——— . 1991. Particles and Waves. New York: Oxford University Press. Babbage, C. 1817. Observations on Analogy Which Subsists between the Calculus of Functions and Other Branches of Analysis. Philosophical Transactions of the Royal Society 107: 197–216. Campbell, L. and W. Garnett. 1882. The Life of James Clerk Maxwell. London: Macmillan. Cat, J. 2011. Master and Designer of Fields: James Clerk Maxwell and Concrete, Constructive and Connective Natural Philosophy. Oxford: Oxford University Press. ——— . 2001. On Understanding: Maxwell on the Methods of Illustration and Scientiﬁc Metaphor. Studies in the History and Philosophy of Science 32 (3): 395–441. Cayley, A. 1857. Report on the Recent Progress of Theoretical Dynamics. In Report of the British Association for the Advancement of Science, 1857. London: British Association for the Advancement of Science. De Regt, H., S. Leonelli, and K. Eigner, eds. 2009. Scientiﬁc Understanding: Philosophical Perspectives. Pittsburgh, Pa.: Pittsburgh University Press. Dorling, J. 1970. Maxwell’s Attempts to Arrive at Non-Speculative Foundations for the Kinetic Theory. Studies in History and Philosophy of Science 1 (1): 229–48. Harman, P., ed. 1995. The Scientiﬁc Letters and Papers of James Clerk Maxwell, vol. 1. Cambridge: Cambridge University Press. Heath, T. L. 2002. Euclid’s Elements. Santa Fe, N.M.: Green Lion Press. Kelland, P. 1839. Elements of Algebra. Edinburgh: Adam & Charles Black. Maxwell, J. C. 1955. Treatise on Electricity and Magnetism. New York: Dover. ——— . 1952. Matter and Motion. New York: Dover. Niven, W. D., ed. 1890. The Scientiﬁc Papers of James Clerk Maxwell. Cambridge: Cambridge University Press. Peacock, G. 1830. A Treatise on Algebra. Cambridge: Cambridge University Press. Thomson, W. and P. G. Tait. 1867. Treatise on Natural Philosophy. Oxford: Oxford University Press. Warwick, A. 2001. Masters of Theory: Cambridge and the Rise of Mathematical Physics. Chicago: University of Chicago Press.

NOTES 1. Achinstein mentions Dorling’s paper in a footnote in Particles and Waves but does not discuss it or give it credit. 2. The subsequent inﬂuence of the Cambridge Tripos has been discussed by Andrew Warwick in Warwick 2001. 3. See also Babbage 1817, 203.

4 Achinstein’s Newtonian Empiricism Victor Di Fate

1. INTRODUCTION One unmistakable characteristic of Peter Achinstein’s work on scientiﬁc method is his emphasis that certain issues, often assumed by philosophers to be logical or conceptual matters, really have an empirical character.1 Achinstein is not alone, of course, in arguing that empirical information is indispensable for methodology, even among his contemporaries; but he does have a distinct point to make. Consider, by way of contrast, Larry Laudan’s so-called Normative Naturalism (Laudan 1996, 125–79). On Laudan’s view, methodological rules are best construed as hypothetical imperatives connecting means to whatever legitimate ends prevail at the present stage of science.2 The methodologist’s charge is then to comb through the historical record and determine which rules are most reliable for attaining these aims—a manifestly empirical issue. Thus for Laudan, “Methodological rules . . . are a part of empirical knowledge, not something wholly different from it . . . [We] can choose between rival methodologies in precisely the same way we choose between rival empirical theories of other sorts” (Laudan 1996, 133). But Achinstein’s point in emphasizing the empirical character of certain methodological problems is not that philosophers should therefore act more like scientists in resolving them; it’s not that the methodology should be thought of as the empirical science of empirical science, with philosophers ﬁnally getting quality time with the beaker. Rather, it is that scientists themselves contribute to the resolution of methodological issues through the empirical information obtained in the normal process of investigating our world, as well as by their own methods and procedures. If this is correct, it would indeed be an important point for philosophers to heed: after all, if science can take care of itself on certain methodological matters, then there is that much less in methodology for a philosopher to do. On the other hand, if Laudan’s

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vision is correct, then the philosopher has for himself a project of a quite different sort than he has become accustomed to. The title of this chapter refers to Achinstein’s empiricism as Newtonian because, as will be argued here, there is good reason to think that Newton and Achinstein share strikingly similar views on the empirical character of certain issues in the epistemology of science, and on the contribution that scientists make in deciding them. First, some of Achinstein’s longstanding views on the nature of evidence will be examined, and these will then be related to some of his more recent work on induction. Next Newton’s views on these issues will be considered, in light of an important interpretation of Newton’s attitude toward metaphysical and epistemological issues more generally. Finally, the question of where Achinstein and Newton may have gone wrong will be taken up.

2. ACHINSTEIN ON EVIDENCE AND INDUCTION Given the nature of much of Achinstein’s work, he clearly thinks that one important methodological project for the philosopher is to analyze certain epistemological concepts employed by scientists, including the concept of evidence (Achinstein 2001). In this respect, Achinstein’s project with evidence is similar to Hempel’s with the related concept of conﬁrmation, in the latter’s seminal “Studies in the Logic of Conﬁrmation” (Hempel 1965, 3–39). As Hempel puts it there, while a scientist might claim that some piece of evidence E conﬁrms a hypothesis H, it is the philosopher’s charge to tell us what that claim means, by giving a precise deﬁnition or criterion of conﬁrmation. The crucial difference between Achinstein and logical empiricists like Hempel, however, is that, for the latter, the conﬁrmation relation is a logical one; this means that, once we have our deﬁnition in hand, we can determine a priori whether E does conﬁrm H. Accordingly, while the scientist will assert that E is conﬁrming evidence of H, it is the philosopher who is best equipped to determine whether that statement is true. To paraphrase Carnap, “E conﬁrms H” is not a statement within science, but one about the statements of science— one about E and H—and thus a statement that the philosopher is in the best position to evaluate (Carnap 1963, 73).3 By contrast, although Achinstein would agree that the philosopher should give precise deﬁnitions of conﬁrming evidence, it would normally be an empirical issue whether some fact is evidence for a hypothesis, and one that the scientist can often be found deciding.4 To make this point, Achinstein appeals to historical cases involving what he calls evidential ﬂaws, a favorite example of which is the Thomson–

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Hertz case. In failing to obtain any deﬂection of cathode rays with electriﬁed plates, Heinrich Hertz concluded that he had strong evidence that cathode rays are not charged. On Achinstein’s account of the episode, when J.J. Thomson repeated the experiment, he was setting out to determine whether Hertz’s results really did provide evidence for his conclusion. Thomson discovered that the charged rays were ionizing the gas in the tube, thereby neutralizing the charge of the plates; for once the tubes were sufﬁciently evacuated, the rays were deﬂected, just as they should be if they carried a charge. Thus, while Hertz’s results may have been evidence in the sense that they constituted his reason for believing that cathode rays are not charged, Thomson is supposed to have shown that the results are not evidence in the sense that matters to science—a result that provides a genuinely good reason to believe that a hypothesis is true.5 Furthermore, Thomson settled the matter not by tracing out the logical relations between Hertz’s evidence-statement and his hypothesis, but through bringing to bear empirical information wrought by experiment. The Thomson case is intended to show not only that the evidential relation can be empirical, but also that it is objective, in the sense that it does not depend upon what anyone believes about E, H, or their relationship. Hertz’s results failed to provide a good reason to believe his conclusion because the charge on the plates was being neutralized; that’s a fact about our world, not what anyone believes about it. As Achinstein likes to put the matter, the concept of good reason to believe functions much like the concepts of sign or symptom: Koplik’s spots are a sign or symptom of measles— and a good reason to believe that the measles virus is present—even if medical experts are completely unaware of the connection; for what makes Koplik’s spots a sign or symptom of the measles—or a good reason to believe that the virus is present—is how things stand in nature, not how we take nature to be.6 Although he has written less on the matter, Achinstein has similar things to say about inductive inference. First, he admits that whether an inference of any kind is reasonable can likewise be an objective issue: “We can ask how reasonable it is to infer or conclude that p from some fact, without considering the knowledge and beliefs of persons, if any, who may be in the position of inferring or concluding that p” (Achinstein 2000, 98). Furthermore, he contends that, in contrast to the evaluation of a deductive inference, the evaluation of an inductive inference would be empirical as well: “whether a syllogism is valid can be determined entirely by a priori formal means. Whether an inductive generalization, or a causal inference, is valid or reasonable cannot be” (Achinstein 2010, 81).7 Thus, whether an inductive inference is reasonable is an objective, empirical matter, just like the evidential relation. But we can connect these two views up directly if

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we claim, plausibly enough, that an inductive inference from E to H is reasonable or valid just in case E is evidence that H, in the sense of providing a good reason to believe it.8 If we make this move, we can say that Thomson was also evaluating the inference from Hertz’s results to his conclusion about cathode rays; what he discovered is that the inference is not a good one, despite the appearances, because the results fail to provide a good reason to believe that the conclusion is true.9 But on such a view of induction, what should we make of inductive rules of the sort offered by Achinstein’s heroes, Newton and Mill? According to the traditional view, such rules are meant to tell us, in very general terms, the conditions under which an inductive inference would be valid; if so, an inductive inference would be valid just when it ﬁts one of these rules. For instance, both an inference from the coloration of observed ravens to all ravens, and one from the melting point of observed samples of an element to all samples, might be good in virtue of conforming to the “straight rule,” or the rule that if n% of observed A’s have been B, we should infer that n% of all A’s are B. Achinstein’s view, however, is not the traditional one, for he holds that no inductive inference would be acceptable by virtue of its ﬁt with a rule alone. Rather, the validity of an inductive inference is contingent upon obtaining facts not typically reported in the premises, and thus an inference ﬁtting a rule may not be justiﬁed at all. For instance, Achinstein claims that the above inference to melting point would be good while inference to raven-coloration would not, because “of the empirical fact that instances of chemical properties of substances tend to be completely uniform, whereas bird coloration . . . tends not to be” (Achinstein 2010, 76). To this extent, Achinstein’s view is similar to John Norton’s “Material Theory of Induction” in holding that the goodness of an inductive inference depends upon the obtaining of some “material fact,” not conformity with an “inductive schema” (Norton 2003). But Achinstein tries to distance himself from Norton by arguing that inductive schemas have substantial value nevertheless. In the ﬁrst place, they are attempts at deﬁning general kinds of inference crucial to scientiﬁc argument. The straight rule, for instance, is an attempt to deﬁne inductive generalization, while “Mill’s methods” are meant to deﬁne causal reasoning (Achinstein 2010, 80). In light of this, scientists can and often do invoke such rules so that their reasoning becomes more explicit and easier for others to follow; Newton does this, as we shall shortly see, in Book 3 of his Principia. Perhaps most importantly of all, however, Achinstein insists it would be wrong to conclude that inductive rules lack a “justiﬁcatory role” altogether, even if we agree with Norton (and him) that empirical information is necessary to determine inductive validity.

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But simply because the validity of an inference to the truth or probability of the system of hypotheses cannot be decided entirely a priori by reference to formal structure, it does not follow that the formal structure of the inference pattern plays no justiﬁcatory or explanatory role. (Achinstein 2010, 83)

Similarly, granting that inductive rules need not be explicitly invoked in an argument, Achinstein again maintains that it would be wrong to conclude that they have no “justiﬁcatory force.” Making a comparison with deductive rules, he writes, But the same is true in a deductive proof: in constructing such a proof one need not invoke or appeal to any of the formal principles of deduction that logicians love to classify and explicitly use. One cannot conclude from this that the principles, in either the deductive or the inductive case, have no justiﬁcatory force. (Achinstein 2010, 85)

Although Achinstein does not outright claim in these passages that inductive rules have a “justiﬁcatory role,” it certainly appears that he wants to leave open the possibility of a middle ground between traditionalists, who claim that rules do all the justiﬁcatory work, and Norton, who claims that they do none. Indeed, why else would he repeatedly insist that we cannot draw Norton’s strong conclusion? I will return to this issue of the potential “justiﬁcatory role” of inductive rules in Section 4. I will argue there that in trying to distance himself from Norton, Achinstein makes statements committing himself to the “justiﬁcatory role” of inductive rules, but that this is incompatible with the views on rules just presented here. But before we march Achinstein into this battle, I ﬁrst want to consider how strong of an ally he can claim Newton to be.

3. NEWTON ON EVIDENCE AND INDUCTION In recent work, Andrew Janiak has identiﬁed what he calls the radical empiricist interpretation of Newton (Janiak 2008).10 On this view, Newton is effectively reordering the Cartesian “tree of knowledge”: whereas Descartes took a priori metaphysics to be the root and physics the trunk of knowledge, thereby giving physics an a priori foundation, Newton sought to reverse the relation, transforming metaphysics from an a priori investigation into a thoroughly empirical one, answerable to the results of physics itself. To use one of Janiak’s examples, consider Newton’s treatment of the so-called mechanical philosophy, a view that ﬁgures such as Descartes, Leibniz and Huygens held a priori.11 Newton thinks he has empirically undermined this position in the Principia, because he has shown there that gravity “acts not in proportion to the quantity of the surfaces of the

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particles on which it acts (as mechanical causes are wont to do) but in proportion to the quantity of solid matter . . . ” (Newton 1999, 943). As this example attests, however, attention is usually focused on Newton’s “empiricalization” of ontological issues; but for Descartes “Metaphysics . . . contains the Principles of Knowledge” (Descartes 1988, xxiv). Thus, if we are going to take seriously this picture of Newton-as-radical-empiricist, there ought to be some way of reading Newton as treating certain methodological issues as scientiﬁc ones as well. It is here that the afﬁnity between Newton and Achinstein really comes out. One attractive way of reading books 1 and 2 of the Principia along these lines is as a treatise on inference and evidence in rational mechanics. For as Newton states in his preface, “the whole difﬁculty” of this branch of natural philosophy is “to discover the forces of nature from the phenomena of motions, and then to demonstrate the other phenomena from these forces” (Newton 1999, 382). Since it is through the phenomena of motion that we are to discover the forces of nature, these phenomena are to serve as evidence for the forces that are acting on bodies; in that case, the “whole difﬁculty” is to work out precisely what forces the motions of bodies are evidence for, and what other motions we can infer given the action of these forces. The solution to this difﬁculty, Newton proceeds to tell us, consists in the general propositions established in books 1 and 2—propositions derived from the laws of motion together with the lemmas constituting the mathematical framework of the book. These propositions therefore lay out the precise evidential and inferential relations that hold between certain forces and certain motions.12 Consider, for instance, a pair of propositions that are crucial to Newton’s argument for universal gravitation in book 3, beginning with proposition 2. Here Newton argues that the rate at which a body in a curved orbit describes areas with respect to a point is actually a measure of the direction of the force acting on the body with respect to that point: if the rate is constant, then the force is directed to the point as a center; if the rate is increasing, the force is off-center toward the direction of motion; if the rate is decreasing, it is offcenter away from the direction of motion. Proposition 45 is similar but concerns instead the magnitude of the force. Here Newton argues that the precession of an orbit measures how the force acting on the orbiting body varies with the distance: if the orbit does not precess at all, then the force is inverse-square; if it precesses forward, then the force falls off more quickly than the inverse-square; if backward, it falls off more slowly.13 What is striking about both of these propositions is their generality: Newton is not just concerned with the evidential relation between one kind of phenomenon and one kind of force, but also between the deviation from that phenomenon and the corresponding deviation from that force. Indeed, it is the generality

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of the evidential relations worked out in advance like this that allows Newton to later use the empirical world as we ﬁnd it to select conclusions about the forces acting on bodies; he uses propositions 2 and 45, for instance, to conclude that the planets and their satellites are all subject to inverse-square centripetal forces, in light of their known motions. The evidential and inferential relations between forces and motions that Newton works out in the propositions of books 1 and 2 would all be contingent and empirical. Sweeping out areas proportional to the times is not measure of a centripetal force in every logically possible world, for instance; in a world where bodies do this by their “natural motion,” without any impressed force, such motions would constitute no reason whatever to believe in the action of a centripetal force. Rather, the evidential relations depend fundamentally on the laws of motion from which the propositions are derived—laws that Newton regards as themselves inductively inferred, empirical generalizations that may well have been false. Accordingly, if the propositions establish evidential and inferential links between forces and motions, then those links are underwritten by other, more fundamental facts about nature that we could only know empirically. As such, these evidential relations are not only contingent and empirical, but also objective, depending upon how nature is in fundamental respects, not how we take nature to be. Is this the only possible way to read what Newton is doing here? Of course not, but it does make better sense of his own expressed attitude than views on which the evidential relation would be a priori. On a hypotheticodeductive construal, for instance, Newton would be assuming his laws as mere hypotheses, deriving from them the propositions of books 1 and 2 so that he can later obtain conﬁrming instances of those laws in book 3.14 But Newton expresses no interest whatever in obtaining conﬁrmation of his laws of motion, treating them in the Principia and elsewhere as antecedently well conﬁrmed and uncontroversial empirical generalizations (Newton 2004, 118). And he does so, on the present reading, for good reason: because those laws underwrite the evidential and inferential relations between forces and motions that he is busy working out in books 1 and 2—something they cannot do if they are mere conjectures. I don’t know whether Achinstein would accept this interpretation of what Newton is doing here, but he would certainly approve of the view of evidence it exhibits. To put it in Achinsteinian terms, what Newton is arguing in propositions like 2 and 45 is that certain motions are “signs” or “symptoms” of certain forces, and thus a “good reason to believe” that those forces are present; and because those claims rest ultimately upon other empirical generalizations, whether those motions are signs or symptoms of those forces—or a good reason to believe they are present—is

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simply an empirical matter. Here, just as on Achinstein’s vision, what counts as evidence for what, or what inferences from motions to forces are good ones, is an ordinary empirical affair, settled by the scientist doing what he normally does. It may seem more of a stretch to claim that Achinstein and Newton agree on the status of inductive rules. After all, the standard interpretation of Newton’s Rules for Natural Philosophy15 is that they are invoked to justify key inferences that Newton wants to make in book 3, as if an inference is justiﬁed when it ﬁts one of those rules.16 But careful attention to how Newton actually uses those rules makes it clear that this is simply not the case, and that he thinks of such rules much like Achinstein does. Newton’s ﬁrst two rules are as follows: Rule 1: No more causes of natural things should be admitted than are both true and sufﬁcient to explain their phenomena. Rule 2: Therefore, the causes assigned to natural effects of the same kind must be, so far as possible, the same.

These rules are invoked together in theorem 4 of book 3, during the so-called “moon-test.” Here we suppose that the moon is deprived of its inertial motion and falls to the earth by the inverse-square force we now know to be keeping it in orbit. Newton calculates that at the earth’s surface the moon would fall 151/12 Paris feet in one second, which happens to be the very speed at which terrestrial bodies fall by gravity. Here we have two true causes—gravity and the inverse-square force on the moon—each of which could account for the acceleration of the moon and terrestrial bodies. Rule 1 says that we cannot admit both, but which one should we eliminate? Rule 2 spares us from making the choice: they are the same cause. Now, if we look no further, it certainly seems that the rules alone are what are supposed to drive the inference through; but consideration of the rest of the text shows that this is not the case. I simply quote Newton. And therefore that force by which the moon is kept in orbit . . . comes out equal to the force of gravity here in earth, and so (by rules 1 and 2) is that very force which we generally call gravity. For if gravity were different from this force, then bodies making for the earth would descend twice as fast, and in the space of one second would by falling describe 301/6 Paris feet, entirely contrary to experience. (Newton 1999, 804)

Newton’s argument here is clearly not that we ought to make the inference because that’s what the rules say. Rather, the argument is that if we decline to infer with the rules, thereby postulating two forces acting in the same space, then we shall have to draw a conclusion “contrary to experience”: we shall have to hold that bodies fall twice as fast as we observe them to fall;

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therefore we should do exactly what those rules say. If this is right, Newton would be using the rules to indicate the inference he wants us to make, while the grounds for that inference consist in our refusal to reject our experiences relating to the fall of terrestrial bodies, which we would have to do if we declined to the follow the rules. Although Newton repeats this strategy throughout his argument for universal gravitation when the rules are invoked, perhaps the most striking instance is when he invokes rule 3 in the 2nd corollary to theorem 6.17 According to this rule, Rule 3: Those qualities of bodies that cannot be intended and remitted and that belong to all bodies on which experiments can be made should be taken as qualities of all bodies universally.

In the 6th theorem, Newton describes a pendulum experiment involving a variety of materials showing that the weight of each material is proportional to its quantity of matter. In the 2nd corollary, where the 3rd rule is invoked, Newton begins by noting that all bodies of which we know near the earth have gravity (including the moon); moreover, we have just found that the weight of any body on which experiments have been made is proportional to its quantity of matter. By the 3rd rule, then, we conclude that these are qualities of all bodies universally: gravity exists in all bodies and is proportional to the quantity of matter in each. Again, if we stop reading here, it certainly seems that bare conformity with the rule is supposed to drive the inference through; but again, a closer look reveals that this is simply not the case. Immediately after invoking the rule, Newton asks us to consider what would follow if we don’t the generalize along with it—if we suppose that “the æther or any other body whatever either were entirely devoid of gravity or gravitated less in proportion to its quantity of matter . . . ” Such a supposition, he continues, would bring us into direct conﬂict with the conclusion of the pendulum experiments. For since in the opinion of “Aristotle, Descartes and others” the hypothetical body would differ from others only in the form of its matter, it could by a change of form be transformed into a body that we know does have gravity, or whose gravity is directly proportional to its quantity of matter, such as any of the bodies in the pendulum experiments;18 but this would mean that the gravity of these latter bodies would depend upon the form of their matter, and not the quantity, in direct conﬂict with what those experiments showed us about them (Newton 1999, 809). Once again, if we decline to follow the rule, we would have to reject something that experience has already told us; we should therefore do as the rule bids. The difference in this case is that Newton makes use of a highly theoretical view about the transformation of bodies to obtain the

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conﬂict with experience; but his attributing the view to “Aristotle, Descartes and others” shows that it is something he thinks parties to the dispute already accept. Newton is therefore not simply invoking his rules with the expectation that they do the justiﬁcatory work, as is usually thought. Rather, he is always supplying a collateral empirical argument to show that the inferences the rules direct us to make would be good ones. At the very least, then, the rules are invoked to characterize the inference Newton wants us to make, by appealing to familiar patterns of reasoning with which his readers will be familiar (inductive generalization, causal simpliﬁcation, etc.). He does so, we can presume, so that the logic of his argument is more explicit and easier for the rest of us to follow; and this is exactly what Achinstein claims inductive rules do. Whether Newton and Achinstein think inductive rules can do anything stronger will be considered shortly. In the meantime, I conclude that there is a case to be made that Achinstein and Newton are simpatico on meta-methodological matters; and in my view, there is no greater compliment of Achinstein. According to their shared brand of empiricism, questions about evidence and good inductive inference are typically empirical matters, and are typically settled by empirical information obtained in the normal work of the scientist, not some special empirical project of a philosopher examining the activities of science from a position outside of it, as on Laudan’s view. And perhaps the ﬁnest example of this brand of meta-methodological empiricism, I claim, can be found in the Principia itself. Nevertheless, there is still substantial work for the philosopher-as-methodologist to do: among many other things, he can deﬁne concepts such as evidence, explanation, and probability, as Achinstein himself has done, and he can deﬁne general patterns of inference important to scientiﬁc argument, as Newton takes it upon himself to do in the very beginning of book 3.19

4. THE “JUSTIFICATORY ROLE” OF INDUCTIVE RULES We have seen that passages cited in Section 2 strongly suggest that Achinstein does not want to foreclose on the possibility that inductive rules have a “justiﬁcatory role” or carry “justiﬁcatory force.” But what do these expressions mean? Does Achinstein actually believe that rules have a “justiﬁcatory role,” or is this just a possibility that he thinks should be explored further? If he does believe this, in virtue of what would they have such a role? In the ﬁrst place, by saying a rule has “justiﬁcatory force” or a “justiﬁcatory role,” I take it one means that it has force as a justiﬁcation, or plays the role of a reason—that citing the rule constitutes at least some defense for

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making an inference that accords with it. Indeed, if citing a rule can be no defense of an inference, then claiming the rule has a “justiﬁcatory role” or “justiﬁcatory force” would be completely out of place. Assuming this is a reasonable interpretation of these expressions, does Achinstein himself believe that citing a rule counts as a defense for making an inference? Well, during his effort to distance himself from Norton, we can ﬁnd him saying that inductive rules “are not trivial or uninformative” because “they tell scientists what to do and not to do in attempting to prove . . . hypotheses” (Achinstein 2010, 83). This is a very telling statement indeed: for if rules do tell scientists “what to do and not to do,” then Achinstein thinks rules are normative, not merely descriptive; the claim is not that rules tell scientists what scientists tend to do and not do when proving hypotheses, but what they are and are not supposed to do in proving hypotheses—what is correct and incorrect to do. If so, then citing a rule could certainly be used as a defense of an inference; it would be a way of saying “I am doing what I am supposed to do in proving a hypothesis.” In conﬁrmation of this reading, during the same effort to create distance with Norton we can ﬁnd Achinstein claiming that “rules have bite to them” because on occasion they can be “cited against scientists who ﬂout them, as in the case of Newton himself criticizing Descartes’ physics for ﬂouting induction from observed phenomena . . . ” (83). But surely one cannot cite a rule as criticism unless one presumes that the rule being ﬂouted states what it is correct to do. And again, if a rule states what it is correct to do, then the rule can be used as a defense of an inference, in addition to being used as criticism. It is settled then: on Achinstein’s view, rules would have a “justiﬁcatory role” or “justiﬁcatory force,” and he presents evidence showing that they would for Newton as well. For if they didn’t have a justiﬁcatory role, then they couldn’t tell scientists “what to do and not to do,” nor could they be used in criticism; they wouldn’t have any “bite” at all, and Achinstein’s view would virtually collapse into Norton’s. The next question, then, is: what does Achinstein say about inductive rules that would explain why they could have a justiﬁcatory role—why they can tell us “what to do or not to do,” or be used as criticism? He says nothing as far as I can tell. We know that rules are supposed to deﬁne types of inference. Granted this, conforming to a rule would trivially be a necessary condition for an inference of that type to be justiﬁed, since otherwise it wouldn’t be an inference of that type (Achinstein 2010, 84); but it certainly does not follow that the rule therefore has a justiﬁcatory role, nor does Achinstein claim this. Rather, citing the rule would simply indicate what kind of inference one is making, not that it is an inference one should or shouldn’t make. We also know that, as deﬁniens of inference-types, scientists can cite rules as “pointers” so we can see what kind of inference they are making, as Newton does; here though, citing the rule does not tell the sci-

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entist “what to do and not to do,” but indicates what the scientist is doing so we can do the same. Whether this is really “what to do” or “not to do” depends upon collateral empirical information, not the rule. Another possibility is that Achinstein thinks citing a rule counts as a justiﬁcation only when we possess ancillary information to the effect that inferences of that type are generally reliable; for instance, perhaps citing the straight rule can count as a defense of an inference if we possess information that this inference-pattern typically leads to true conclusions. But there are several problems with this suggestion. Most important, I don’t think this is what Achinstein has in mind. Consider, again, the inference to raven-coloration and the inference to the melting point of an element. Achinstein thinks that only one of these inferences is valid, and not because of the reliability of a rule for inductive generalization, since they both conform to it, but because of our collateral empirical information about birds and chemical properties. Second, what else is information about the reliability of a rule besides still more collateral empirical information? Accordingly, what would do all the justiﬁcatory work is clearly the collateral information; once again, the bare citation of the rule would still have no “justiﬁcatory role.” But this, as far as I can see, exhausts the options: citing a rule does not by itself have a justiﬁcatory role, because that simply identiﬁes what sort of inference it is, and thus what inference the scientist wants us to make, but doesn’t show that it is a good or bad inference; and additional information that the rule is reliable would count as part of the empirical information that Achinstein thinks is already necessary for justiﬁcation, in which case— once again—the citation of the rule itself has no justiﬁcatory role. Why, then, does Achinstein insist inductive rules “have bite to them”? Why can they be used as criticism? And why do they tell scientists “what to do and not to do” when proving hypotheses? On the contrary, Achinstein’s position should be—just as Norton’s is—that the collateral empirical information “has bite to it,” can “tell scientists what to do and not to do,” and can be used in criticism, and not that the rules have these qualities. If this is right, then Achinstein’s view comes much closer to Norton’s than he wishes; he only creates distance with Norton at the expense of internal consistency. Contrary to Achinstein’s assertions in Section 2, then, we can conclude from what he says about inductive rules that “the formal structure of the inference pattern plays no justiﬁcatory role.”

ACKNOWLEDGMENTS Thanks to Greg Morgan and Peter Achinstein for comments on an initial draft of this essay.

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REFERENCES Achinstein, P. 2010. Evidence, Explanation, and Realism. New York: Oxford University Press. ——— . 2002. Is There a Valid Experimental Argument for Scientiﬁc Realism? Journal of Philosophy 99 (9): 470–95. ——— . 2001. The Book of Evidence. New York: Oxford University Press. Carnap, R. 1963. Intellectual Autobiography. In The Philosophy of Rudolf Carnap, ed. P. A. Schilpp. La Salle, Ill.: Open Court. Descartes, R. 1988. Principles of Philosophy, trans. V. R. Miller and R. P. Miller. Lewiston, Pa.: E. Mellen Press. Harper, W. 2002. Newton’s Argument for Universal Gravitation. In The Cambridge Companion to Newton, ed. I. B. Cohen and G. E. Smith. New York: Cambridge University Press. Hempel, C. G. 1965. Aspects of Scientiﬁc Explanation. New York: Free Press. Janiak, A. 2008. Newton as Philosopher. New York: Cambridge University Press. Laudan, L. 1996. Beyond Positivism and Relativism. Boulder, Colo.: Westview Press. McMullin, E. 2001. The Impact of Newton’s Principia on the Philosophy of Science. Philosophy of Science 68 (3): 279–310. Newton, I. 2004. Philosophical Writings, ed. Andrew Janiak. Cambridge: Cambridge University Press. ——— . 1999. The Principia: Mathematical Principles of Natural Philosophy, trans. I. Bernard Cohen and Anne Whitman. Berkeley: University of California Press. Norton, J. 2003. A Material Theory of Induction. Philosophy of Science 70 (4): 647–70. Smith, G. E. 2007. Newton’s Philosophiæ Naturalis Principia Mathematica. http:// plato.stanford.edu/entries/newton-principia/index.html (accessed November 16, 2010). ——— . 2002. The Methodology of the Principia. In The Cambridge Companion to Newton, ed. I. B. Cohen and G. E. Smith. New York: Cambridge University Press. ——— . 2001. Comments on Ernan McMullin’s “The Impact of Newton’s Principia on the Philosophy of Science”. Philosophy of Science 68 (3): 327–38. Whewell, W. 1996. The Philosophy of the Inductive Sciences, Vol. II. London: Routledge and Thoemmes Press.

NOTES 1. By scientiﬁc method I mean the theory of how scientiﬁc hypotheses are to be appraised—including, of course, by evidence. 2. For example, instead of “Avoid ad hoc hypotheses,” we might have: “If you want theories that make reliable predictions, avoid ad hoc hypotheses.” 3. In particular Carnap claims that a statement about the probability of a hypothesis on the evidence is not a statement within science but is a statement about the statements of science—that is, a statement about E and H. 4. Achinstein does allow that some evidential claims can be evaluated a priori, although this is not the usual case.

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5. One of Achinstein’s distinctive points about evidence, hinted at here, is that there are several different concepts of evidence, and something can be evidence under one concept but not another. Not every concept of evidence is important to the scientist, however. 6. The comparison with the concepts of sign and symptom underlines another important feature of Achinstein’s treatment of good reason: E can be a good reason to believe that H is true, even if H is not true, just as some ailment can be a symptom of a disease, even if one doesn’t have the disease. To be more precise, Achinstein thinks there are two concepts of good reason, one requiring the truth of the hypothesis (veridical evidence), the other just its high probability (potential evidence). 7. Achinstein has qualiﬁed this claim in personal correspondence, remarking that that there are unusual occasions on which an inductive inference can be evaluated a priori, much like an evidential claim. 8. I take it that a “valid” inductive argument is one in which the premises, if true, render the conclusion probable. And on Achinstein’s view, E provides a good reason to believe H, only if H is probable given E. Hence, I think it is a reasonable assumption that Achinstein would require the premises of a valid inductive argument to provide good reasons for the conclusion. 9. What Achinstein will likely say is that there is a sense in which the inference was good, but this is not the sense that matters to science. 10. To be clear, Janiak does not entirely agree with the radical empiricist interpretation of Newton, but ﬁnds the view in the work of inﬂuential Newton scholars such as Howard Stein and Robert DiSalle. 11. Roughly, this is the view that physical phenomena are to be explicable only in terms of the size, shape and motion of bodies that comprise the physical world. 12. George E. Smith (Smith 2002, 143) has called these propositions inferencetickets, since they specify which inferences from motions to forces and forces to motions would be warranted. He says he derives the term from Arthur Prior, but I believe it originates with Gilbert Ryle. 13. I borrow these ways of stating the propositions from William Harper (Harper 2002). 14. Hypothetio-deductive interpretations of the Principia have been around for a long time, but Ernan McMullin (McMullin 2001, 279–310) has recently argued that the theory of the Principia is “a single extraordinarily complex hypothesis” which is credible because of how well it is shown to “organize the inductive evidence already at hand.” George Smith (Smith 2001, 327–38) responds to McMullin’s claims that the laws of motion are hypotheses, not inductively grounded generalizations. 15. Newton states these four rules at the beginning of the third edition of book 3 of the Principia. I will talk about rules 1 though 3 here; the 4th rule is a sort of meta-rule, saying that that we should not reject an inductive inference on the grounds that its conclusion is possibly false. I do not have space to discuss the 4th rule here. 16. For instance, William Whewell (Whewell 1996, 441) says of the rules that they are intended to “protect,” “strengthen,” and “justify” Newton’s inferences to

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universal gravitation. More recently, George E. Smith (Smith 2007) claims that the rules are meant to “authorize” inferences. 17. In the scholium to theorem 4, Newton uses rules 1 and 2 in the same fashion as he does in the theorem itself; in theorem 5, he uses rule 2 without rule 1, but also together with collateral empirical information. I suppress the details due to lack of space. 18. That Newton holds this view as well is suggested by his invoking it in the ﬁrst edition without attributing it to anybody, simply stating it as fact (Newton 1999, 809 fn. aa). 19. Lest it be thought that providing deﬁnitions is the only thing in methodology for a philosopher to do, consider, very brieﬂy, Achinstein’s treatment of scientiﬁc realism in “Is There a Valid Experimental Argument for Scientiﬁc Realism?”(Achinstein 2002). Achinstein’s answer to the question posed by the title is “yes,” and so it is experiment that provides the crucial empirical information for settling the realism issue. But the experiment is in need of defense from philosophical objections by anti-realists—objections regarding, for instance, the aims of science—which Achinstein provides in the remainder of the paper. What Achinstein does not do in the paper is, say, a meta-inference-to-the-best-explanation on the success of science. Again, he doesn’t seem to be advocating the view that methodological issues, such as the Realism issue, are to be resolved by philosophers reasoning in ways similar to the scientist.

5 Evidence and Objectivity in Achinstein’s Philosophy of Science Gerald Doppelt

Peter Achinstein’s work is sharply focused on fundamental epistemological concepts in science such as explanation, evidence, probability, and objectivity. His work advances bold and original accounts of these concepts. It is informed by rigorous criticism of standard accounts and illuminating case studies of key episodes in the history of science. I studied with Achinstein from 1962 to 1966 and completed my PhD in 1969 under his supervision at John Hopkins University in philosophy. Peter Achinstein was an excellent teacher and I owe much of my interest in philosophy of science to the courses and guidance he provided. In this essay, I focus on the account of evidence in science developed by Achinstein in The Book of Evidence (Achinstein 2001). I argue that shortfalls in his account motivate an alternative account associated with “inferenceto-the-best-explanation” scientiﬁc realism (Doppelt 2005; 2007; 2011). Achinstein’s aim is to provide a conception of evidence that (1) captures the assumptions of scientists when they claim that certain facts e constitute evidence that a certain hypothesis h is true; and (2) can resolve scientiﬁc disagreements concerning what is evidence for what (Achinstein 2001, 3–4). I call this aim the test of relevance to scientists’ inferential practices. Achinstein argues that standard philosophical conceptions of evidence—Bayesianism, hypothetico-deductive accounts, enumeratative induction views, inference-to-the-best-explanation, and others fail the relevance test. They fail for three reasons (5–10, 44–95). First, these standard accounts are too weak to capture the conditions under which scientists take facts e to be evidence for some hypothesis h. Scientists do not take e to be evidence for h if and only if it satisﬁes the Bayesian condition of increasing the probability of h over its prior probability; similarly, they do not take e to be evidence for h if and only if h deductively implies e and e occurs, as the hypothetico-deductive account claims. The second failing of

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such standard accounts of evidence is that they offer a priori analysis of the notion, whereas an empirical approach is more promising. The third failing is that they fall short of the notion of objectivity operative in successful scientiﬁc inquiry. Achinstein has provided a demanding standard for evaluating his own account of evidence. I argue that his account falls short of meeting his “relevance test” and that a rival scientiﬁc realist account of evidence promises more success.

1. DOES ACHINSTEIN’S NOTION OF VERIDICAL EVIDENCE MEET THE “RELEVANCE TEST”? Achinstein advances illuminating distinctions among four notions of evidence in scientiﬁc inquiry and argues that the demanding notion of veridical evidence is the most important in science (Achinstein 2001, 13–44). These four notions are: (1) Subjective Evidence: First is a notion of evidence for a subject—an individual or group (22–4). This notion relativizes evidence to what some particular person or group takes to be evidence e for some hypothesis h on the basis of some mode of reasoning R that the subject takes to be valid. Because subjective evidence is wholly dependent on the beliefs of a subject, it obtains even if e and h are false and the reasoning from e to h is mistaken. (2) Epistemic Situation Evidence: This second notion relativizes evidence to an epistemic situation, but not to the subjects who occupy it in a given time and place (19–22). We abstract a framework of beliefs from the subjects who inhabit it, and determine whether any subject in this epistemic situation could reasonably take e to be evidence for h. (3) Veridical Evidence: Achinstein’s stronger notion of veridical evidence excludes the errors that can undermine “contextual” evidence in an epistemic situation. Thus where e is veridical evidence for h, Achinstein requires that h is true, e is true, and the reasoning from e to h is correct (24–7). (4) Potential Evidence: Potential evidence requires that e is true and the reasoning from e to h is correct, but allows that h may be false (27–8). Achinstein’s account of evidence puts the cart before the horse. On his account, scientists possess veridical evidence e for a hypothesis h only if the hypothesis is true and the reasoning from e to h is correct. But the determination of whether any h is true, and whether the inference from

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e to the truth of h is correct, is what an account of evidence is supposed to provide. Achinstein’s stipulation, that veridical evidence requires the truth of the hypothesis and correct reasoning, does not identify which inferential practices of scientists are correct and generate evidence that make it reasonable to believe the truths of the hypotheses. However, this is precisely what the “Relevancy Test” requires of an account of evidence. The difﬁculties with Achinstein’s notion of veridical evidence can be exposed by examining one of his key case studies. The question is whether Hertz’s cathode ray experiments provided evidence that the rays are not negatively charged particles because they do not provide electrostatic effects (Achinstein 2001, 13–9, 24–38). Hertz reasoned that pure cathode rays—isolated from the electric current moving between the cathode and anode—would trigger the needle of an electrometer, if cathode rays are charged particles. When the needle failed to move, Hertz took the experiment (and others) to provide evidence that cathode rays are not negatively charged particles. Hertz’s experiments provided subjective and epistemic situation evidence for his conclusion that cathode rays are not charged particles. Taking into account Hertz’s epistemic situation in 1883—what was known and believed about cathode tubes and rays, magnetic and electrical phenomena, devices such as the electrometer, the behavior of waves and charged particles in a medium, and so on—anyone in this epistemic situation could, with good reason, take Hertz’s experiments to be evidence for the truth of his conclusions. Nonetheless Hertz lacked veridical and potential evidence for his hypothesis. Why? J.J. Thomson provided compelling evidence that cathode rays are negatively charged particles (Achinstein 2001, 29–31). Thomson’s work showed that Hertz’s experimental reasoning was fatally ﬂawed. Thomson’s experiments revealed that as gas is removed from cathode tubes, generating a greater vacuum, electrostatic effects are observed. Hertz’s reasoning was ﬂawed because his cathode tubes were insufﬁciently evacuated to provide a veridical test for the presence of electrostatic effects and charged particles. On Achinstein’s account, Hertz lacked veridical evidence. This verdict requires that we take Thomson’s experiments to provide veridical evidence and his hypothesis to be true. These judgments rest on our current epistemic situation—the body of data, modes of reasoning, and claims about nature embodied in our best current physical theories. Thomson’s work creates a new epistemic situation S2 that includes a knowledge of Hertz’s epistemic situation S1 and provides more compelling evidence for Thomson’s hypothesis and against Hertz’s than is available in S1. The fact of the matter is that one epistemic situation Sx can include a knowledge of others S1 – Sn, and provide good reasons for believing the

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theories and evidential reasoning in Sx and rejecting that of S1 – Sn. On my account, evidence is always a function of some epistemic situation or other—a view that threatens relativism, a loss of objectivity, and the abandonment of scientiﬁc truth/realism. But these fatal consequences are avoided if there are objective standards of evidence, reasoning, conﬁrmation, predictive and explanatory success, and so on discovered in scientiﬁc inquiry that indicate which epistemic situation provides the best evidential reasoning for the truth of its hypotheses (Doppelt 2007; 2011). How far is this notion of evidence from Achinstein’s conception of veridical evidence? It is very far indeed, because “epistemic situation” evidence must fall short of the objectivity required by Achinstein’s notion of veridical evidence. On his notion, there is simply a fact of the matter in nature that determines whether any fact is evidence e for a hypothesis or state of affairs h, independent of any epistemic situation (Achinstein 2001, 25–6). On Achinstein’s analysis of veridical evidence, e is evidence for h only if the probability of h, given e, is greater than one half [prob. h, e > 1/2]. Achinstein takes this to imply that e provides a good reason to believe h (95–116). On his notion of the objectivity of veridical evidence, e is a good reason to believe h, independently of any epistemic situation and any scientists’ practices of reasoning. This notion severs the natural connection between something being a reason to believe something else and actual practices and standards of reasoning within scientiﬁc inquiry. This “a priori” disconnection between “reasons” and the inferential practices of scientists in their respective epistemic situations is an odd view for an approach that promises to be “empirical.” Can such a notion of evidence meet Achinstein’s test of “ﬁdelity to scientiﬁc practice”? It is this epistemological test that Achinstein uses to criticize standard accounts of evidence. Scientiﬁc realists hold the view that the existence of nature, its causal laws, its entities and mechanisms, and what is true about these matters do not depend on human thought or on any epistemic situation. As a realist, I agree with Achinstein’s claim that if the presence of a rash is a symptom of a certain disease, “it is so whatever epistemic situation is imagined” (Achinstein 2001, 25). But far more problematic is his view that “good reason to believe” and thus veridical evidence function “in much the same ways as the concept of ‘x’ as a sign or symptom of a disease ‘y ’ ” (25). In one case, we are dealing with the existence of a causal connection between a disease and its effects. In the other case, the question is how—by what reasoning—scientists establish that the symptoms are “signs” or “evidence” of the presence of this disease. Detaching the causal connection between a disease and its effects from our epistemic situation is one thing. A realist accepts this, though even reference to a physical state of affairs as “a disease” and others as its “signs”

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and “symptoms” already implies a body of medical knowledge. Detaching the notion of a rash as evidence for, a reason to infer, the existence of a given disease from our epistemic situation—that is, current medical knowledge—is quite another thing and implausible. But the proof is in the pudding. My worries may dissolve in light of Achinstein’s full analysis of the evidential relation between e and h.

2. ACHINSTEIN’S NOTION OF AN EXPLANATORY CONNECTION BETWEEN EVIDENCE AND HYPOTHESIS We have seen that e constitutes evidence for h only if prob. h, e > 1/2, which Achinstein understands to mean that e provides a good reason for believing that h is true. Potential and veridical evidence imply more demanding conditions: for veridical evidence, e and h must both be true and the inference or reasoning from e to h must be correct; potential evidence requires these conditions, minus the constraint that h must be true. Achinstein’s account does not inform us of how scientists determine whether any e is evidence for believing some h. Therefore, a key move is Achinstein’s argument that an additional necessary condition for evidence is the presence of an explanatory connection between e and h (Achinstein 2001, 148–51). There is such a connection between e and h if and only if either h, if true, would correctly explain e, or e, if true, would correctly explain h, or some third fact b, if true, would explain e and h. Achinstein’s argument brings his notion of evidence close to that of “inference-to-the-best-explanation” scientiﬁc realism, which holds that certain facts e are evidence for a hypothesis h if and only if h provides the best explanation of e (Achinstein 2001, 148–51). Achinstein rejects inferenceto-the-best explanation realism (IBER) on the grounds that there are many hypotheses—including improbable ones—that would, if true, explain the relevant facts (158). On Achinstein’s notion of evidence, two conditions must be satisﬁed: the evidence must both make the hypothesis probable and exhibit an explanatory connection with it. The combination of these two criteria excludes explanatory hypotheses that, if true, would explain the facts, but are improbable given background knowledge. Achinstein rejects IBER’s account of evidence on the grounds that realists provide no analysis of explanation (149). Achinstein underestimates the resources of IBER’s account of evidence. IBER need not accept that the best explanation is one that is improbable given background knowledge. Though IBER does not imply one single analysis of explanation, it shows agreement on the standards governing the best explanation. Achinstein’s problem of improbable explanations is

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accommodated because IBER holds that the best explanation must exhibit initial plausibility in light of background knowledge (Psillos 1999, 171). Beyond that, IBER characterizes the best explanation as the one that best meets scientiﬁc standards of accuracy (in prediction and explanation), uniﬁcation, variety of evidence, internal consistency, completeness in what it can explain and predict, and possibly “novel” predictions/explanation. My aim is to compare IBER’s account of evidence with Achinstein’s notion of veridical evidence. Achinstein is right that the best explanation can turn out to be incorrect and its hypotheses can turn out to be false. IBER’s notion of evidence approximates epistemic situation evidence and falls short of veridical evidence for two reasons. First, Achinstein’s notion of veridical evidence requires that the hypothesis is true. IBER is a fallibilist view and rejects the idea that a conception of evidence should guarantee the truth of the hypothesis, a virtue of IBER. What is gained by making the truth of a hypothesis h a logical or semantic precondition of anything’s being veridical evidence for h? Second, Achinstein’s notion of objectivity requires that veridical evidence is not dependent on any epistemic situation. This notion extends to his account of an explanatory connection between any e and h. There is a fact of the matter concerning the existence in nature of an explanatory connection between e and h, independent of any epistemic situation (Achinstein 2001, 160–4). The conﬂict with IBER is sharp. For IBER, evidence is a function of which hypothesis among rivals best satisﬁes the standards of explanatory virtue operative in an epistemic situation. This notion brings IBER’s account closer to scientists’ actual inferential practices than Achinstein. Consider the uniﬁcation of terrestrial and celestial motion achieved by Newtonian mechanics and responsible for the inference to the truth of Newton’s laws by many of his contemporaries. That epistemic situation included not just implicit standards of uniﬁcation, variety of evidence, accuracy, and so on, but also the knowledge that rival hypotheses treated celestial and terrestrial motion as different natural kinds, requiring different theories. Because current relativity physics replaces Newtonian mechanics, the evidence in its favor was not “veridical” in Achinstein’s sense. But for IBER, this verdict depends on our current epistemic situation and the existence of theories, which meet much higher standards than Newtonian mechanics and the explanatory connections it posited. Our only access to “true” explanatory connections between states of affairs is by means of the standards of predictive and explanatory success that inform the inferential practices of scientists embedded in the epistemic situations of our best current theories. From this standpoint, the application of Achinstein’s notions of objectivity,

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veridical evidence, and true explanatory connection implicitly assumes the epistemic situation of our best current theories. But my argument may beg the question against Achinstein’s notion of veridical evidence because his account of true explanatory connection may provide a viable alternative to IBER. There are two sources in Achinstein’s work for determining how scientists should determine that any e and h exhibit a true explanatory connection: (1) what is said by way of a general account of this notion and (2) what is conveyed by Achinstein’s case studies of speciﬁc episodes of reasoning in the history of science. As for the ﬁrst, Achinstein despairs of the effort to provide any general criterion of true explanatory connections. He suggests that we might treat the notion of true explanation as primitive—more basic and opaque to analysis than the notion of veridical evidence (Achinstein 2001, 161). Achinstein observes that on pain of circularity, we cannot provide an account of correct explanation in terms of the (veridical) evidence required to establish it in any particular case (164). Rather, all we can say is that h provides a correct explanation of e if and only if h is true and describes the state of affairs that truly causes and/or explains e. But as Achinstein tartly observes, whether any explanation is correct “is just what we want a deﬁnition of ‘correct explanation’ to tell us how to determine”; and his condition for the correctness of an explanation “doesn’t do that at all” (164–5). In that case, it is hard to see how Achinstein’s account of veridical evidence provides any way of determining whether any e is veridical or potential evidence for any h. This disappointing result implies that Achinstein’s notion of evidence cannot satisfy the empirical test of relevance to scientiﬁc practice by which he measures the failures of the standard accounts of evidence. However ﬂawed, the standard accounts criticized in Achinstein do seek to meet this test and provide standards of evidence. Has Achinstein changed the rules of the game, criticizing standard accounts for failing to meet an epistemological test, which his account simply abandons? Achinstein’s account backs him into this corner because he embraces a notion of objectivity that detaches correct explanation and veridical evidence from any and all epistemic situations, namely, the actual inferential practices of scientists in such situations. IBER provides standards that govern the explanatory success of theories and thus evidence itself. Such standards and their application to bodies of theory, data, argument, reasoning, and so on presuppose epistemic situations, or concrete contexts of inquiry. Nonetheless, provided there are powerful continuities of impersonal and objective standards across the epistemic situations of scientiﬁc inquiry, IBER contains the resources for a more plausible notion of objectivity than is defended by Achinstein.

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I am getting ahead of my argument. Achinstein’s case studies of historical episodes of scientiﬁc reasoning present a second source of his notions of explanatory connection and evidence. The cases may illustrate Achinstein’s view of how scientists establish explanatory connections and evidential relations between hypotheses and data.

3. WAVES AND PARTICLES: ACHINSTEIN’S NOTION OF ELIMINATIVE-CAUSAL REASONING In the 19th century, wave and particle physicists competed to explain well-known optical phenomena—the rectilinear propagation of light, reﬂection, and refraction—using their rival hypotheses that light is a wave motion in a medium of ether or that it is a stream of particles in motion. As Achinstein represents the epistemic situation, wave and particle theorists could each provide explanations of these optical phenomena (Achinstein 1991, 3–151; 2001, 157–60). Yet on his analysis, their reasoning is “more complex and more interesting” than “inference-to-the-best explanation” (Achinstein 2001, 158). Key theorists employed what Achinstein characterizes as “eliminativecausal reasoning” (Achinstein 1991, 136–7, 142–3; 2001, 158–60). They utilized background knowledge as evidence to establish some hypotheses and eliminate others, illustrating Achinstein’s view that there are selective strategies of reasoning to separate probable from improbable hypotheses and explanations. Background knowledge was employed as evidence that light is either a wave motion or the motion of particles, in each case moving with a ﬁnite velocity in a ﬁnite amount of time. Furthermore, wave theorists exploited background knowledge to infer that particle theory is improbable. In the epistemic situation characteristic of the period, theories of light were expected to explain patterns of diffraction. The only way particle theory could explain diffraction rested on the hypothesis that there were forces of attraction and repulsion between particles of light whose magnitude failed to be a function of the mass or shape of the particles. But this hypothesis was improbable, so reasoned the wave theorists, because all forces known to science at the time involved magnitudes that were a function of the mass or shape of the entities. Therefore, the wave theorists possessed evidence to eliminate the particle theory of light as improbable and establish the causalexplanatory power of the wave theory concerning optical phenomena, which were thus evidence for wave theory. Achinstein employs this case of “eliminative-causal reasoning” to show that there must be a probabilistic connection, as well as an explanatory one between evidence and hypothesis, which IBER accommodates through the criterion of intuitive plausibility and coherence with background knowledge.

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Can Achinstein’s notion of eliminative-causal reasoning do without IBER’s account of the standards governing the best explanation and evidence? Suppose particle theorists refrained from providing any explanation of diffraction, in light of the improbability of their hypothesis. Could they have nonetheless established an explanatory connection between the particle hypothesis and the phenomena of propagation, reﬂection, and refraction? In the epistemic situation described in Achinstein’s case study, wave theory possesses a completeness, uniﬁcation, and variety of evidence that particle theory lacks—with or without its improbable hypothesis concerning diffraction. Or imagine that wave theory falls short of a unifying explanation of the variety of optical phenomena it is expected to explain in its epistemic situation. In these two cases, there would be “insufﬁcient” evidence for both particle and wave theory, which shows that something close to the IBER’s standard of uniﬁcation is operative in that epistemic situation and tacitly assumed by Achinstein’s own account of the explanatory connection achieved by wave theory. Achinstein’s notion of “eliminative-causal reasoning” is a species of IBER’s account and not an alternative to it. It also shows that Achinstein’s account of epistemic situation evidence needs to be enriched to include the standards of explanatory success operative in that situation. Which of Achinstein’s four concepts of evidence is the “Particles v. Waves” case supposed to illustrate? Achinstein takes his account to show that the wave theorists’ evidence “comports with the explanatory connection condition” posited by his analysis on which e is evidence for h only if it is reasonable to believe the hypothesis, on the evidence, and to believe that there is an explanatory connection between the hypothesis and the evidence (Achinstein 2001, 157, 159). Is the case supposed to illustrate subjective evidence, epistemic situation evidence, potential evidence, and/ or veridical evidence? Does the case study support Achinstein’s notions of veridical and potential evidence? His case study illustrates subjective and epistemic situation evidence, not the more demanding notions he is after. The case cannot illustrate veridical evidence because to the best of our knowledge, the hypothesis that light is a wave in an ethereal medium is false. Maxwell’s theory of the electro-magnetic ﬁeld and subsequent developments in quantum physics imply that wave theorists got light wrong. Does the case illustrate Achinstein’s notion of potential evidence? My answer is that it does not, though Achinstein’s verdict is equivocal and confusing. Achinstein raises the question of whether the optical phenomena explained by the wave theory are potential evidence for the wave hypothesis. His answer is that they are potential evidence—not if they are taken by themselves; but if taken “in conjunction with diffraction and ﬁnite motion, they do constitute evidence” (Achinstein 2001, 159). But,

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subsequently, Achinstein reasons that wave theorists had epistemic situation evidence, not potential evidence. Their hypotheses that light is either a wave or a particle—a crucial step in their “eliminative-causal” reasoning—were probable given their background knowledge (that is, their epistemic situation). But given our background knowledge—quantum physics that “preclude classical waves and particles”—the wave theorists’ reasoning, not just their theory, is ﬂawed, and so they lacked even potential evidence (225–6). Achinstein’s study of wave and particle theory does not vindicate his notions of potential and veridical evidence. The case may be different for Achinstein’s study of Perrin’s evidence for the existence of molecules (Achinstein 2001, 243–66). Though Achinstein’s account is about Perrin’s epistemic situation and use of “eliminative-causal” reasoning to establish Avogadro’s number for molecules in a liquid, our best current theories tell us Perrin’s hypothesis and reasoning were correct. In my view, Salmon gets the matter right when he observes that Perrin’s experiments to establish Avogadro’s number were successful because “in each of the physical procedures . . . the experiments were dealing with substances composed of atoms and molecules—in accordance with the theory of matter that we have all come to accept . . .”—an ineliminable appeal to our current epistemic situation! (249, my emphasis). Does the Perrin case study illustrate and vindicate Achinstein’s notion of veridical evidence? Does Achinstein’s notion of “eliminative-causal reasoning” confront a difﬁculty similar to the problem raised for IBER by the so-called pessimistic meta-induction? IBER holds that inferenceto-the-best explanation can be applied to justify scientiﬁc realism—the view that we can know that successful scientiﬁc theories are true or approximately so. On the well-known Boyd-Putnam realist argument, the empirical success of theories in science would be a miracle—inexplicable phenomena—if they were not true (Boyd 1973; 1981). For IBER, the difﬁculty is that many successful theories turn out to be false and to contain theoretical terms, which are non-referential (Laudan 1981a; Chang 2003). On this basis, the pessimistic meta-induction reasons that our currently most successful theories are also probably false, and more generally that empirical success is never evidence of the truth of theories. Achinstein’s cases exemplify a form of reasoning that provides a way to discover explanatory connections. In that case, his notion of “eliminativecausal reasoning” would allow his notion of evidence to meet the test of relevance to scientiﬁc practice where standard accounts fail. Though the wave theorists employed this reasoning, their hypothesis concerning the nature of light is false and the explanatory connection between it and optical phenomena is both improbable and incorrect. Thus “eliminative-causal

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reasoning”—much like “inference-to-the-best explanation” is fallible. Both modes of reasoning fail to yield potential or veridical evidence. Why assume that Perrin’s employment of “eliminative-causal reasoning” generates veridical evidence concerning the existence of molecules? What differentiates the case of the wave theorists’ reasoning and evidential situation from Perrin’s? We require some “objective” way of distinguishing between our current epistemic situation and superceded ones. We need to justify the view that our best current theories are true and rest on veridical evidence. My own solution to the pessimistic meta-induction requires a different version of IBER, which I call “best current theory realism” or BCTR. On BCTR, it is reasonable to believe that our best current theories are true because the hypothesis that they are true provides the best explanation of the most striking and singular fact about them: they realize the highest standards of explanatory and predictive success (accuracy, uniﬁcation, completeness, variety of evidence, internal consistency, etc.) in the whole history of their ﬁeld of scientiﬁc inquiry (Doppelt 2007; 2011). This is a feature of our current epistemic situation that justiﬁes us in taking the singular success of our best current theories as veridical evidence that they are true. On BCTR, the success of superseded theories, in their respective epistemic situations, can best be explained without the hypothesis that they or any of their theoretical components were (or are) true. How? By invoking the features of their epistemic situations, which allowed the limited or ﬂawed successes of such “falsiﬁed” theories. I thus arrive at a position close to Achinstein’s verdict—because I hold that our best current theories rest on true “conﬁrming” evidence and I employ this verdict to characterize the evidence for superseded theories as merely subjective and epistemic situation evidence. But my argument violates Achinstein’s notion of objectivity and his insistence that epistemic situation evidence and veridical evidence are distinct and independent notions. My BCTR presupposes our current epistemic situation and argues for realism—the truth of our best current theories—as the best explanation of distinctive features of our epistemic situation described above. So realism and authentically “conﬁrming” evidence depend on an epistemic situation. From this perspective, the objectivity of conﬁrming evidence is based on the standards of success it realizes, not on Achinstein’s view of the imagined independence of veridical and potential evidence from our knowledge and beliefs. But if my scientiﬁc realism and notion of conﬁrming evidence rests on BCTR—a form of IBER—I am in the dark concerning Achinstein’s argument for a realist view of Perrin’s hypothesis. While his notion of “eliminative-causal” reasoning may well meet the test of relevancy, it does not justify the realist treatment of Perrin nor distinguish the case from

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that of the wave theorists. Achinstein owes us an argument to close the gap between “eliminative-causal” reasoning and the attainment of veridical evidence and realist truth. He faces a version of the anti-realist pessimistic meta-induction—which I have tried to meet with my turn to BCTR. Achinstein’s notion that scientiﬁc inquiry can attain true theories and veridical evidence must stake out a response to the central problem of successful-but-false theories, which inspire anti-realists and threaten scientiﬁc realism at every turn!

4. BRIEF CONCLUDING REMARK Achinstein’s notion of veridical evidence is not the most important notion at work in scientiﬁc inquiry. He is right that scientists “seek veridical evidence” and “want their theories to be true” (Achinstein 2001, 34–5). Scientists seek true theories, but they do so by producing compelling evidence and arguments for others in the epistemic situation. An empirical approach is hampered if it does not recognize that (a) scientists’ claim to truth is inseparable from (b) their claim to achieve the rational consent of experts in their epistemic situation. (B) is just as powerful as (a) and in fact is the path that scientists assume may lead them from (b) to (a). As Achinstein observes, Thomson may need to “set the stage” for the acceptance of his hypothesis about cathode rays “by including sufﬁcient information so that others can be in an appropriate epistemic situation and can become justiﬁed in believing (his) hypothesis for that reason” (35). Evidence in science is always bound by just such an epistemic situation. REFERENCES Achinstein, P. 2001. The Book of Evidence. New York: Oxford University Press. ——— . 1991. Particles and Waves: Historical Essays in the Philosophy of Science. New York: Oxford University Press. ——— . 1983. The Nature of Explanation. New York: Oxford University Press. Boyd, R. 1981. Scientiﬁc Realism and Naturalistic Epistemology. In PSA 1980: Proceedings of the 1981 Biennial Meeting of the Philosophy of Science Association, vol. 2, ed. P. D. Asquith and T. Nickles. East Lansing, Mich.: Philosophy of Science Association. ——— . 1973. Realism, Underdetermination, and the Causal Theory of Evidence. Nous 7: 1–12. Chang, H. 2003. Preservative Realism and Its Discontents: Revisiting Caloric. Philosophy of Science 70 (5): 902–12. Doppelt, G. 2011 (Forthcoming). Best Current Theory Realism. Journal of General Philosophy of Science.

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——— . 2007. Reconstructing Scientiﬁc Realism to Rebut the Pessimistic Metainduction. Philosophy of Science 74 (1): 96–118. ——— . 2005. Empirical Success or Explanatory Success: What Does Current Scientiﬁc Realism Need to Explain? Philosophy of Science 72 (5): 1076–87. Laudan, L. 1981a. A Confutation of Convergent Realism. Philosophy of Science 48 (1): 19–49. ——— . 1981b. The Epistemology of Light: Some Methodological Issues in the Subtle Fluids Debate. In Science and Hypothesis. Dordrecht, Holland: Reidel. Psillos, S. 1999. Scientiﬁc Realism: How Science Tracks Truth. London: Routledge.

6 A Defense of Achinstein’s Pragmatism about Explanation Adam M. Goldstein

1. INTRODUCTION The nature of explanation is a central theme of Peter Achinstein’s work, as indicated by his book of that title. He has consistently advanced a view that may be alternatively called the pragmatic view, the illocutionary theory, or contextualism about explanation. Moreover, he can lay title, I think, to the claim of having elaborated this view in greater detail, and with greater breadth, than any other philosopher. Bas van Fraassen might be considered by many to be a contender for this title—although according to Achinstein, van Fraassen is not even in the game: one of Achinstein’s bolder claims is that van Fraassen’s views about explanation, advanced as pragmatic, are not so at all (Achinstein 1984). Achinstein’s pragmatic theory of explanation is at odds with deeply entrenched views about explanation that originate with Carl Hempel, a central ﬁgure in contemporary studies in explanation. Achinstein’s pragmatism informs a pluralistic view: there are many kinds of good explanations, because success in explanation depends on features of the context in which the explanation is requested. In contrast, Hempel, as exempliﬁed by his deductive-nomological model of explanation, views success in explanation as invariant across contexts. To the disappointment of pragmatists, and contrary to what many of them believe, Hempel’s position is more resistant to one of the central lines of argument they advance against it. I present a stronger argument that takes the explanatory aims of evolutionary biology as a starting point, and that addresses the central motivations of Hempel’s position.

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2. HEMPELIANISM AND UNIVERSALISM Hempel is rightly regarded as the founder of the twentieth century discussion of explanation. Although withering criticisms have shown that Hempel’s D-N and I-S models of explanation are inadequate, their inﬂuence remains strong: many philosophers ﬁnd the central commitments embodied in them deeply compelling, and aim to preserve them in their own theories of explanation. One set of Hempel’s views is particularly inﬂuential. Hempelianism. The aim of scientiﬁc explanation is to answer why-questions by citing laws of nature to the effect that the event to be explained ought to have been expected.

Hempel states that explanation-seeking questions in science can “be expressed in the form ‘Why is it the case that p,’ where the place of p is occupied by an empirical statement specifying the … [phenomenon to be explained]” (Hempel 1965a, 334). These are remarks he repeats elsewhere (337). His many examples of explanation-seeking questions answered by D-N explanations include, for instance, “Why did Hitler go to war against Russia?” (Hempel 1965a, 334). “Reliance on general laws is essential” (1965a, 337) is one among many of Hempel’s statements that explanations require laws (Hempel 1965a, 231, 298–303; 1965b, 246). The famous “thesis of the structural identity of prediction and explanation” (Hempel 1965a, 366) exempliﬁes Hempelianism. According to the thesis, if a statement S is an explanation of an event E, then S would have served, before the fact, as a prediction of S; and if S can be used to predict E, then it explains E after the fact. Predicting an event requires showing that it ought to be expected, which just means that a successful prediction, advanced after the fact, meets the central cognitive standard for explanation as Hempel sees it, namely, showing that E ought to have been expected. Some important theories of explanation conform to Hempelianism, some adapting it to a probabilistic context. On Wesley Salmon’s statistical relevance theory (Salmon 1971) and his later causal theory (Salmon 1984), explanations aim to answer explanation-seeking why-questions by reference to laws of nature; rather than show that the event to be explained ought to have been accepted, Salmon requires only that the law indicate the degree to which the event ought to have been expected. Peter Railton’s D-N-P model is similar (Railton 1988). Hempelianism exempliﬁes what I term “universalism” about explanation. Universalism. The conditions for evaluating scientiﬁc explanations are invariant across contexts: there is one and only one set of criteria for

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evaluating scientiﬁc explanations, and those criteria apply regardless of the intentions or cognitive states of the audience of the explanation, or of its producers.

Hempel’s view is that explanations are like mathematical proofs, because success in both cases is independent of context (Hempel 1965a, 425–8). If a mathematical proof is a success, its conclusion follows from its premises, a matter independent of the intentions or cognitive states of its intended audience. The universalists’ belief that explanation can be characterized in an abstract manner accounts for their practice of inventing models of explanation, which describe relationships among statements that must obtain if an explanation is to be successful. Salmon and Railton, whose views are mentioned above, are universalists; Philip Kitcher (1988) and Michael Friedman (1988), though not Hempelians, are universalists. Unlike Salmon and Railton, whose theories of explanation require that explanations contain laws, Friedman and Kitcher argue that uniﬁcation is required, regardless of the context in which explanation-seeking questions are posed.

3. ACHINSTEIN’S PRAGMATISM The overview of Achinstein’s ordered pair theory of explanation (section 3.1 below) and his pragmatism (section 3.2) I present here is drawn primarily from his “The Pragmatic Character of Explanation” (Achinstein 1984), which encapsulates central ideas in The Nature of Explanation (Achinstein 1983).

(1) The ordered pair theory Achinstein takes the explaining act as fundamental. Consider an explanation-seeking question Q with an indirect form q. Broadly speaking, according to Achinstein, one person (the “tutor”) explains something to another person (the “tutee”) under the following circumstances. First, the tutor says, writes, or otherwise communicates with the tutee with the intention of using his or her communication to cause the tutee to be in a certain cognitive state, namely, knowing the answer to q; and the tutor intends that the tutee is caused to enter this cognitive state because the tutee knows that what the tutor has said is a correct answer to q. (In The Nature of Explanation (1983), Achinstein elaborates at length on the intentions, cognitive states, and the types of statements particular to explanation, the details of which are not required for my aims in this paper.) For instance, I might explain Sewall Wright’s shifting balance theory to a friend by telling her about the three

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stages of the shifting balance process and other related phenomena, with the intention that she recognizes that what I say is true and relevant. The condition that I intend that she understand the shifting balance theory by causing her to recognize that what I say to her is a correct answer to her question is meant to rule out cases in which I do something like direct her to a book that has the answer to her question. This might put her in the appropriate cognitive state eventually, but not by explaining the shifting balance theory: I have simply given her instructions. There is no one alive today to whom Darwin explained natural selection, for the simple reason that there is no one alive today who could have been a tutee of Darwin. Nonetheless, there is surely some important sense in which Darwin intended the explanatory value of his work to extend beyond his own lifetime. Indeed, Darwin was successful in this, his work being of a piece with our efforts today to explain natural selection. There must be some way to talk about the products of conversational exchanges in which explaining occurs. In order to do so, Achinstein develops what he terms the “ordered pair” theory of explanation. Let T mean “explaining act type T ” and Cq mean “a correct answer to the indirect form of an explanation-seeking question Q.” Achinstein’s view is that explanations have the following form:

The correct answer to the question q conveys the information required to bring about understanding in the tutee. The type of explaining act is necessary because a correct answer to a question need not be offered with the intention of promoting understanding. Someone might correctly answer an explanation-seeking question in order to show off or to succeed on an exam, or to provide context for a discussion of the person who ﬁrst discovered it, or begin a criticism of its relevance or usefulness to one purpose or another, for instance, in policy decisions.

(2) Correct explanations and good explanations The ordered pair theory is intended to delineate explanations from the products of other speech acts by describing the truth conditions for statements of the following type, which I will call “categorial” statements about explanation. Statement 1 (Categorial). φ is an explanation of q.

Achinstein points to a further question that might be asked: how good is a given explanation? A general account of a good explanation will offer truth conditions for statements of a kind I will term “evaluative” statements about explanation.

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Statement 2 (Evaluative). φ is a good explanation of q.

According to Achinstein, evaluative statements are pragmatic in the sense that they are true for any given explanation only if context-speciﬁc conditions are met. Although there are differing views about what pragmatism about explanation is, few will disagree that the following is allowed by it. Statement 3 (Pragmatic Explanation). Explanation φ is a good explanation of q for tutee T1, but not for tutee T2.

This description of pragmatism about explanation is intended to capture cases in which different tutees have different cognitive and practical abilities and aims, so that what constitutes a good explanation in response to an explanation-seeking question Q for one tutee is not a good explanation for another. As described above, the ordered pair theory requires that explanations include correct answers to explanation-seeking questions, that is, they require that the answer be true. For instance, it would be correct to explain how evolution occurs by mutation simply by saying “Heritable DNA is physically altered by radiation or some mutation-causing interaction with the environment, resulting in a new gene, which has an effect on its bearer’s ability to survive or reproduce.”This might sufﬁce for someone who knows almost nothing about genetics or evolution, but not for a college-level biology student.

4. ARGUMENTS ABOUT PRAGMATISM Hempelianism about explanation, as described above, is a two-part claim about the aim and strategy of scientiﬁc explanation: laws of nature are required for explanation, the aim of which is to answer explanation-seeking why-questions. From this point of view, much of what might appear to be, for instance, explanatory claims about the explanation of events in human history and in the history of life, are not in fact so. The central problem is that there are generally no laws of nature about historical events. A law of nature, at least on the Hempelians’ account, is a true generalization describing a physical necessity. Physical necessity is notoriously difﬁcult to understand, although it is widely agreed upon that laws of nature must “support” counterfactuals. An example often provided of a law-like generalization is “there are no 100 kilogram spheres of plutonium,” in contrast with “there are no 100 kilogram spheres of gold.” Any attempt to create a 100 kilogram sphere of plutonium is bound to fail, because a chain reaction would destroy the sphere before it reached that size. A 100 kilogram sphere of gold, in contrast, is not physically impossible, although no one has to date attempted to construct one.

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Consider an example taken from the history of life: “Why did species S come into existence, and why does it have the particular characteristics it does?” Scientists generally agree that neither the time and place at which a new species will come into existence nor the characteristics of that species can be reliably predicted. According to the thesis of the symmetry of prediction and explanation, it follows, according to the Hempelian, that the reason for the origin and nature of a new species cannot be explained. Consider a set A of ecological and biological conditions of the habitat and organisms in a species S; and suppose that there exists a true law-like statement L to the effect that, if the conditions in A obtain for a species S, a new species S1, a daughter of S, will be created, having characteristics C in virtue of which it differs from S. At present, scientists know of no such set of conditions A or law-like statement L, so there can be no explaining why a new species emerges and why it has the characteristics it does. The view that there is a range of “levels” at which an explanation can be formulated, and that the appropriate level depends upon the purpose of the tutee, is central to the pragmatist’s strategy against the Hempelian, a point made by Achinstein (2000). Statement 4 (Levels of Explanation). Suppose that entities of type L1 depend for their existence on entities of type L0, entities of type L1 having that relationship to entities of type L0 because entities of type L1 supervene on entities of type L0. Explanations formulated in terms of entities of type L1 are “at a higher level” than those formulated in terms of L0.

Statement (4) characterizes, very roughly, a dependence relationship— entities at a “higher level” depend for their existence on entities at a “lower level”; for instance, water molecules depend for their existence on atoms of hydrogen and oxygen, and species depend for their existence on the organisms of which they are composed. The relationship of dependence I have in mind, as indicated in statement (4), is a type of supervenience relationship, a comprehensive account of which is given by Jaegwon Kim (1993). The simplest form of such a relationship is described by the slogan “no change in L1 without a change in L0.” For instance, a species cannot become extinct unless each organism of which the species is composed dies. Similarly, a change in the density or distribution pattern of a species can only occur in case of a change in the location of its organisms. The pragmatist claims that different contexts call for explanation at different levels. Some tutees are interested in higher-level explanations, some in lower; and so what may be a good explanation for one tutee may be a very poor explanation for the other. The pragmatist allows that a tutee might be interested in some level of explanation at which there are

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no laws of nature that apply. This is the case in the example above: there are no laws of nature that apply to the origin of species, but the tutee may still want to ask, “How are new species formed?”—a question that the pragmatist is willing to accept as explanation-seeking. This explanation will address higher levels: for instance, population density, geography, migration patterns, mating strategies, and the like. The natural Hempelian response to this is to point out that, while there may not be any laws that apply at the higher level, there may be laws that apply at the lower level. The description of how species are formed is not an explanation; Hempel (1965a) would consider it a “sketch,” a rough outline of an explanation that is to be ﬁlled in with further details about the science. For instance, there may be laws of nature at molecular levels concerning the genetics, spatial distribution, neurobiology and endocrinology, functional morphology, and behavior, which, if they were known, and if sufﬁcient information could be obtained about antecedent conditions, could be used to reliably predict when a new species will originate, and what it will be like when it does so. The pragmatist rejoinder might go as follows. Suppose there were a Laplacian demon whose knowledge and computational skill could be put to work, and could supply evolutionary biologists with information about when and where every new species would arise, and what each would be like. The evolutionary biologist would still not be satisﬁed, because questions in evolutionary biology are not formulated at levels of explanation so low as the demon would require. For instance, the issue of whether geographical isolation is required for a new species to originate has been hotly contested since the 19th century. The demon’s information cannot answer this question, because the information it uses is not formulated in terms of “higher level” entities such as geographic locales. The Laplacian demon does not provide information the evolutionary biologist wants—it does not serve the cognitive aims required by the context. The Hempelian should not be afraid of this response by the pragmatist. No new argument is introduced here. The pragmatist is reasserting the idea that some explanations are better than others, and that whether one explanation is better than another depends upon the context in which the explanation is advanced. If the Hempelian does not accept this, then there is no reason why he or she should accept that a higher-level explanation is better than a lower-level explanation. Perhaps a higher-level account—which is not an explanation, on the Hempelian’s view—is easier to understand, more compact, or has some other virtue that makes it better for one tutee than another. Nonetheless, a higher-level explanation cannot be formulated in terms of laws of nature, nor can it explain why the event to be explained ought to have been expected.

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5. PRAGMATICS IN EVOLUTIONARY BIOLOGY The Hempelian must be confronted on his or her home terrain, so to speak. The Hempelian claims that the aim of scientiﬁc explanation is to answer explanation-seeking why-questions: rather than win against the Hempelian by interpreting and re-interpreting cases to show that they exemplify pragmatism, the pragmatist ought to argue the more fundamental point that there are other aims of scientiﬁc explanation. In this section, I would like to argue for just this point, taking evolutionary biology as my starting point. I begin by considering alternative theories of the change in allele frequencies due to natural selection across a single generation, represented by Δsp. The following scheme of symbols will be used throughout. Let p indicate the frequency of the A1 allele; q, the frequency of the A2 allele; s, the selection coefﬁcient, a ratio of the ﬁtness values of the A1 and A2 alleles; h, the heterozygous effect, a measure of how much a heterozygote’s ﬁtness – represent the mean ﬁtness of differs from either homozygote; and let w the population. By convention, the A1 allele represents the allele with the higher ﬁtness value. The ﬁrst theory of Δsp I will consider here is as follows (Gillespie 1998, 52). Δ s p = pqs[ ph + q(1 − h)] w

(1)

The second theory (59) is as follows. Δs p =

pq dw 2w dp

(2)

On the one hand, equation (1) “is probably the single most important equation in all of population genetics and evolution”; on the other hand, “it isn’t pretty, being a ratio of two polynomials with three parameters each” (Gillespie 1998, 52). In contrast, equation (2) has virtues above and beyond describing the time-course of Δsp due to natural selection. There is something unsatisfying about the description of . . . [directional, balancing, and disruptive forms of] natural selection. They come off as a series of disconnected cases. One might have hoped for some unifying principle that would make all three cases appear as instances of some more general dynamic. In fact, Sewall Wright found unity when he wrote . . . [equation (1)] in the more provocative form [of equation (2)]. (Gillespie 1998, 59)

The differences between equations (1) and (2) make a good test case for Hempelianism. Both ﬁt well with Hempel’s theory of explanation and Hempelianism more generally. Given information about the allele frequencies and ﬁtness values at a time T0, each can be used to deduce

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the value of Δsp at a time T1. In a large enough population, a prediction can be made with a high degree of accuracy, and after the fact, can be used to explain (on the Hempelian view) why the value of Δsp turned out as it did. Equations (1) and (2) may be regarded as laws of nature because they are empirical generalizations that support counterfactuals. Moreover, they are precisely equivalent to one another in the sense that they both depend on the same biological assumptions, apply to all and only the same cases, and can be deduced from one another. Nonetheless, there are two purposes for which equation (2) is better than equation (1)—purposes fundamental to the broader aims of science, and which are not attained by explaining why events occur by reference to laws of nature. First, science aims at advance. According to realism, broadly speaking, the aim of science is to arrive at true theories; according to anti-realists, broadly speaking, the aim of science is to arrive at empirically adequate theories. Looking at the full range of scientiﬁc disciplines, it is easy to ﬁnd phenomena concerning which there do not exist true or empirically adequate theories. To explain phenomena in a way that suggests new hypotheses is intrinsic to the aim of advancing science. This need not come at the expense of correctness or other criteria for good explanations: ceteris paribus, an explanation that promotes scientiﬁc advance is better than an explanation that does not. In order to see how this works, consider equation (2) in greater detail. It shows Δsp as a function of the frequency of the A1 allele p and mean ﬁtness w̅ . By inspection of the two main terms of equation (2), it can be seen that as the frequency of p increases, Δsp decreases; and the greater the ﬁtness difference between the ﬁtness of the A1 allele and the A2 allele, the larger Δsp. This provides a good deal of information about the dynamics of allele frequencies under natural selection, and explanations using it promote advance by placing Δsp in context. Contrast this with equation (1). It is derived from algebraic manipulations of a straightforward and intuitively appealing description of allele frequencies changing due to natural selection; but, as Gillespie notes, “it isn’t pretty.” If the frequencies and ﬁtness values of each allele are known, Δsp is easily computed with equation (1), but there is not much to be gained by looking at the expression itself. It is not likely to generate any insights and so explanations of which it is a part are not as good as those formulated in terms of equation (2). The second aim of science I want to call attention to is broader than promoting advance. Science aims to enlighten questions central to our conception of ourselves and our place in the universe, which I will call metaphysical questions. Hempelianism contributes to this aim by recognizing that scientiﬁc explanation tells us something about why the world works: what are the regularities, presumably grounded in the way

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things are, that make things happen as they do? Let me consider equations (1) and (2) in light of the idea that science is in part good for answering these larger questions about who we are, where we came from, and where we are going. Equation (2) illustrates how an explanation can serve to answer fundamental questions about the universe and the place of human beings in it. Equation (2) is an element of a model of the evolutionary process, proposed by Sewall Wright (1986; 1988) and known as an “adaptive landscape,” or a “surface of selective values.” In this model, Wright describes the genetic structure of a population as analogous to a topographical map: each genotype is associated with an “altitude,” its ﬁtness. Natural selection operates on the population to increase the frequency of alleles of greater ﬁtness, causing the mean ﬁtness of the population to increase. By representing Δs p as a function of allele frequency and mean ﬁtness, equation (2) describes this “hill-climbing” behavior. The reason that describing this “hill-climbing” behavior is important is that it speaks to a deeper question about whether evolution is progressive, at the root of which lies the question of whether it is possible for human beings as a group to progress. Equation (2) describes circumstances under which natural selection will push mean ﬁtness to the top of an adaptive peak; if other processes do not intervene, according to Wright, a population will improve until it has reached its maximum state of adaptation. R. A. Fisher, whose “fundamental theorem of natural selection” is intended to address the same issue, was clearly motivated by the question of whether one species in particular—ours—can progress. The ﬁrst seven chapters of Fisher’s Genetical Theory of Natural Selection (1958) contain some of the most profound insights about natural selection; the last eight chapters, probably not included on any science class syllabus, concern the conditions under which natural selection in the human population will result in increases in its mean ﬁtness, understood by Fisher in terms of social class and directly connected with differences in fecundity and fertility in lower and upper strata of British society. This preoccupation is not peculiar to Fisher. Many people who reject Fisher’s eugenic aims share his interest in using evolutionary biology to learn about human nature and society.

6. CONCLUDING REMARKS My defense of pragmatism about explanation is intended to challenge the claim that scientiﬁc explanations have a single aim—the central claim of

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universalism about explanation. I propose that an explanation aiming at promoting scientiﬁc advance is better, all other things being equal, than one that does not. I also propose that science aims at responding to deeper curiosities about human nature and our place—small though it may be—in the universe. I believe that these two aims of science are important enough, and that the case I present concerning alternative explanations of population-genetic change is compelling enough to establish that universalism about explanation is in error. Besides the intrinsic importance of this result, it plays an important role in the larger project of characterizing the explanatory strategies used by evolutionary biologists. The population-genetic models I offer as evidence can be interpreted along Hempelian lines, because, as I mentioned above, they are true empirical generalizations that can support counterfactuals, and so are laws of nature. In addition, I claim, there is an important role for historical explanations in evolutionary biology. Arguing for this claim takes direct aim at Hempelianism, because it aims to displace explanation-seeking why-questions as the sole kind of explanation-seeking questions asked by scientists. What remains is to describe these strategies of historical explanation by characterizing the kinds of explanation-seeking questions they are intended to answer, and the contexts in which they most naturally arise. REFERENCES Achinstein, P. 2000. The Symmetry Thesis. In Science, Explanation, and Rationality: Aspects of the Philosophy of Carl G. Hempel, ed. J. Fetzer. New York: Oxford University Press. ——— . 1984. The Pragmatic Character of Explanation. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984: 275–92. ——— . 1983. The Nature of Explanation. New York: Oxford University Press. Fisher, R. A. 1958. The Genetical Theory of Natural Selection. 2nd edition. New York: Dover. Friedman, M. 1988. Explanation and Scientiﬁc Understanding. In Theories of Explanation, ed. J. Pitt. New York: Oxford University Press. Gillespie, J. 1998. Population Genetics: A Concise Guide. Baltimore, Md.: The Johns Hopkins University Press. Hempel, C. G. 1965a. Aspects of Scientiﬁc Explanation. New York: The Free Press. ——— . 1965b. Studies in the Logic of Explanation. In Theories of Explanation, ed. J. Pitt. New York: Oxford University Press. Kim, J. 1993. Supervenience and Mind: Selected Philosophical Essays. New York: Cambridge University Press. Kitcher, P. 1988. Explanatory Uniﬁcation. In Theories of Explanation, ed. J. Pitt. New York: Oxford University Press. Provine, W. B. 1986. Sewall Wright and Evolutionary Biology. Chicago: University of Chicago Press.

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Railton, P. 1988. A Deductive-Nomological Model of Probabilistic Explanation. In Theories of Explanation, ed. J. Pitt. New York: Oxford University Press. Salmon, W. 1984. Scientiﬁc Explanation and the Causal Structure of the World. Princeton, N. J.: Princeton University Press. ——— . 1971. Statistical Explanation. In Statistical Explanation and Statistical Relevance, ed. W. Salmon. Pittsburgh, Pa.: University of Pittsburgh Press. Scriven, M. 1988. Explanations, Predictions, and Laws. In Theories of Explanation, ed. J. Pitt. New York: Oxford University Press. ——— . 1959. Explanation and Prediction in Evolutionary Theory. Science 130 (3374): 477–82. Wright, S. 1988. Surfaces of Selective Value Revisited. The American Naturalist 131 (1): 115–23. ——— . 1986. The Roles of Mutation, Inbreeding, Crossbreeding and Selection in Evolution. In Evolution, ed. W. Provine. Chicago: University of Chicago Press.

7 On the Very Idea of a Theory of Evidence Philip Kitcher

1. There was once a dean who was a scientist, and by all accounts intelligent. One day, this dean became irritated with an eminent philosopher of science on his faculty, and suggested that philosophers of science have made no useful contributions to science. In response to the dean’s challenge, the eminent philosopher wrote a book about evidence. That book distinguished various different notions of evidence, criticized a large number of philosophical positions, offered a new account of what it means to say that one statement is evidence for another, tackled some traditional philosophical puzzles, and discussed two major examples from the history of late nineteenth century physics. Should the dean have been convinced? It’s possible to approach The Book of Evidence, Peter Achinstein’s rich and interesting book (Achinstein 2001), in many different ways, but I choose to begin, as he does, with the dean’s challenge, because I think it is important to ask what a philosophical account of evidence should be trying to accomplish. A resolution of the paradox of the ravens or of the grue puzzle would surely be worth philosophical celebration, but we should remember that these and similar conundrums arose in the course of an attempt to understand scientiﬁc inference. Laying the puzzles to rest may not automatically achieve the broader goal. The dean can serve as a ﬁgure who reminds philosophers that we should be producing a kind of understanding that practitioners will ﬁnd illuminating. We need to know more about this dean and the kind of questions that would move him. So let’s invent two deans. One is a utilitarian dean, and what he wants from a book of evidence is an account that will sort out the difﬁcult judgments about evidence that confront him in his scientiﬁc work—and, perhaps even more, that will help his social science and

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medical faculties resolve their disputes about evidence. The other dean is more contemplative, and what he hopes for is an abstract account of the judgments that he and his colleagues make in their everyday research— something perhaps like an abstract account of syntax that might reveal the structures behind complexities of usage but that wouldn’t help anyone speak more grammatically. I suspect that the utilitarian dean would be quite unsatisﬁed by Achinstein’s book. Let’s let him speak. “Peter,” he says, “this is all very clever. You are very good at thinking up examples to show what is wrong with particular proposals, and you show that your own suggestion—that evidence requires a probability greater than half of an explanatory connection between hypothesis and evidence—survives the various cases you have used to test other ideas. But how do we scientists ﬁgure out these probability judgments? Most of the time you deal with toy examples, in which the probabilities come for free; occasionally that’s true in scientiﬁc research, but most of the time it isn’t. When you do turn to live examples from the history of physics, it’s not at all easy to see how your preferred notion is supposed to apply: how did Thomson, Hertz, and Perrin make judgments about the probability of explanatory connections? Moreover, your own solutions to traditional philosophical puzzles, ingenious though they are, take for granted one of the most difﬁcult notions in assessing evidence in scientiﬁc life, that of an appropriate (nonbiased) selection procedure. So I don’t see how any practicing scientists could use your ideas to resolve their puzzles about evidence.” The contemplative dean will probably be more sympathetic, recognizing the possibility that the appropriate probability judgments are made tacitly by scientists all the time. But he too may wonder how these tacit judgments are made, whether we can ﬁnd evidence for people making them, whether the ways in which scientists present their evidence and their reasoning reﬂect them, and so forth. So I suspect that the dean’s response will fall somewhere between impatience and polite skepticism. Like Achinstein, I take the dean’s challenge seriously, but I have a different diagnosis of the shortcomings of the philosophical tradition. It’s not simply, I suggest, that philosophers embraced too weak a notion of “e is evidence for h”, or that they thought such judgments were a priori. Further difﬁculties arose from making the problem too hard in one respect (wanting an account of evidence that would apply to each pair of sentences) and too easy in another (focusing on contexts in which probabilistic machinery is readily applicable). So I’m going to try to take up the challenge in a different way, although I try to incorporate some of Achinstein’s many insights.

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2. Plainly there are contexts in which we are very interested in, and able to assign, probabilities to outcomes: a lot of people ask their doctors questions of the form, “What’s the chance of avoiding X if I do Y?” But much of life, and science, isn’t at all like this. Consider my current predicament (as of May 2010); like about two billion other people, I’m interested in who will win the World Cup. Barring events we discount as so improbable as not to be worth considering (an outbreak of global warfare, rioting in South Africa, a sudden discovery that one or more teams must be disqualiﬁed), there is a space of 32 possibilities. How should I assign probabilities across this space? And on what evidence should I assign them? I am particularly interested in the fate of three teams: the USA, England, and Germany. Suppose I ask which of these is most likely to win. I have a pretty clear view that American chances are slim. On form, though, both England and Germany have a serious shot. On which of these should I put my money? If I had to make a Jamesian forced choice, it would probably be to prefer Germany’s chances. But I’m really uncertain. And that isn’t because I have too little evidence, but because, in a way, there’s so much. In England’s favor is the fact that they were brilliant in the qualifying stages. They have so much individual talent. But how will they play together? Will Lampard and Gerard ﬁnally click? Will someone support Rooney? And will he refrain from trampling on some opponent’s groin? Will the much-ballyhooed sexual scandals cause uncertainties in the British defense (where exactly will the minds of Ashley Cole and John Terry be)? On the other hand, is Ballack too old to be the midﬁeld mastermind? Can Lahm repeat his magic of 2006? Will the German defense be porous? And will someone (Podolski, Kerenyi, Gomez?) lead the attack? In the end, my hunch that Germany’s chances are better depends on the thought that, playing alongside one another for a signiﬁcant time, they are likely, especially under the coaching of Joachim Löw, to function better as a team. By contrast, I steel myself for the prospect that English chemistry will be lacking, and that, once again, the promise will ﬁzzle. Yet, this is only a hunch. My problem is that I don’t know how to balance all the considerations (of which I’ve listed only a very few) against one another. Even when I consider the situation seriously I ﬁnd it hard even to survey the things I know to be relevant; and, of course, I know that there are lots of relevant factors that I don’t know about. As I read his work, one of the major points made by Thomas Kuhn (1962) is that these kinds of predicaments occur in the large changes he calls “scientiﬁc revolutions.” Kuhn was sometimes inclined to consider

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them intractable, and, in consequence, to draw pessimistic conclusions about scientiﬁc rationality. My own view is that there are genuine difﬁculties in weighing and balancing evidence, that these are indeed prominent in the episodes studied by Kuhn, that they are not intractable, and that they occur in a variety of scientiﬁc contexts. I think the utilitarian dean would like philosophers to provide him with clear ways of sorting out these situations, and the contemplative dean would like some account of what goes on when scientists actually do sort them out. Let’s consider a variety of examples, at various “scales.” (1) Darwin recognizes that the geographical distribution of certain kinds of organisms (cave insects, South American mammals) could be understood in terms of their radiation and descent with modiﬁcation. He wonders how widely this approach to biogeography can be pursued. There are some apparent difﬁculties— plants and animals on remote islands, groups with apparently discontinuous distributions (Alpine plants are a good example). He considers a wide variety of instances, taking on cases that appear most challenging. He then conducts experiments to estimate the extent to which seeds can be transported across bodies of water, and so forth. He concludes that the problematic examples can be resolved, and that biogeographical data can be explained by the hypothesis of descent with modiﬁcation. (2) Hertz is interested in whether cathode rays are electrically charged particles. He sets up an apparatus designed to detect electrostatic deﬂections, and his experimental runs show none. He probes various possibilities of why there might be a null result even if cathode rays were present. Hertz concludes that there’s no good rival explanation, and that cathode rays aren’t composed of electrically charged particles. (3) A molecular biologist is trying to track down the analog of a known gene in a previously unsequenced genome, and she wants to get the sequence data as rapidly and accurately as possible. There is a wide variety of available restriction enzymes for chopping up the DNA into manageable chunks, and she wants to choose a good combination. She asks around and gets conﬂicting reports on the merits of various possibilities; some of her colleagues, working on related organisms, have had good results with the same combination that hasn’t done well for others. She eventually decides, with considerable uncertainty, that a particular combination of enzymes has a good chance of doing what she wants. She goes to work with it, and tinkers as the research proceeds.

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(4) An aspiring student (an advanced undergraduate or beginning graduate student) reads a lot of discussions of Wolfram (2002); some of them tell her that this is the work of an exceptionally talented scientist, who has large original ideas; others tell her that this is old hat, that similar approaches have been tried before, and that they’ve petered out. She doesn’t know quite what to make of this, but since she has, for once, a bit of free time, she decides to read the book. The reading has considerable impact on her subsequent scientiﬁc career, on the problems she selects and the approaches she considers. The concept of evidence is important to scientists (including deans) because they want the judgments they make to accord with the evidence. They have a conception of scientiﬁc responsibility that embodies: (R) A scientist, S, is responsible only if S’s judgments accord with the evidence.

What is it for a judgment to accord with the evidence? To a ﬁrst approximation, we might say that there are three forms of judgment: one may accept a statement, reject it, or withhold assent; judgment accords with the evidence just in case one accepts those statements that are supported by the totality of available evidence, rejects those whose negations are supported by the totality of available evidence, and withholds assent in cases where neither the statement nor its negation is supported by the totality of available evidence. Here the totality of available evidence must be taken to include not simply the class of experiences that the scientist has actually had or the class of reports actually received from other sources, but the experiences and reports that would have been acquired by an imaginative, diligent, and well-informed inquirer interested in the question at hand. Now as Achinstein rightly points out (2001, 34, 174), scientists want what he calls veridical evidence—evidence that really does support the judgments they make. But it’s not obvious that this concept can ﬁgure in an account of scientiﬁc responsibility. Responsible scientists do the best they can. Giving them the instruction “Believe only statements for which the total available evidence provides veridical evidence” isn’t much more helpful than telling them “Believe only statements that are true.” Further, it’s quite possible that making a judgment that accords with the evidence (in the sense pertinent to scientiﬁc responsibility) will later prove wrong, and that the evidence available will be viewed as misleading. So the concept of evidential support that ﬁgures in (R) looks much more like what Achinstein terms ES evidence. Hence, if Achinstein is going to help the

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scientist be responsible, he’d better have a sharp conception of ES evidence. His ofﬁcial deﬁnition, however, is that ES evidence is a true statement that someone in the appropriate context would be justiﬁed in believing was (probably) veridical evidence for the hypothesis in question. At this point the dean’s challenge arises with a vengeance: for we seem to require conditions for justiﬁcation (one might even think that giving such conditions is tantamount to offering a theory of evidence), and to know how such conditions apply to assessing the probability of there being a probability greater than half of an explanatory connection between the evidence statement and the hypothesis. Let’s now return to my examples. (2) is Achinstein’s own, and we’ll do well to begin with it. Following Jed Buchwald, Achinstein judges that there’s a sense in which Hertz was responsible, in which his judgments accorded with the evidence. After all, Hertz worked hard to exclude alternative possibilities, and, as Buchwald remarks, his “arguments and experimental work were tightly closed, carefully wrought to prevent damaging criticism” (Buchwald 1994, 168). Hertz was unlucky in that it turned out that there was a possibility he didn’t consider—even though he was neither lazy nor unimaginative. Notice that it’s this notion of according with the evidence, the one based on ES evidence, that has to ﬁgure in an account of scientiﬁc responsibility: whether we’re giving advice to improve scientiﬁc judgment (trying to satisfy the utilitarian dean) or explaining responsible scientiﬁc judgment, speciﬁcally accounting for Hertz’s responsible, but unlucky, practice (trying to satisfy the contemplative dean), we are focusing on ES evidence. But Achinstein’s ofﬁcial account of ES evidence, with its unexplained notion of justiﬁcation and its nested probabilities, does little to help us go beyond the intuitive judgment Buchwald makes. Next, let’s consider Darwin. His own experiences (on the Beagle voyage) and his wide knowledge of the work done by others on geographical distribution convince him that there are problems with the view that species invariably occupy ranges especially well-suited to them (there are, as he points out, “woodpeckers where no tree grows” [Darwin 1964, 186]). He understands that many facets of biogeography would be better accounted for by supposing that plants and animals are where they are as the result of a history of radiation and descent with modiﬁcation. Yet there are obvious doubts about the abilities of plants to radiate across stretches of ocean. He assembles evidence about dispersal that eliminates these doubts, and thus supports his general conclusion about why organisms inhabit the ranges they do. Neither the molecular biologist of (3) nor the aspiring researcher of (4) succeeds in eliminating doubt as Hertz (unluckily) or Darwin (more fortunately) do. They are left with uncertainty, but both have to do something.

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Are their choices irresponsible? I don’t think so. If the molecular biologist is to acquire her sequence data, she’ll have to use some combination of restriction enzymes. From the evidence available to her she concludes that there are probably unknown factors that affect the performance of various combinations; the best she can do is to try one that seems to have sometimes worked for others, being prepared to modify—and even switch—if things don’t pan out. Similarly, the student doesn’t have any basis for judgment that Wolfram’s book is everything its most ardent fans declare it to be, but she is perfectly reasonable in judging that there may be something to it, and, if she sacriﬁces little by exploring, there’s nothing irresponsible about that decision. All these situations involve a common structure. There’s a question that arises, and a framework of potential answers to it. The individuals involved attempt to ﬁnd a unique answer, either by eliminating rivals or by eliminating doubt about the answer ultimately accepted. Sometimes they succeed, and their answer survives subsequent challenges (Darwin); sometimes they succeed, and the answer doesn’t survive a change in the framework (Hertz); sometimes they don’t succeed, and it’s clear that the framework is inadequate (the molecular biologist); sometimes the entire situation seems thoroughly unclear (the student). This structure is, I submit, far closer to the ways in which judgments are actually made than the probabilistic machinery philosophers love. Interestingly, the idea that eliminative strategies are central to the ways in which scientists acquire evidence for their judgments surfaces in Achinstein’s own account. He notes, for example, that Perrin uses “eliminative-causal reasoning” to reach his main conclusions (Achinstein 2001, 255). Further, even in the special examples Achinstein deploys to assess the merits of various philosophical theories, attention to the eliminative role that evidence plays yields a more convincing account of what is occurring. Consider, for example his “Second Lottery Counterexample” (70). Here we have two pieces of potential evidence—e1, which tells us that the New York Times has reported that Clinton owns all but one of the tickets in a 1000-ticket lottery, and e2, which tells us that the Washington Post makes the same report. Achinstein believes that e2 provides evidence that Clinton will win the lottery, even when e1 is already known. I agree. But I think that the source of this intuitive judgment is that e2 makes us more conﬁdent that the Times hasn’t made a mistake. There’s a space of possibilities that include “the Times has the story right and Pr(Clinton wins) = 0.999” and “the Times has made a mistake and Pr(Clinton wins) is unknown.” The Post report contributes, I suggest, by eliminating the second of these. (Interestingly, this view of the matter accords with how the judgment would adjust to the discovery that the Times and the Post

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used the same source; one can tell the story so that e1 and e2 come to be more like “my copy of the Times reports that Clinton has 999 of 1000 tickets” and “your copy of the Times reports that Clinton has 999 of 1000 tickets.”)

3. What the deans (in either version) want is a theory that illuminates how scientists actually make judgments based on evidence (to the extent that they do). That doesn’t seem to be what The Book of Evidence delivers, valuable and interesting though it is in responding to a host of traditional philosophical questions. But maybe Achinstein was unnecessarily provoked into taking up a challenge that philosophers can’t be expected to answer. I’ll consider this possibility by trying to develop a bit more carefully the approach to scientiﬁc judgment I’ve gestured at above, and I’ll try to do so in a way that brings out my differences with Achinstein. Start with the notion of a context of judgment. I’ll assume that this consists of a question Q, a set of entertainable answers A, and a set of total available evidence statements E. There will be contextually variable standards of signiﬁcance that restrict the class of signiﬁcant questions, and also determine what counts as an acceptable answer. The entertainable answers will be further restricted: hypotheses using odd disjunctive predicates won’t be included, hypotheses involving certain kinds of functional relationships among variables won’t be included, hypotheses suggesting certain skeptical possibilities won’t be included. (Remarks: (1) there are interesting philosophical puzzles about why these exclusions are made, so that it is illuminating to have a response to the grue-problem—Achinstein provides a detailed and interesting one—and to have discussions of various types of skepticism; (2) there are other interesting philosophical puzzles that have received less attention, puzzles that concern the conditions under which one tries to ﬁnd a functional dependency of a particular form and resolves to focus on different variables if no such form will do.) The total available evidence should consist not just of what the inquirer knows, but of what he would know if he were neither lazy nor unimaginative. The simplest version of the eliminativist approach goes as follows. In a context of judgment the evidence supports p just in case (a) p ε A, (b) p is consistent with E, and (c) for any q ε A different from p, q is inconsistent with E. (Remark: for cases that involve probabilistic answers, the notion of consistency has to be replaced by a statistical analog.) Now there are some pure cases in the practice of science that look just like this;

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that’s what has fueled the abiding interest among scientists in the notion of a crucial experiment, and it’s a large part of what has made Karl Popper’s views so attractive to researchers (Popper 1959). In general, however, matters are more complicated. The simple version of eliminativism yields a different conception of evidential support (one that is allied to the idea of increase in probability, against which Achinstein argues). I suggest that this should be seen in explicitly comparative terms: in a context of judgment , the evidence favors p over q just in case (a) p, q ε A, and (b) p is consistent with E and q is inconsistent with E. Obviously, when the evidence supports p, it favors p over each other member of A, but in cases of incomplete elimination— when more than one member of A is consistent with E—no statement is supported, although some statements may be favored over others. In a context of judgment, a selection procedure is deﬁcient if there’s some p ε A consistent with the total available evidence such that it’s guaranteed that p will continue to be consistent with any statements added through the selection procedure. A selection procedure is ideal if it is guaranteed to yield statements that will be inconsistent with all except (possibly) one of the members of A that are currently consistent with the total available evidence. Unfortunately, simple eliminativism is too simple. The trouble is that the majority of scientiﬁc contexts are ones in which the available evidence is inconsistent with all the answers. Sometimes the solution is to expand the set of answers, to think of a possibility nobody has considered before. Often, however, what needs to be done is to revise statements one was previously inclined to accept, showing how there’s a modiﬁcation E* of E that (a) doesn’t ﬂout the rules for accepting statements on the basis of observation and (b) preserves the explanatory and predictive successes of E. Call such a modiﬁcation of E an acceptable modiﬁcation. Now if we allow for acceptable modiﬁcations to support hypotheses in cases where we start from inconsistency with all the answers, we ought also to permit “rescues” by acceptable modiﬁcation when one or several answers are consistent with the available evidence. The accounts of support and favoring have to be revised to accommodate this. Improved eliminativism must thus be developed along the following lines. In a context of judgment the evidence supports p just in case (a) p ε A, (b) p is consistent with E or with some acceptable modiﬁcation E* of E, and (c) for all q in A distinct from p, and for every acceptable modiﬁcation E* of E, q is inconsistent both with E and E*. Similarly the evidence favors p over q just in case (a) p, q ε A, (b) p is consistent with E or some acceptable modiﬁcation of E, and (c) q is inconsistent both with E and any acceptable modiﬁcation of E.

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But this is still problematic. Scientists are not always in a position to specify an acceptable modiﬁcation of E that will satisfy the (b) clauses, and they’re almost never in a position to survey all the acceptable modiﬁcations of E and show that the (c) clauses obtain. Often their predicament is that they have speciﬁed an acceptable modiﬁcation of E for which some of the previous inconsistencies have been resolved, and for which there’s a possibility that the remaining inconsistencies might be tackled by further modiﬁcation; on the other hand, all the acceptable modiﬁcations of which they (and their rivals) have been able to think don’t manage to resolve the inconsistencies for alternative answers. Thus a standard strategy of scientiﬁc argumentation is to identify ways of solving what have appeared to be puzzles for your favored view and to multiply the difﬁculties for your rival. Any number of claims about evidential support in the sciences exhibit this strategy. Back now to my four examples. I’ve tried to show in previous work (Kitcher 1993, 263–272) how Darwin’s research on biogeography proceeds by a complex eliminative argument; effectively Darwin eliminates doubts about his hypothesis in terms of descent with modiﬁcation by showing how it’s acceptable to amend commonsensical views about the transportation of organisms, and thereby remove some of the sources of inconsistency. Darwin got rid of a lot of the trouble, but, even after his detailed work, there were still puzzles to be mopped up later (some of them only resolved after the acceptance of continental drift, others that still remain). The track record of puzzle removal gives reason to believe that the appropriate (b) clause is satisﬁed; the track record of Creationist biogeography suggests that the main rival is still as badly off as it was in 1859. At ﬁrst sight, one might think that the case of Hertz shows simple elimination at work. But this would be a mistake. Hertz does consider the possibility that cathode rays consist of charged particles and that the result of his experiment might still be null. The problem is that he doesn’t consider the right modiﬁcation of the total available evidence—the one Thomson offered in 1897. It’s not that Hertz is lazy, or unimaginative, or irresponsible in any way; he’s unlucky in that a rather subtle possibility doesn’t occur to him. The molecular biologist of my third example knows that something is wrong with the way she’s setting up the problem. She wants to know a good combination of enzymes for tackling her favorite organism. So she considers various generalizations of the form “such-and-such combination is good for so-and-so kinds of organisms.” The conﬂicting reports she gets teach her that there’s a ﬁner grain of classiﬁcation that needs to be introduced, but she doesn’t yet know what that is. If she were interested in the abstract problem, then she could explore various

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possibilities. But that’s not really what she’s after. Since her goal is to obtain a good set of DNA fragments, she goes to work on the basis of whatever seems most promising, prepared to tinker, and even to try alternatives. The student of example 4 is in an equally problematic context. She knows that not all of the reports about Wolfram she’s received can be authoritative, but she doesn’t have a way of deciding which ones to trust and which to throw out. All she can do is take the plunge. (I suspect that situations like this, in which one just has to forge ahead, are quite common in the practice of the sciences. This may by no means be a bad thing; for if investigators are led to make different choices—whether because of differences in temperament, the appeal of social rewards, or whatever—the community inquiry may beneﬁt from their diverse explorations; I’ve explored this conception of “social learning” in Kitcher 1993, 303–389).

4. So how would the deans respond to this? I think (hope) they’d feel that the account I’ve sketched stays closer to the phenomenology of scientiﬁc judgment than philosophers typically manage. But I also think they’d be skeptical about how illuminating it is. Once again, the deans speak: “Okay, this is a reasonable description of what we do; but everything clear and precise you’ve told us we already knew. The idea of inconsistency is pretty obvious (at least when probabilistic hypotheses aren’t involved, and you’ve ducked that issue). What’s hard, and where we might look for advice in a theory of evidence, is in understanding how contexts of judgment are properly set up, how we decide what an “acceptable modiﬁcation” is, and, above all, how we properly make the judgments that there’s a way of eliminating the inconsistencies that beset one answer and no way of doing the same for its rivals, given that you admit, as you should, that we can never solve all the problems. That’s where we want a theory. Come back when you have one.” I agree. Is any such theory possible? Let me suggest an analogy. The elements of tactics in chess—pins, forks, skewers, and so forth—are very well understood. We’re unlikely, I think, to improve our account of them, to arrive at a deeper and more precise theory. By the same token, I think we have a clear view of the tactics of scientiﬁc reasoning; if eliminativism is right, it’s fundamentally a matter of spotting inconsistencies, and we’re not going to get much more by way of a theory of that. The trouble in both cases lies in understanding strategy—the sort of thing that grandmasters understand about space, pawn structure, weaknesses of various kinds

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and so forth, and the sort of thing scientists understand about when inconsistencies really matter and when they can be trusted to get sorted out in due time. Studies of chess strategy are by no means as precise as the explanations of tactics. I’m not sure that we philosophers can produce much by way of precise theory about the strategy of scientiﬁc argument. What we can manage, on occasion, is analogous to the analyses of games that expert chess players are able to provide: that is, a reconstruction of the considerations that have led a particular scientiﬁc community to a judgment. Doing that is both non-trivial and potentially valuable. Think, for example, of controversies that occupy the public: the IQ debate, the disputes over evolutionary theory, the claims made on behalf of human sociobiology or evolutionary psychology. It would be wonderful if we had an illuminating reconstruction of the scientiﬁc consensus on anthropogenic climate change. I contend that providing insights of the kind just mentioned requires no formal account of evidence. Yet, for reasons that might move both my imagined deans, a formal theory, if we could get it, would be a good thing to have. The Book of Evidence develops a theory that provides intricate and interesting solutions to problems that have worried philosophers for several decades. For that it deserves to be celebrated. But I don’t think it answers the dean’s challenge. To do so would require a very different kind of theory. I wish I knew how to provide it. REFERENCES Achinstein, P. 2001. The Book of Evidence. New York: Oxford University Press. Buchwald, J. Z. 1994. The creation of scientiﬁc effects: Heinrich Hertz and electric waves. Chicago: University of Chicago Press. Darwin, C. 1964. The Origin of Species. Cambridge, Mass.: Harvard University Press. Kitcher, P. 1993. The Advancement of Science. New York: Oxford University Press. Kuhn, T. 1962. The Structure of Scientiﬁc Revolutions. Chicago: University of Chicago Press. Popper, K. 1959. The Logic of Scientiﬁc Discovery. New York: Basic Books. Wolfram, S. 2002. A New Kind of Science. Champaign, Ill.: Wolfram Media.

8 Mill on the Hypothetical Method: A Discussion of Achinstein’s Defense of Mill and Newton on Induction Frederick M. Kronz

1. INTRODUCTION Following Newton and Mill, Peter Achinstein maintains in Evidence, Explanation, and Realism that there are universal rules of induction (Achinstein 2010). He also maintains that such rules may be formalized, but that their validity cannot be determined formally, as in deduction. More precisely, he maintains that inductive inferences are warranted by material facts or empirical assumptions, in contrast with deductive inferences in logic and mathematics, which can be evaluated by formal means alone. These elements of Achinstein’s view are provisionally accepted. Two additional components of his view, that induction and hypotheticodeduction are mutually exclusive and that induction is the core of the scientiﬁc method, are not. The corresponding themes defended here are that induction and hypothetico-deduction are mutually complementary, that one is not subsidiary to the other, and that the scientiﬁc context determines which of the two modes is most appropriate. In doing so, I argue that neither Mill nor Newton (following Mill, I focus on Newton’s actual practice of science) is really averse to the use of hypotheses in science, contrary to what Achinstein suggests. I also provide a new formal characterization of hypothetico-deduction that incorporates key insights of Mill, Whewell, and others. This development is in support of Achinstein’s general approach. The upshot is that Achinstein should regard both hypothetico-deduction and induction (in the narrow sense, as characterized by Newton and Mill) as distinct universal and abstract rules (or sets of rules) of induction (in the broad sense, which includes any empirically defensible mode of non-deductive reasoning).

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2. ACHINSTEIN ON INDUCTION Achinstein (2010) defends the inductivist views of Newton and Mill against those of Whewell. He focuses on the rules that each uses to characterize induction: Newton’s Rules for the Study of Natural Philosophy and Mill’s Deductive Method, which essentially involves his Four Methods of Experimental Inquiry. Achinstein’s take on the inductivists is presented later in this section after I brieﬂy discuss Mill’s Methods. Since Mill acknowledges an essential (though subsidiary) role for the Hypothetical Method and sees clear parallels between it and his Deductive Method, they are presented together in the next section. Mill’s Four Methods of Experimental Inquiry are his Method of Agreement, Method of Difference, Method of Residues, and Method of Concomitant Variation (Mill 1879, 278–92).1 The ﬁrst two are the core methods. In presenting the Four Methods, Mill puts forth Five Canons of Reason; the third canon combines the Method of Agreement and the Method of Difference to form a hybrid method that is often characterized in the literature as a ﬁfth method (referred to by Mill as the Indirect Method of Difference, and as the Joint Method of Agreement and Difference). The Method of Residues and the Method of Concomitant Variation are also derivative with respect to the ﬁrst two. In presenting these methods, he uses capital letters ABC (short for A, B, C, …) to denote antecedent conditions and small letters abc (short for a, b, c, …) to denote consequent conditions. He also distinguishes causal laws (laws of cause and effect) from other laws, such as phenomenological laws and accidental generalizations. The ultimate goal in using the methods (according to Mill) is to obtain causal laws; he regards the Method of Difference to be of paramount importance for attaining that goal. It is unnecessary to elaborate further on Mill’s Methods for what follows.2 In developing his interpretation of Newton’s and Mill’s rules, Achinstein claims that they are contrary to other methodologies, particularlyWhewell’s method, which involves the use of hypotheses. However, there is very little in Newton’s Rules of Reasoning per se and nothing in Mill’s characterization of the Deductive Method that precludes the use of hypotheses in science. It is necessary to look elsewhere in their writings in order to make a determination as to their respective views. As it turns out, their expressed views diverge drastically: Newton expresses adamant opposition to any use of hypotheses in science, whereas Mill regards the Hypothetical Method as essential to science. But expressed views can be misleading. As Mill is careful to point out, one must distinguish between what Newton says about hypotheses and what he does with them in

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practicing science. Indeed, Mill makes a good case (presented below) that Newton does not deprive himself of the use of hypotheses in the Principia and elsewhere. In the Third Book of his famous treatise, Newton puts forth four methodological rules. The fourth is the only one that has direct bearing on the role of hypotheses in science. Rule 4: In experimental philosophy we are to look upon propositions inferred by general induction from phenomena as accurately or very nearly true, notwithstanding any contrary hypotheses that may be imagined, till such time as other phenomena occur, by which they may either be made more accurate, or liable to exceptions. (Newton 1999, 943)

It gives substantial epistemic status to propositions that are inferred by general induction from phenomena and dictates against any attempt to use hypotheses to undermine that status. However, it says nothing about the use of hypotheses in other situations. For example, it does not preclude their use to account for phenomena not amenable to general induction nor does it preclude their use to enhance the epistemic status of propositions obtained via an induction from phenomena. Thus, Achinstein overstates the case concerning Newton’s Rules; they really do not exclude the Hypothetical Method. Although Newton’s Rules do not dictate broadly against the use of hypotheses in science, he does issue much more general declarations elsewhere that do. His clearest and best known statement to that effect is the following quotation from the General Scholium, which immediately follows his characterization of his Four Rules; it is known as Newton’s Hypothesis non ﬁngo (a Latin expression meaning “I do not feign hypotheses”). I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction. (Newton 1999, 943)

The declaration above is not a corollary to Newton’s Rules; it is a separate claim. One could elevate it to the status of a Rule and thereby reject the Hypothetical Method, the approach ascribed to Achinstein. Or, one could follow Mill and adopt a mitigated stance towards Newton’s declaration and accept the Hypothetical Method, which is the approach followed here. Interpreting Mill as an advocate of the Hypothetical Method has ramiﬁcations for interpreting the Mill–Whewell debate. Achinstein characterizes it as a debate about which of two mutually incompatible methods

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(induction or hypothetico-deductivism) should be used by scientist. A more subtle interpretation is proposed here, that they regard the two methods as mutually complementary while giving prominence to one over the other. Mill regards the Hypothetical Method as subsidiary to Induction, while Whewell does the reverse.3 The upshot for Achinstein is that he should interpret Mill as promoting both methods. Moreover, he should regard each of them as corresponding to a universal, abstract rule of induction (in the broad sense). It is also recommended that neither method be regarded as subordinate to the other (contrary to the contrasting views of Mill and Whewell). Both methods are needed to do science, and it is the scientiﬁc context that determines which is appropriate. This is an attractive view, and meshes well with the fundamental structure of deductive logic, a system of independent and mutually complementary rules. It is reasonable to suppose, following Achinstein, that the analogy with deductive logic breaks down over validity.

3. MILL ON THE DEDUCTIVE METHOD AND THE HYPOTHETICAL METHOD Mill characterizes the Deductive Method in Section 3.11.1: The mode of investigation which . . . remains to us as the main source of the knowledge we possess or can acquire respecting the conditions and laws of recurrence of the more complex phenomena, is called, in its most general expression, the Deductive Method, and consists of three operations—the ﬁrst, one of direct induction; the second, of ratiocination; the third, of veriﬁcation. (Mill 1879, 325)

He focuses on causal laws in elaborating on the three components of the Deductive Method. A direct induction is an inference to a law governing a separate cause that shares in bringing about an effect; his Four Methods are used in making such inferences. The second stage essentially involves deductive reasoning; it consists in calculating how the separate causes (from the ﬁrst stage) operate in combinations. The third is a comparison of the calculated effects of combined causes (from the second stage) with known phenomena or the empirical laws known to characterize those phenomena. Mill notes that the Hypothetical Method has fairly close counterparts to the second and third stages of his Deductive Method; once a hypothesis is formulated, one deduces observational consequences from it and then compares them with the phenomena. They differ drastically on the ﬁrst stage; in the Hypothetical Method one conjectures a hypothesis

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whereas in the Deductive Method one infers a general law from observations. The Deductive Method does not preclude the use of hypotheses. Mill says that it is the main source of scientiﬁc knowledge; he does not say nor does he imply that it is the only legitimate method for science. There is nothing in what Mill says in characterizing the method that precludes the use of hypotheses in science. Indeed, not only is it consonant with the passage cited above for hypotheses to play an essential though subsidiary role with respect to the Deductive Method, but that is precisely the view that he explicitly puts forth several chapters later (in Section 3.14.5). This function, however, of hypotheses, is one which must be reckoned absolutely indispensable in science. When Newton said, "Hypotheses non ﬁngo," he did not mean that he deprived himself of the facilities of investigation afforded by assuming in the ﬁrst instance what he hoped ultimately to be able to prove. Without such assumptions, science could never have attained its present state: they are necessary steps in the progress to something more certain; and nearly everything which is now theory was once hypothesis. (Mill 1879, 353)

Mill characterizes this indispensible function in the paragraph immediately preceding this passage: A hypothesis can serve to suggest observations and experiments that later serve to provide independent evidence for that hypothesis, if such evidence is obtainable. The passage itself is striking for several reasons. It provides a drastically mitigated interpretation of Newton’s claims about the role of hypotheses in science, and in doing so suggests that Newton really did make use of hypotheses in doing science (despite what he says in his famous declaration). It also provides a sufﬁcient reason for regarding the Hypothetical Method as complementary to (rather than incompatible with) the Deductive Method, given that science could not have obtained its present state without it. The passage under discussion might be taken to suggest that Mill actually regards the Hypothetical Method as being on a par with, rather than subsidiary to, the Deductive Method, but that would clash with the passage cited earlier in which he says that the Deductive Method is the “main source” of scientiﬁc knowledge. This apparent tension is substantially mitigated by his assertion that the proper use of the Hypothetical Method must include a key element of the Deductive Method, the Method of Difference (broadly construed—see Section 2 of this essay above), for it to work properly. An elaboration of that point follows. In Section 3.14.4 (the section preceding the passage cited just above), Mill explains that Newton uses the Hypothetical Method when he conjectures that there is a force that instantaneously deﬂects a planet from its

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rectilinear path at each instant and tends directly toward the sun so that the planet sweeps equal areas in equal times in its curved path about the sun. He suggests that Newton proceeds similarly when he conjectures further that the force varies inversely as the square of the distance in order to deduce Kepler’s other two laws (that planets move in elliptical orbits and the harmonic law). He also makes a crucially important point that contrasts with Newton’s expressed views and serves to distinguish his methodological views from Whewell’s with regard to the Hypothetical Method: namely, that Newton uses the Method of Difference to legitimize his use of the Hypothetical Method and thereby to “fulﬁll the conditions of a complete induction.” Now, the Hypothetical Method suppresses the first of the three steps [of the Deductive Method], the induction to ascertain the law, and contents itself with the other two operations, ratiocination and verification, the law which is reasoned from being assumed instead of proved. This process may evidently be legitimate on one supposition, namely, if the nature of the case be such that the final step, the verification, shall amount to and fulfill the conditions of a complete induction . . . It is thus perfectly possible, and indeed is a very common occurrence, that what was an hypothesis at the beginning of the inquiry, becomes a proved law of nature before its close. But in order that this should happen, we must be able, either by deduction or experiment, to obtain both the instances which the Method of Difference requires. (Mill 1879, 350–1)

The Method of Difference requires positive instances (such as ABC and abc) and negative instances (such as Ā BC and ābc). Mill explains that Newton uses it to show the centripetal (center-directed) character of gravitational forces; Newton provides positive instances by showing that centripetal forces yield Kepler’s ﬁrst law (equal areas swept out in equal times), and negative instances by showing that non-centripetal forces violate the law.4 Mill explains that Newton also does so in showing the inverse square character of gravitational forces; he shows that Kepler’s second and third laws hold for inverse square forces (positive instances) but not for non-inverse square forces (inferred negative instances). In the last paragraph of Section 3.14.4 Mill suggests that he has effectively provided (via his Method of Difference) an explication of Newton’s notion of a vera causa, a Latin term that means true cause. Newton uses this term in his ﬁrst rule of reasoning, but he never indicates what serves to promote a causal hypothesis to a vera causa despite his having used multiple evidentiary modes in supporting causal hypotheses. In any case, the upshot of the paragraph at issue seems to be that when there is a demonstrated difference for a causal hypothesis, that demonstration

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constitutes a proof that the hypothetical cause is a true cause (according to Mill, that is). In particular, Newton’s demonstrated differences for his law of gravitation show gravity to be a true cause. It is worth mentioning that knowing that an antecedent condition is a true cause and knowing how to describe the causal relationship mathematically are not sufﬁcient for understanding how the cause operates. Newton makes it very clear that he does not understand how it is that one body instantaneously inﬂuences another at a distance, and asserts that he will “feign no hypothesis” in that regard. The section of Mill’s logic under discussion (Section 3.14.4) is a crucial one, though it is rather obscure. For example, he introduces the distinction between a real cause and a ﬁctitious one, and then puts forth the claim that there are real causes for which the associated laws are merely supposed, and ﬁctitious causes for which the associated phenomena are characterized by known laws. A bit later he mentions another distinction between “already ascertained” causes and unknown causes, but he does not indicate what it means for a cause to be “already ascertained.” It is not clear whether that means known or real or something else, and if known whether that means observed or inferred. A careful exegesis of the associated text cannot be provided here. For the purposes of this section of the paper the general thrust will sufﬁce, which seems to be that one must sufﬁciently articulate the precise mode of dependence of factors in a hypothetical law in order to be in a position to use the Method of Difference either to prove or to disprove the law and, in the case of hypothetical causal laws, to show whether the associated hypothetical cause is a true cause. It appears, then, to be a condition of the most genuinely scientiﬁc hypothesis, that it be not destined always to remain an hypothesis, but be of such a nature as to be either proved or disproved by comparison with observed facts. This condition is fulﬁlled when the effect is already known to depend on the very cause supposed and the hypothesis relates only to the precise mode of dependence; the law of variation of the effect according to the variations in the quantity or in the relations of the cause. (Mill 1879, 352)

In contrast with Mill, Whewell explicates Newton’s notion of a vera causa using his notion of a Consilience of Inductions. In explicating Newton’s ﬁrst rule he says the following. When the explanation of two kinds of phenomena, distinct, and not apparently connected, leads to the same cause, such a coincidence does give reality to the cause, which it has not while it merely accounts for those appearances which suggested the supposition. This coincidence of propositions inferred from separate classes of facts, is exactly what we noticed . . . as one of the most

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decisive characteristics of a true theory, under the name of Consilience of Inductions. (Whewell 1860, 190–1)

In the text immediately following this passage, Whewell points to Newton’s use of the inverse square force to explain both planetary orbits and the moon’s orbit, and to explain the precession of the equinoxes, as concrete examples of Newton’s use of Consilience (since these distinct phenomena were at the time not apparently connected). It is remarkable that Mill focuses on the Method of Difference to the exclusion of Consilience and that Whewell does the reverse. That is to say, each was aware of the other’s preferred evidentiary mode, but was unwilling to give it serious consideration. This is especially puzzling given that each thought of his respective evidentiary mode as providing an operational characterization of Newton’s notion of a vera causa. In that regard, the view suggested here is that they each overstated the case;5 an argument to that effect is developed elsewhere (Kronz 2011).

4. A PROVISIONAL FORMALIZATION OF THE ENHANCED HYPOTHETICAL METHOD In light of the discussion above, it is reasonable to regard the Hypothetical Method as a general methodological rule that is complementary to the notion of Induction characterized by Achinstein. Following Achinstein’s inspiring claim that methodological rules are general and formalizable, a provisional formulation of the Enhanced Hypothetical Method is presented below that synthesizes key insights of Mill, Whewell, Charles S. Peirce, Karl Popper, Thomas Kuhn, and others concerning the effective use of hypotheses in science. The Hypothetical Method is often presented in a simple form. It is named here the Naïve Hypothetical Method.

Naïve Hypothetical Method 1. Conjecture a hypothesis as a solution to a problem or as a possible explanation of some puzzling phenomena. 2. Deduce empirical consequences from the hypothesis together with other empirically justiﬁable assumptions. 3. Conduct observations or experiments to determine whether the empirical consequences obtain. 4. Make an inductive inference to the hypothesis, provided that the empirical consequences obtain.

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The Naïve Hypothetical Method does not bring into play any of the subtleties discussed above. As a result, it is susceptible to simple-minded counterexamples, a case in point being Russell’s involving the hypothesis “Pigs have wings.” That hypothesis together with the well-known fact that some pigs are good to eat entails the empirical consequence that some winged things are good to eat. But, it is unreasonable to regard that consequence as providing even a modicum of evidence for the hypothesis. Clearly, other considerations must be involved before step 4 is epistemically justiﬁed. As noted above, both Mill and Whewell require the satisfaction of an additional condition for the effective use of the Hypothetical Method. Consequently, it is reasonable to suppose that they would advocate replacing step 4 with the following: 4'. Make an inductive inference to the hypothesis, provided that the empirical consequences obtain and provided that there is X.

For Mill, X = a demonstrated difference (an effective use of his Method of Difference, broadly construed). For Whewell, X = a Consilience of Inductions. It is not necessary to determine whether either is correct. A better approach (the one adopted in this essay) is to suppose each is partially so, the upshot being that X = a demonstrated difference or a Consilience of Inductions or . . . (the ellipsis here corresponds to a disjunction of some other suitable set of conditions). Newton’s use of the Hypothetical Method supports this view; he sometimes used the Method of Difference and sometimes a Consilience of Inductions, as noted above. In light of the considerations in this section and related considerations in previous sections, a more sophisticated but provisional formalization of the Hypothetical Method is put forth. It is referred to here as the

Enhanced Hypothetical Method 1. Conjecture a hypothesis as a solution to a problem or as a possible explanation of some puzzling phenomena. 2. Deduce empirical consequences from the hypothesis together with other empirically justiﬁable assumptions. 3. Conduct observations or experiments to determine whether the empirical consequences obtain. 4. Make an inductive inference to the hypothesis, provided that the empirical consequences occur and provided that there is a. a consilience of inductions (in Whewell’s sense), or b. a demonstrated difference (in Mill’s sense), or c. a novel prediction (in Peirce’s sense),6 or d. a new organization of facts that facilitates solving a problem,7 or

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e. a suitable condition (other than those already mentioned) is satisﬁed.8 5. If the empirical consequences do not obtain, then revise the hypothesis or revise an auxiliary assumption used to derive the empirical consequences, and then proceed as before (starting from step 2).9 The formal characterization above should be regarded as provisional and partial; a brief consideration of each of stage will sufﬁce to show why. With regard to the ﬁrst, the form of the hypothesis requires elaboration. Both general and statistical hypotheses are used in science, so it would be useful to characterize a range of formal features of such hypotheses. With regard to the reason for the conjecture, although it is often characterized in terms of its serving to solve a problem or to explain some puzzling phenomena, there may be other scientiﬁc reasons for making conjectures, and these should be included in the formulation. The nature of the act of conjecture also requires further characterization. Although some (such as Popper) have maintained that this stage is not inferential and merely involves making an educated guess or an intuitive leap, others (such as Peirce) maintain that this step involves a type of explanatory inference. In that case, the form of the inference and the underlying notion of explanation need to be explicated. In addition, it is possible that other formal modes are sometimes involved in the act of conjecture, such as an underlying process of pattern recognition; such modes would need to be appropriately formalized. The second step should be supplemented by an explication of what constitutes an empirically justiﬁable assumption. The third might appear to involve a straightforward comparison, and sometimes it does, but it is just as often a delicate matter especially when statistical hypotheses are involved. In some cases it might be better to use Neyman-Pearson statistical methods and in others Bayesian methods or something else; it would be worth providing formal criteria for distinguishing such cases to the extent that is possible. The fourth step should be elaborated with regard to the nature of the inductive inference, such as whether it constitutes an increase in the probability that the hypothesis is true (or approximately true), or perhaps crosses a threshold making it more likely than not that it is (approximately) true; moreover, the nature of that inference very likely depends on which conditions in step 4 are met. There is also the very interesting question as to what speciﬁc conditions alluded to in 4e could serve to “validate the induction” (notably weaker than what Mill intended in his desire to “fulﬁll the conditions of a complete induction”). With regard to step 5, one representative issue that needs to be addressed is the well-known Duhem-Quine thesis. Imre Lakatos (1970) has presented some provocative suggestions involving the notions of progressive

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and degenerative problem shifts that counter that thesis to some extent, but his overarching view is not regarded as viable. Most of the issues mentioned in connection with each of the ﬁve stages identiﬁed above have been discussed in the literature (in many cases rather extensively). They are far from settled and further discussion of them is beyond the scope of this essay.

5. CONCLUDING REMARKS Achinstein interprets the Whewell–Mill debates as a dispute over which of two incompatible modes of inference, hypothetico-deduction and induction, is right for science. He sides with Mill and defends the view that there are universal rules of induction. He regards the rules put forth by Newton and by Mill as exemplary, and he maintains that they exclude the hypothetico-deductive method. But Achinstein fails to appreciate that their rules really do not exclude that method, and that neither Mill nor Newton (at least on Mill’s interpretation of Newton, which is based on Newton’s actual practice of science) is truly averse to its use in science. Furthermore, the Whewell–Mill debate is really a dispute about which of two compatible modes of inference, hypothetico-deduction and induction, is subsidiary to the other. Rather than side with Whewell or Mill, an alternative approach is advocated above: They are regarded as mutually complementary rather than hierarchically related, and it is the scientiﬁc context that determines which of the two (if either) is appropriate. Consonant with this approach and with Achinstein’s view that there are general methodological rules that govern the practice of science, a new version of the hypothetico-deductive method, the Enhanced Hypothetical Method, is provisionally formulated. It synthesizes key insights (put forth by Whewell, Mill, Peirce, Popper, Kuhn, and others) concerning the effective use of hypotheses in science.

ACKNOWLEDGMENTS The views expressed are those of the author. They do not represent the position of the National Science Foundation (NSF). No endorsement by NSF should be inferred. The author wishes to acknowledge the helpful comments and suggestions by Leslie Kronz and Melissa Jacquart, which served to improve an earlier draft of this essay, and the substantial editorial assistance of Greg Morgan in producing the ﬁnal version.

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REFERENCES Achinstein, P. 2010. Evidence, Explanation, and Realism. New York: Oxford University Press. Dewey, J. 1991. The Later Works, 1925–1953: Logic: The Theory of Inquiry, ed. J. A. Boydston. Carbondale: Southern Illinois University Press. Ducheyne, S. 2008. J. S. Mill’s Canons of Induction: From True Causes to Provisional Ones. History and Philosophy of Logic 29 (4): 361–76. Kronz, F. M. 2011. Scientiﬁc Method. In Leadership in Science and Technology, ed. W. S. Bainbridge. Thousand Oaks, CA: Sage. Kuhn, T. 1977. The Essential Tension: Selected Studies in Scientiﬁc Tradition and Change. Chicago: University of Chicago Press. Lakatos, I. 1970. Methodology of Scientiﬁc Research Programs. In Criticism and the Growth of Knowledge, ed. I. Lakatos and A. Musgrave. Cambridge: Cambridge University Press. Mackie, J. L. 1967. Mill’s Methods of Induction. In The Encyclopedia of Philosophy, vol. 5, ed. P. Edwards. New York: MacMillan. Mill, J. S. 1879. A System of Logic, 8th edition. New York: Harper & Brothers. Newton, I. 1999. Philosophiae Naturalis Principia Mathematica, 3rd edition. Trans. I. B. Cohen and A. Whitman. Berkeley: University of California Press. Peirce, C. S. 1998. The First Rule of Logic. In The Essential Peirce, vol. 2, ed. N. Houser, A. De Tienne, C. L. Clark, D. B. Davis, J. R. Eller and A. C. Lewis. Bloomington: Indiana University Press. Popper, K. 1968. The Logic of Scientiﬁc Discovery. New York: Harper Torchbooks. Russell, B. 1939. “Dewey’s New ‘Logic’” in Paul Arthur Schilpp ed. The Philosophy of John Dewey. New York: Tudor. Skyrms, B. 2000. Choice and Chance: An Introduction to Inductive Logic, 4th edition. Belmont, Calif.: Wadsworth Publishing Company. Whewell, W. 1860. On the Philosophy of Discovery. London: John W. Parker and Son. ——— . 1858. The Philosophy of the Inductive Sciences, 3rd edition. London: John W. Parker and Son. ——— . 1849. On Induction, with Especial Reference to Mr. J. Stuart Mill’s System of Logic. London: John W. Parker, West Strand.

NOTES 1. Section 3.8.1 denotes Book 3, Chapter 8, Section 1. 2. For further discussion of these methods, see Skyrms 2000, Chapter 5 or Ducheyne 2008. For further elaboration including additional variants and hybrids, see Mackie 1967. 3. Whewell has little to say about Mill’s Deductive Method per se, though he does argue that Mill’s Methods play only a secondary role in science (Whewell 1849, 43–54). He also notes other inductive methods aside from Mill’s (Whewell 1858, 202–32). 4. In each case, the negative instances are inferred rather than observed, which means (as Mill suggests) that Newton actually used a generalized form of the Indirect Method of Differences.

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5. As noted by Peirce (1998, 56), it is best to regard any scientiﬁc hypothesis as provisionally accepted rather than as true no matter how well supported it might be (in other words, despite the strongest modes of evidentiary support that might be brought to bear in support of its truth), since it is always possible that an alternative hypothesis will be developed at some later time that will supersede the ﬁrst. 6. That is, the predictions need not be future events, rather they need only to be derived antecedently to the investigator’s knowledge of their truth. 7. This criterion is suggested by Dewey (1991, 60). 8. Other criteria might include the ﬁve mentioned by Kuhn (1977) in connection with competing hypotheses; they are discussed brieﬂy below. 9. A good starting place for developing criteria along these lines is Lakatos’s (1970) elaboration of Popper’s views on falsiﬁcation (Popper 1968).

9 Waves, Particles, Independent Tests, and the Limits of Inductivism* Larry Laudan

In this paper, I shall be taking exception to a few of the ideas in Particles and Waves by Peter Achinstein (1991). In some of these cases, I think he is ﬂat wrong. But that does not diminish in the least my admiration for his book, which is, in my judgment, the best extended piece of work we have on the epistemological problems posed by nineteenth-century physics.

1. INTRODUCTION Three decades ago, I told a story about the development of nineteenthcentury optics and empiricist epistemology (Laudan 1981). It went roughly as follows: the inductivist epistemology that became popular in the philosophical aftermath of Isaac Newton made it methodologically precarious to postulate theoretical entities, especially if those entities had properties unlike those of observed objects. This, in turn, meant that a variety of theories—including the wave theory of light—were to receive a hostile reception at the hands of many eighteenth-century empiricists and those natural philosophers heavily inﬂuenced by them. After all, theories that postulated the existence of elastic, imperceptible, and imponderable ﬂuids were not the sorts of beliefs that an eighteenth-century empiricist could happily countenance. It was the moral of my story that, before such theories could begin to enjoy a wide acceptance, changes had to occur in prevailing methodological standards. Speciﬁcally, as I put it then, a shift was needed away from a narrow inductivism and toward a recognition of the merits of the method of hypothesis. Such a shift would enable ﬂuid theorists to argue for their theories by pointing to their explanatory and predictive resources, even if the entities they postulated were quite

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beyond the reach of ordinary observation and inductive generalization from the observable. As I showed, this hypothetico-deductive sort of inference (which I will subsequently call H-D), from a conﬁrmation of consequences to the probability of the theory itself, carried no weight among traditional empiricists such as Bacon, Newton, Hume, or Reid. When Newton said “hypotheses non ﬁngo,” it was this sort of inference he was repudiating. I suggested that it was thus no accident that the reviviﬁed wave theory of light and the method of hypothetico-deduction gained ascendancy at about the same point in the nineteenth century. The wave theorists needed the method of hypothesis to justify their approach, and the successes of the wave theory managed, in turn, to constitute vivid examples of the scientiﬁc fruits of hypothetico-deduction. I claimed that this linkage between the advocacy of ethereal ﬂuids and anti-inductivism explains how, for instance, that principal advocate of the method of hypothesis in the ﬁrst half of the nineteenth century, William Whewell, became one of the leading spokesmen for the wave theory. At about the same time that I was doing this research, a British historian of physics—Geoffrey Cantor—was coming to a complementary conclusion from a different direction (Cantor 1983). He had been studying the writings of such corpuscularians as Brougham and was struck by how heavily their criticism of the wave theory was imbued with inductivist language. Like me, he came to the conclusion that there was a close connection in the Enlightenment and early nineteenth-century science between where one stood on the wave/particle question and what theory of scientiﬁc method one espoused. Such a happy consilience of perspectives convinced Cantor and me that we were right, of course, especially as there were few demurrals to be heard from other scholars for more than a decade. Or that was this case until Peter Achinstein published his extremely interesting book, Particles and Waves.1 In that book, he has a different story to tell about this episode. According to Achinstein, there was no major methodological divide separating the corpuscularians from the undulationists. Methodological consensus happily prevailed among the physical scientists of the period. Still worse, at least as far as Cantor and I were concerned, the consensus that Achinstein detects was an agreement that induction, not the method of hypothesis, is the appropriate epistemology for science. Achinstein devotes two lengthy chapters of his important book to developing a probabilistic, quasi-Bayesian analysis of the episode, purporting to show that optical theorists in the early nineteenth century were all, at least implicitly, Bayesian conditionalizers. Now, I cannot speak for Cantor, but I want to say for my part that I think that Achinstein’s analysis has—on this particular point—got both the philosophy and the history wrong. It will be the purpose of my remarks today to

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motivate that reaction. For those of you who are saying to yourselves, “Who cares how the nineteenth-century light debates went?” I will try in passing, although this obviously cannot be my main concern today, to draw out some lessons from this episode for debates in contemporary philosophy of science. Several points about the historical record are uncontested. Let me begin with a summary of those: through much of the eighteenth century, Huygens’ wave theory of light was eclipsed by Newton’s corpuscular theory, not least because it seemed that Huygens could not explain the rectilinear propagation of light. At the turn of the nineteenth century, Thomas Young attempted to revive the wave theory using it to explain phenomena of diffraction and optical interference such as the colors of thin ﬁlms and diffraction. Young’s theory in turn failed to be able to account for polarization. Then Fresnel came up with a kinematic model that conceived light as a transverse vibration transmitted in an elastic ethereal ﬂuid. This enabled him to explain polarization and double refraction and to predict a number of surprising phenomena, including the famous bright spot at the center of a shadow cast by a disk. During the early 1830s, Cauchy developed a dynamical wave theoretic model that explained dispersion as well. After intense debate among physicists in the 1820s and early 1830s, most scientists had come to accept the superiority of the wave theory by the late 1830s, although a few hold-outs persisted for another generation. So much for the common ground. What is in dispute here, to put it in its most general terms, is this: what sorts of epistemic virtues led to the triumph of the wave theory? In very brief compass, the Laudan reply was this: the wave theory made a series of surprising predictions that turned out to be right and for which there were no counterparts in the corpuscular theory. It also explained a broader range of phenomena of diverse types without resorting to ad hoc adaptations.2 In sum, it solved more empirical problems than its corpuscularian rival and did so with less ad hocery. These, however, are virtues from an H-D perspective, not from an inductivist one. Achinstein’s answer—to which I shall turn in a moment—is, in brief: the wave theorists managed to show that the corpuscular theory had a vanishingly small probability and this created, by a kind of method of exclusion, a presumption that the probability of the wave theory was close to 1. Such positive conﬁrmations and surprising successful predictions as the wave theory enjoyed merely reinforced this conclusion; they were, Achinstein insists, insufﬁcient to motivate it. In other words, Achinstein denies that the ability of the wave theory to explain and predict a broad range of empirical phenomena, many of them surprising, did, or even in principle could have done, much to enhance its credibility. In what follows, I shall sketch out the two stories in more detail and indicate why I remain skeptical about Achinstein’s version.

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2. THE ACHINSTEIN ACCOUNT It is important to note at the outset that Achinstein’s analysis is simultaneously working at two levels, the normative and the descriptive. What drives his normative analysis is a conviction that a Bayesian theory of evidence and testing is the only sound one. Descriptively, Achinstein is concerned to show that the participants in the light debates of the early nineteenth century were in fact making appraisals in accordance with Bayesian recipes. My principal concern here will be with the descriptive adequacy of Achinstein’s rational reconstruction rather than with its normative underpinnings. But if, as I expect to show, the Bayesian story falls short of being able to capture the reasoning of the agents involved, then it will be appropriate to ask, time allowing toward the end of my comments (or perhaps in the discussion to follow), whether Bayesianism could possibly capture the character of the scientiﬁc use of evidence in cases like this one. Achinstein’s rational reconstruction of the episode goes as follows. The wave theorists, he says, adopted a four-step strategy: 1. Start with the assumption that light is either a wave phenomenon or a stream of particles. 2. Show how each theory explains various optical phenomena. 3. Show that the particle theory, in explaining one or more of the observed phenomena, introduces improbable hypotheses while the wave theory does not. 4. Conclude that the wave theory is (very probably) true, because the particle theory is (very probably) false. Achinstein then proceeds to offer slightly more formal characterizations of these four steps. Step 1, he says, is tantamount to asserting that, relative to certain observations O and background knowledge b, (1) p(T1 or T2 / O & b) ~ 1(~ means ²is close to²)

where T1 is the wave theory and T2 is the particle theory. Step 3 above amounts to the claim that the particle theorists had recourse to certain auxiliary assumptions, h, such that although the auxiliaries are very plausible given the corpuscular theory, namely, although (3a) p(h /T2 & O & b) = 1,

the fact is that there is strong evidence against the truth of those auxiliaries, namely,

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(3b) p(h / O & b) = 0.

A quick application of Bayes’s theorem to (3a) and (3b) yields the result that (3c) p(T2 / O & b) = 0.

Combining (3c) with (1), Achinstein infers that the wave theory is very probably true, namely, (4) p(T1 / O & b) = 0.

Such then, in schematic form, is Achinstein’s proposed reconstruction of the arguments of the wave theorists. But what about step 2 and the comparison of the wave theory with optical phenomena? One might have thought that the single most important bit of evidence in appraising the wave theory was an examination of how it fared against the phenomena. But this process of checking the empirical consequences of the wave theory, according to Achinstein, can—even if the hypothesis stands up successfully to these tests—do little to enhance the probability of the wave theory. As he sees it, Bayesian inference insists that predictions and “explanations (no matter how numerous or varied) do not sufﬁce to give an hypothesis high probability” (Achinstein 1991, 135). All such successes can do is to “ensure that the hypothesis retains whatever probability it has on other data” (135). This is quite a remarkable claim. It would certainly have come as a shock to many of the wave theorists who were impressed by the ability of the wave theory to make surprising predictions successfully and to explain many puzzling features of light. To someone like Whewell, who made a point of underscoring such successes of the wave theory, Achinstein’s rebuff is quick. An explanatory strategy of the sort advocated by Whewell and other supporters of the method of hypothesis will not be enough to guarantee high probability for h, no matter how many phenomena h explains, even if consilience and coherence . . . are satisﬁed. (137)

On Achinstein’s view, the only thing that can give the wave theory, or any other theory, a high probability is the demonstration that the probability of the disjunction of all its rivals is vanishingly small. Discrediting rivals is the only signiﬁcant way of enhancing the probability of one’s pet hypothesis. A good offense it seems is not only the best defense; it is the only defense. The eliminative refutation of rivals is, for Achinstein, the only signiﬁcant way of enhancing the credibility of a theory.

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I think that his analysis is ﬂawed both conceptually and contextually. I will now try to show why. First, and more brieﬂy, philosophically:

(1) The conceptual problem There is a crucial equivocation at the beginning of Achinstein’s characterization of the problem facing theorists of light in the early nineteenth century. The wave theorists, on his reconstruction, began with the assumption that light is either a wave or a particle. That was itself fairly controversial since, even if we ignore possible theories and limit ourselves to then extant theories, there were theories that saw light as a ﬂuid—very like heat was conceived in the 1820s—a hydrodynamic conception that is, strictly speaking, neither particulate nor undular. But leave that reservation to one side. Let us suppose that they and Achinstein were right in thinking that light almost certainly was either a wave or a particle. The equivocation I have in mind comes in the move from the claim that (0) p(light is a wave or light is a particle) = 1

to the claim that Achinstein needs for his reconstruction, namely, that the probability of a speciﬁc theory of light is close to 1 (viz., thesis [4]). The fact is that, even if it could be settled with certainty that light is not a corpuscle, and even if it could be inferred therefrom that light is almost certainly a wave-like phenomenon, it manifestly would not follow that we could thereby assign any particular probability—let alone a probability close to 1—to any speciﬁc wave theory of light. To establish by disjunctive elimination the high probability of a particular theory of light, one must not only discredit corpuscular approaches but, equally and obviously, one must show that rival wave conceptions to the one in question have a vanishingly small aggregated probability. For that reason, even if it is virtually certain that light is a wave, it does not follow without further ado that any particular theory of light is highly probable. This is more than a quibble since there were several different versions of wave theory on offer in the ﬁrst half of the nineteenth century.3 To remind you of but two of them, recall that Young’s wave theory of light did not involve transverse vibrations, while Fresnel’s theory did. Other alternatives involved translational motion of the ether while some supposed only vibratory motion. For which of these many alternative wave theories is Achinstein claiming a probability close to 1? And how can he possibly get that claim from the refutation of a particular version of the

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particle theory, or even from the refutation of every known version of the corpuscular theory? Insofar as the undulationists were generally arguing for one speciﬁc version or other of the wave theory, Achinstein’s machinery is of no avail. Take the case of Fresnel during the 1820s. He did not see himself as addressing the ontological question “Is light a wave?” so much as he was attempting to ascertain the credibility of speciﬁc wave models or theories of light. Refutations of the corpuscularian hypothesis were powerless to guide him with respect to choices among rival wave conceptions. But perhaps, when Achinstein tells us that the probability of the wave theory is close to 1, he has in mind no particular, full-blown version of the wave theory but rather some generic Ur-wave theory that contains only those assumptions held in common between the various wave theories. Let us give him the beneﬁt of the doubt here and suppose that it is that body of assumptions that he means by the term “wave theory.” What would such a theory look like? Absolutely essential to any attempt to characterize the common or generic elements of early nineteenth-century wave theories is the idea of a luminiferous ether. Although the student of twentieth-century physics, in contemplating a wave theory of light, has been trained to resist asking the question, “In what medium are the waves propagated?” no early nineteenth-century physicist could be so ontologically blasé. According to both its opponents and its detractors, the wave theory—in all its known versions—was committed to the existence of an all pervading, highly elastic, uniformly dense ether whose constituent parts were imponderable, that is, without weight. To accept the wave theory (in any sense stronger than as a useful predictive instrument) was, in this epoch, to claim to have a warrant for postulating such a medium. Much of the debate between the wave theory and its critics—a side of the debate that Achinstein largely ignores—is about the appropriateness of this commitment to a highly theoretical entity. Indeed, once one realizes that c is committed to this principle, we can recast Achinstein’s earlier prima facie eliminative disjunction into this form: (1¢) p(light is a particle or light is propagated through an elastic, homogeneous, imponderable ﬂuid/ O & b) = 1

When thus recast, the core premise of the Achinstein reconstruction suddenly becomes, I submit, a great deal less plausible. What might have looked initially as a virtually exhaustive disjunction now comes to seem much less so. We can readily imagine that both disjuncts may be false and therefore that the initial assignment of a probability close to 1 to their disjunction is no longer compelling. And in that case, wave theorists are going to have to do a great deal more than argue negatively for a low probability that light is

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a corpuscle. Of course, Achinstein is right that the wave theorists tried to show that light is not corpuscular, but if that was all that they had done, or the principal thing they had done, then they would have had no license whatever for supposing themselves to have provided a warrant for accepting the wave theory, not even in its generic version, given the implausibility of (1¢). And argue they did. Over and again, the wave theorists claimed that the strongest bit of their case rested on the ability of wave theories to solve a large range of empirical problems, including many that had been anomalous both for corpuscularian and for earlier undular theories.4 The philosophical point here about the precariousness of eliminative induction is a familiar one but it continues to be often ignored by Bayesians in our time, as it was ignored by Mill and his followers in the nineteenth century. Any account of evidence and theory evaluation that requires the enumeration of all the possible hypotheses for explaining some phenomenon, or in more modem probabilistic parlance, any approach that requires the enunciation of a set of hypotheses that are mutually exhaustive and pairwise exclusive, is, when applied to real scientiﬁc choices, almost guaranteed to fail. Scientists are rarely in a position to assert that they have canvassed all the relevant possibilities for explaining any body of phenomena. Indeed, properly viewed, the history of science is a record of refutations of such claims, whenever scientists have been so cheeky as to imagine that their extant theoretical options exhaust the available conceptual space. If Achinstein is right in claiming that hypotheses can acquire high credibility only by the exhaustive elimination of rivals, then we have to conclude that few if any scientiﬁc theories ever become credible. The alternative, of course, is to suggest that it is a reduction of the Bayesian position if it insists that credibility can be achieved by a theory only when all possible rivals to that theory have been both enumerated and vanquished. Before I move on to discuss what I earlier called the contextual problem, there is another conceptual problem that I want to mention. Full treatment of it would require another essay, but I can brieﬂy summarize my worries in this fashion: as should already be clear, Achinstein believes that the accumulation of positive instances of a theory or hypothesis, however numerous, makes, at best, only a marginal difference to its probability. With that in mind, let us review Achinstein’s reconstruction of the wave theorists’ argument. Recall that the crucial step 3 in Achinstein’s reconstruction of the wave theorists’ argument involves their showing that auxiliaries introduced by the corpuscularians are highly improbable. In particular, their argument goes as follows: the corpuscular theory requires that the deﬂecting force is independent of the mass and shape of the deﬂecting aperture. This, say the wave theorists, is very unlikely, given that in the other cases of forces acting at a distance of which we are aware, the force in question is related to both the

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mass and the shape of the acting body. Now, how do the wave theorists know this? Well, one has to suppose they know it by virtue of an enumeration of known cases of bodies acting at a distance, combined with the knowledge that the force in question has thus far always depended on the mass and shape of the body exerting the force.5 In sum, the wave theorists are supposing that we have lots of instances of the hypothesis that forces exerted are dependent on mass and shape. It is that generalization that makes the corpuscularian hypothesis unacceptable. But, by Achinstein’s lights, such information can do nothing whatever to make probable the hypothesis that force depends on mass and shape. Instances of a generalization cannot—in his view—make that generalization probable. Only an eliminative argument can do that. As Achinstein himself points out, Thomas Young’s argument that the shape of bodies determines the kind of force they exert is based upon the fact that this is what we observe to be the case “with other known forces acting at a distance” (Achinstein 1991, 87). But, as I have said, on Achinstein’s own theory, such observations cannot possibly establish with high probability the claim that “all distance forces are dependent on the shape of the body exerting the force.” Yet that latter hypothesis is precisely the one that, on Achinstein’s reconstruction, the wave theorist needs. A similar argument could be made about the ﬁrst premise of the wave theorists, namely, that all cases of motion involve either the transmission of a particle or of a disturbance in a medium. If you deny to the wave theorist the possibility of making a hypothesis credible by citing positive instances of it, then the wave theorist cannot begin to get (Achinstein’s version of) his argument against the corpuscular theory off the ground.

(2) The contextual problem I want now to turn away from the eliminationist issue in order to focus on what seems to me to be the central issue at stake in the debates between early nineteenth-century corpuscularians and undulationists. But we do not need to move too far aﬁeld, since (1¢) already allows me to direct attention to what I think was the core methodological divide between the wave theorists and the corpuscularians. Ever since Newton, corpuscularians had insisted that any theory about natural phenomena must not only be sufﬁcient to explain the appearances, it must also involve postulating only true causes, or verae causae. This requirement, sometimes called the vera causa rule, is close to the core of late eighteenth-century empiricism; it was generally understood to mean that any entities postulated by theory must be ones to which we have independent access. Independent of what? Independent of the phenomena that the theory would be used to explain.

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Between the time of Newton and Whewell, there was extensive discussion and reﬁnement of this principle. Reid, Stewart, Priestley, Lyell, and Herschel were among its most ardent proponents. By the early nineteenth century, the vera causa demand had generally come to mean that any properties attributed to theoretical entities or processes must be a subset of the properties of observable bodies. The vera causa requirement, in other words, forbade attributing properties to unseen objects that were not exhibited broadly (perhaps universally) by objects accessible to inspection. Such a methodological demand was satisﬁed by the corpuscular theory of light; that indeed was one reason for the popularity of the corpuscular theory in the late eighteenth century. It postulated particles of light that, although obviously too small to be seen, behaved very like macroscopic objects, subject to Newton’s laws and to familiar forces of attraction and repulsion. Within the wave theory, however, the requirement of independent access or vera causa was apparently violated by the luminiferous ether.6 That ether consisted of particles that, being imponderable, had no weight. Corpuscularian critics of the wave theory like Brougham and Brewster claimed that no responsible empiricist had a license for propounding theories that, whatever their predictive or explanatory successes, involved entities whose properties were not drawn from common experience.7 When the corpuscularians demanded that there should be independent warrant for theories, this was what they had in mind.8 This was not a demand in which the wave theorists could acquiesce. A ponderable ether, which might have passed the vera causa test, would not do the jobs they required of their ether. Nor could they point to imponderable bodies in ordinary experience. It is for this reason, in my view, that the wave theorists found the method of hypothesis congenial, for what it offered was a way of freeing oneself from the vera causa requirement. The method of hypothesis allowed that a theory could be made plausible simply by examining its consequences (especially if they were of a broad and surprising character), without imposing any speciﬁc constraints on the sorts of entities postulated by the theories. Reading Whewell on this matter is instructive. A keen advocate of the wave theory, he goes to considerable lengths to castigate Newton and his followers for advocating the vera causa principle. Whewell sees that rule as an impediment to discovery and innovation and a gratuitous demand to make of a theory, especially if its consequential conﬁrmation is impressive. Whewell saw clearly that, so long as the vera causa principle of independent warrant for a theory persisted, the wave theory of light would have tough sledding. Achinstein acknowledges that early nineteenth-century methodological standards required that there be independent support for theoretical

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entities. But, having acknowledged that, he proceeds to construe that requirement, when applied to the wave theory, as being satisﬁable, by evidence that the corpuscular theory is erroneous! It is via that construal that Achinstein is able to act as if methodological consensus prevailed. The corpuscularians and the undulationists, he says, all accepted the principle that there must be independent empirical warrant for theories.9 Indeed, he characterizes the undulationists’ procedures as described in his steps (1) to (3) as a principle of independent warrant. What Achinstein fails to note is that the wave theorists’ form of independent warrant—if that is what it is—is completely unlike the traditional empiricist requirement of independent warrant.10 How the wave theorists established independent warrant, according to Achinstein, was by showing the implausibility of the auxiliaries used by the corpuscularians. But that has nothing whatever to do with satisfying the requirement of independent warrant as inductivists and corpuscularians then understood it. To the eighteenth-century empiricists and their successors in optics like Brougham and Brewster, independent conﬁrmation of a theory T consisted in showing that ordinary bodies exhibited all the properties that T attributes to the entities it postulates. By contrast, Achinstein’s version of the independent support requirement dispenses with any constraint on the sorts of permissible entities. Rather, all it demands is evidence that the rivals to T are false or unsupported. I submit that no eighteenth-century empiricist, no advocate of the vera causa requirement and few if any corpuscularians would have accepted Achinstein’s characterization of the independent warrant requirement as an explication of what they were about. If the wave theorists’ strategy consists of the four steps that Achinstein attributes to them, then it automatically follows that—far from being inductivists in the then accepted sense of that phrase—they were entirely abandoning the inductivists’ project for subjecting theory to the vera causa requirement. Whewell saw clearly that the wave theory could not satisfy the traditional demand for being a vera causa; that is why he argued at length against the legitimacy of that requirement in scientiﬁc methodology. But even if Achinstein has got the corpuscularians wrong, it remains to ask whether his analysis of the case is one that wave theorists would have found congenial or close to the spirit of their project. I have my doubts. For reasons already indicated, the discrediting of known rivals—and that is all Achinstein’s independent conﬁrmation requirement requires—is not sufﬁcient grounds for asserting a theory. The wave theorists understood that and therefore spent much ink arguing that the principal virtue of the wave theory consisted in its ability to predict and explain a large range of phenomena, including many surprising phenomena. Achinstein’s philosophi-

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cally-motivated conviction that this particular virtue cannot confer high probabilities on theories leads him to give less than its due to the prominent role accorded to positive evidence by the wave theorists. Convinced that positive conﬁrmation, of whatever sort, cannot confer high probability on a theory, Achinstein supposes that nineteenth-century wave theorists must have accepted this point and acted accordingly. But I can ﬁnd no evidence whatever, either direct or circumstantial, that they believed that positive conﬁrmation was as impotent as Achinstein thinks it is. Let me put the challenge directly: where is the evidence that the wave theorists believed, as Achinstein does, that conﬁrmation of salient instances cannot confer high credibility?11 Where is the evidence that they regarded the low probability of corpuscular theories as the principal ground of credibility for their own views? And if they did believe that, why were they so concerned with ﬁnding impressive corroborations of the wave theory?12 Indeed, if they really believed—as Achinstein suggests—that the wave theory acquires virtual certainty simply from the discrediting of the corpuscular theory, why give pride of place, in assessments of the wave theory, to its successful positive instances?13 John Stuart Mill, himself no friend of the wave theory, believed that the ability of theories to make surprising predictions successfully was of no epistemic moment. Such phenomena are, he said, designed only to impress “the ignorant vulgar.” I trust that it goes without saying that Achinstein is a Millian on these matters, even if his language is less ﬁgurative than Mill’s. But I see no historical basis for claiming that the wave theorists shared this dismissiveness about positive evidence in general, or about surprising instances in particular. For that reason, I doubt that eliminationism was the dominant methodological strategy of nineteenth-century theorists of light. Had it been so, nineteenth-century optics—both on its theoretical and on its experimental side—would look radically different from the way it actually does. REFERENCES Achinstein, P. 1992. Waves and Scientiﬁc Method. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association Volume Two: Symposia and Invited Papers (1992), pp. 193–204. ——— . 1991. Particles and Waves. Oxford: Oxford University Press. Airy, G. 1831. Mathematical Tracts on the Lunar and Planetary Theories, 2nd edition. Cambridge: Cambridge University Press. Brewster, D. 1838. Review of Comte’s Cours de Philosophie Positive. Edinburgh Review 67: 271–308. Buchwald, J. 1981. The Quantitative Ether in the First Half of the 19th Century. In Conceptions of Ether: Studies in the History of Ether Theories, 1740–1900, ed. G. Cantor and M. Hodge. Cambridge: Cambridge University Press.

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Cantor, G. 1983. Optics after Newton. Manchester, England: University of Manchester Press. Herschel, J. 1830. Preliminary Discourse on the Study of Natural Philosophy. London: Longman. ——— . 1827. Light. In Encyclopaedia Metropolitana vol. 4, ed. P. Barlow. London: Grifﬁn. Laudan, L. 1981. The Medium and Its Message: A Study of Some Philosophical Controversies about Ether. In Conceptions of Ether: Studies in the History of Ether Theories, 1740–1900, ed. G. Cantor and M. Hodge. Cambridge: Cambridge University Press. Powell, B. 1837. Recent Progress of Optical Science. British Annual and Epitome of the Progress of Science 1: 162–210. ——— . 1835. Remarks on the Nature of Evidence in Support of a Theory of Light. Edinburgh New Philosophical Journal 18: 275–85.

NOTES * Reprinted with permission from PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association Volume Two: Symposia and Invited Papers (1992), pp. 212–223. 1. Except where otherwise noted, all references to Achinstein will be to Particles and Waves (Achinstein 1991). 2. I claim no originality here. Whewell (1840) gave exactly the same analysis of the case. 3. To mention only a few: there was Young’s wave theory (without transverse vibrations), Fresnel’s wave theory of 1818, Fresnel’s 1821 ether (consisting of molecules acting at a distance) and Cauchy’s ether of the early 1830s. There were divergences among wave theorists about such matters as: the range of the molecular force associated with a particle of the ether (does it extend only to the next particle or fall off according to a l/r4 law, as Cauchy thought?); and how do ether particles and ordinary matter interact? These were not idle questions, as answers to them determined what sorts of empirical consequences a wave theory of light would have. Buchwald (1981) has convincingly argued that divergences among wave theorists about the nature of matterether interactions were “extremely important” in debates about the wave theory. 4. Thus, Herschel in his important monograph on light (Herschel 1827, 538) claims that “nothing stronger can be said in favour of an hypothesis, than that it enables us to anticipate the results of . . . experiment, and to predict facts opposed to received notions.” He was to make a similar point three years later in his 1830 classic: The surest and best characteristic of a well-founded and extensive induction, however, is when veriﬁcations of it spring up, as it were, spontaneously into notice, from quarters where they might be least expected, or even among instances of the very kind which were at ﬁrst considered hostile to them. Evidence of this kind is irresistible, and compels assent with a weight which scarcely any other possesses (Herschel 1830, 170). These and like sentiments to be found in much of the writings of the wave theorists are scarcely the views of folks who think that the refutation of a rival hypothesis is the primary vehicle for establishing the credibility of a theory.

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5. Achinstein himself describes the reasoning of the wave theorists here as a form of “inductive generalization” (Achinstein 1992). I fail to see how, by his lights, such inductive generalizations are capable of establishing the high probability of the claim that forces depend on masses and shapes. 6. I might ask in passing how, since Achinstein believes that it establishes a low probability for the corpuscular theory because it requires that the diffracting effect of an aperture is independent of its mass and shape, he can ignore the corpuscularians’ argument that the wave theory must have a low probability because of its commitment to imponderable particles of the ether? If light-deﬂecting apertures whose deﬂection depends on neither their shape nor mass is contrary to previous experience, it is surely as contrary to experience to postulate particles that have no weight. Although Achinstein claims that “no auxiliary assumption is introduced [by the wave theorists] whose probability given the theory is very high but whose probability on the phenomena alone is low” (Achinstein 1992), it seems to me beyond dispute that the hypothesis of the existence of an imponderable ether—although very probable given the wave theory—is a hypothesis whose probability “on the phenomena alone is low.” 7. David Brewster inveighed against the luminiferous ether because it was “invisible, intangible, imponderable [and] inseparable from all bodies” (Brewster 1838). On those grounds, he held that it could not be postulated as a legitimate causal agent. 8. The widespread acceptance of the vera causa demand shows up not only in the writings of the corpuscularians. During the 1820s and 1830s, there was a sizable group of optical theorists who, while opportunistic about using the mathematical and analytic tools of the wave theory, balked at the full acceptance of the wave theory because they did not see a warrant for the postulation of the optical ether. George Airy, for instance, claimed that the positive evidence as to the composition of the ether was too incomplete to enable one to judge which of the various ether models was correct (Airy 1831, vi). Baden Powell, happy to use the principle of interference, drew the line at accepting the ether precisely because it was not a vera causa whose existence had been independently established (Powell, 1835; 1837). 9. Three decades ago, I pointed out that the wave theorists’ idea of independent support “ought not be confused with the earlier empiricist requirement that theories must involve verae causae” (Laudan 1981, 175). 10. Achinstein writes that “both methodologies [those of the wave theorists and the particle theorists] stress the need for independent empirical warrant” (Achinstein 1991, 108). That may be so, but the fact remains that the two camps construed the demand for independent warrant in wholly different ways. 11. I am not here asking the normative question of whether they were correct in believing that positive conﬁrmation can confer high probability. It is the descriptive issue that is at stake here. 12. Discussion of the conﬁrmation of surprising predictions made by the wave theory was commonplace in this period. In 1833, for instance, Hamilton used Fresnel’s biaxial wave surface to predict (what was previously unknown) conical refraction. Within a year, Humphrey Lloyd, another partisan of the wave theory, had conﬁrmed this result, triumphantly announcing the conﬁrmation to the

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British Association meeting in 1834. Why, on Achinstein’s account, make such a fuss over results that could at best only marginally increase the credibility of the theory? 13. The only answer that I can ﬁnd Achinstein offering to this question is that “the wave theorist wants to show that his theory is probable not just given some limited selection of optical phenomena but given all known optical phenomena” (Achinstein 1992,). That, I think, is not how the wave theorists express themselves. They are not saying: “Look, see how our theory retains its high probability even when it is extended to new phenomena.” Rather, they are saying: “The ability of the wave theory to be successfully extended to new phenomena vastly enhances its credibility.” Achinstein does not want them saying the latter, since his epistemic apparatus has no resources for making sense of such claims. But I think there can be no doubt that that is what they were claiming, justiﬁably or not.

10 What’s So Great about an Objective Concept of Evidence? Helen Longino

1. INTRODUCTION Peter Achinstein begins The Book of Evidence with an anecdote. At a faculty meeting, a university dean replies to a remark of Achinstein’s with “Peter, you have never made a contribution of interest to scientists” (Achinstein, 2001, 1). Wisely interpreting this rebuke as directed to philosophers of science in general, Achinstein decides to engage in a philosophical project that will be of value to scientists: a philosophical analysis of evidence, that, unlike other philosophical accounts, will address the questions scientists actually have about evidence, and is sensitive to the ways in which the concept of evidence works in actual research contexts. Achinstein’s exposition covers many questions of interest to philosophers, including interpretations of probability and their relevance to the analysis of evidence, the role of explanation in scientiﬁc inference, and holism. Along the way, he deploys many of his hallmark strategies, including the devastating counterexample and the absurd consequence. Most of Achinstein’s scientiﬁc examples are from its history, however, not from its present. I propose to pull out from the book-length treatment the central ideas about evidence that Achinstein develops, as well as some of the philosophical claims he makes on their basis, and put the ideas to work in thinking about issues in a contemporary research context. I will argue (1) that the account does have some utility for scientists, but (2) that it requires supplementation to achieve that utility, and (3) that the philosophical claims (in which I am interested) are not really supported by the analysis.

2. ACHINSTEIN’S CONCEPT(S) The basic idea Achinstein sets out to elaborate is that evidence is that which offers a good reason to believe that something else is true. One

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starting point is that whatever serves as evidence is a fact. The question about this fact is whether it counts as a good reason to believe that something else is true. It doesn’t matter whether anyone actually believes this something else. The question at issue is the relationship between this fact and some further (supposed) fact. The ambition is to provide a robust account of evidence that entitles us to say that the evidence relation is objective, non-trivial, and, ideally, non-contextual or nonrelative. Achinstein ﬁrst distinguishes four concepts of evidence. ES evidence is a fact that counts as evidence for someone in what he calls a speciﬁc epistemic situation. An epistemic situation consists in beliefs or knowledge that certain propositions are true, the epistemic inaccessibility of the truth or falsity of certain other propositions, and knowledge (or the absence of knowledge) of how to reason from the proposition one takes to be true and some hypothesis of interest. In such a case, which characterizes all those cases in the history of science in which we take an individual or community to have had good reason to believe some hypothesis on the basis of the facts they had available to them, although those facts do not constitute good reasons for us, we can say that Sn has evidence e for hypothesis h relative to E-Sn. But what is evidence? Three additional deﬁnitions are provided to answer this question. The most important is that of potential evidence. Potential evidence is, for Achinstein, an objective concept, not relativized to an epistemic situation. e is potential evidence that h if i ii iii iv

p (h/e) > ½ p (there is an explanatory connection between e and h/h & e) > ½1 e is true e does not entail h

Potential evidence statements can be incomplete, in the sense that whether the fact that e does raise the probability of h above the threshold of ½ may depend on other facts about the situation, for example, that the experimental setup that produces the fact e is working as assumed. Potential evidence is distinguished from ES evidence in that the relativization to an epistemic situation is removed, although potential evidence can be subject to some relativizations (either to those just-mentioned assumed facts about a situation or to one of three types of “harmless” relativizations involving temporality, the assumption of non-interference by outside conditions, and the assumption that microconditions that may affect the precise value of measurements can be disregarded). Thus a more correct characterization of potential evidence includes reference to such assumptions: e is potential evidence that h, given b,2 if

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p(h/e & b) > ½ p(there is an explanatory connection between e and h/e & b) > ½ e and b and true e does not entail h

Why is the second condition requiring an explanatory connection required? Why is it not sufﬁcient to require that the probability of some hypothesis, on some fact e and assuming the truth of some set of background beliefs, be greater than the probability of its negation in order that e count as evidence for the hypothesis? Formally speaking, the following is possible. A set of statements can be assembled that satisfy the conditions set out in the deﬁnition of potential evidence, but the evidential work, one might say, is performed by the facts reported in the background assumption b, rather than by e which adds nothing to the probability conferred on h by b. Furthermore, attempts to overcome such a counterexample by requiring a deductive relationship will rule out some important cases in which we want to say that some fact, given background information b, is evidence.3 The concept of explanatory connection is not directional. There can be an explanatory connection if h, if true, would explain e, if e, if true, would explain h, or if there is a common explanation for both h and e. For simplicity’s sake, I will just use the former. Achinstein draws on his prior work on explanation to explicate the kind of relation that is involved. Some p1 explains p2 if p1 is a complete content-giving proposition with respect to a question whose complete presuppositions are given in p2. Such explanations can take the form: “The reason that p2 is that p1.” Suppose our question is, “Why did our colleague C remain in Europe until April 26?” The presuppositions of this question are that C was in Europe and remained in Europe until April 26. The answer to the question of why this was so is that European air trafﬁc was shut down during the passage of a (very large) cloud of volcanic ash. Of course, there is additional information that could be included, but is presupposed: that C intended to return via air, that C was in one of the cities affected by the ash cloud, and so on. So the account of evidence is one according to which some e is evidence for some h if e makes it more reasonable to believe h than to believe not-h, glossed as p(h/e) > ½ or p(h/e & b) > ½,4 and that there is an explanatory connection (understood as just described) between h and e, given h and e has a probability greater than one half. These probabilities are understood as objective probabilities, and the reasonableness of belief is understood as supervenient on physical facts in the world. This is what makes the concept an objective concept: claims of evidential relevance are understood as true in virtue of facts in the world, whether these are causal facts, correlational facts, or other associational facts. The probability statements involved

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in this analysis are, as a consequence, empirical statements. They might be false, and anyone believing them would be wrong in their belief. It is the facts, not what anyone believes about the facts, that make beliefs reasonable. For any h, e pair, there may be an epistemic situation that would make it reasonable for someone in that epistemic situation to believe h given e, but, Achinstein emphasizes, “I am denying that a nonrelativized abstract evidential claim must always be understood as implicitly relativized to some particular epistemic situation” (Achinstein 2001, 97). Achinstein has a great many subtle observations to make about concepts and theories of probability and about alternatives to his exposition of reasonableness of belief in terms of probabilities. Among such alternatives are the Royall “likelihood” analysis and the Mayo error-statistical approach. My own concerns have to do not with these more technical issues, but with, granting the broad outlines of his analysis, understanding the reach of the claim that a nonrelativized evidential need not be understood as implicitly relativized to some particular epistemic situation.

3. EVIDENTIAL HOLISM AND CONTEXTUALISM Achinstein’s chapter called “Old-Age and New-Age Holism” in The Book of Evidence engages most directly with this question. “Old-age” holism is the holism attributed to Duhem and elaborated by Quine. It is expressed as, “Nothing can be evidence for or against an individual, isolated hypothesis, but only for or against some theoretical group of hypotheses” (Achinstein 2001, 231). Because Duhem uses a modus tollens setup in arguing that a piece of data is never evidence against a hypothesis considered in isolation but only against a hypothesis together with a body of theory that establishes the relevance of the datum to the hypothesis. Achinstein reads him as committed to a hypothetico-deductive account of evidence, which he has argued previously provides neither sufﬁcient, nor necessary, conditions for evidence (146–8). But, of course, he realizes that one can express the relevant heart of the holist view without being committed to the hypothetico-deductive account. This is what he calls “new-age” holism, which is also recognizable as contextualism with respect to evidential relations.5 This he expresses as “where h is some isolated hypothesis and e is some isolated fact, it is never true that e is evidence for h [full stop]. Rather e is evidence for h, relative to some set of assumptions b.” Achinstein’s argument against this claim has several stages. First, he notes that one can always take those assumptions b and place them in the statement of e. As an example, consider a lottery. That Sylvia owns 95 tickets is evidence that Sylvia will win the lottery against the background

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assumption/information that there are 100 tickets and the lottery is fair. But one can transform this into an unrelativized statement: that Sylvia owns 95 of 100 tickets in a fair lottery is evidence that Sylvia will win the lottery. But (1) this seems trivial and (2) it turns an empirical evidence statement into an a priori one. Lotteries play a large role in Achinstein’s explications of probability. One might argue that they are a misleading category of example to use for the explication of a probability concept relevant to cases in science, since in a lottery, there is a determinate (and known to someone) number of tickets, which makes probabilities of winning, given various distributions of tickets, quite objective. In this case, it is trivial to transform the relativized empirical statement into an unrelativized one. How might the “new-age” holist, or contextualist, object? One way might be to focus on the statements in b that are absorbed into the evidence statement. Achinstein puts a somewhat different objection into the mouth of the new-ager: that the unrelativized statement becomes a priori. This generates a restatement of the holist position: if an unrelativized evidential claim is empirical, then, on pain of incompleteness and/or lack of perspicuity, it must be understood as relativized to a set of assumptions that are necessary and sufﬁcient for the truth of the claim. Achinstein’s response to this restatement is that if the argument is that the claim is somehow incomplete, the same can be said for any empirical claim. But this is unreasonable. Is the claim that a muon decays to an electron, an electron-antineutrino, and a muon-neutrino incomplete without a statement of the assumptions that are necessary and sufﬁcient for its truth? If we were to demand this, we would not be able to distinguish a claim from what might be offered in its defense, what might be advanced as evidence for the claim. But surely this misrepresents the concern of the (let us now say) evidential contextualist. The contextualist is not motivated by distress over evidence statements interpreted to be a priori, nor is the contextualist saying that only if relativized to a statement of conditions necessary and sufﬁcient for its truth is an evidential claim complete and perspicuous. Nor is the contextualist making a fuss about the “harmless relativizations” Achinstein allows. The contextualist is motivated by arguments about the underdetermination of hypotheses by evidence. The concern is not that evidence is not deductively determinative, but that the relevance of some state of affairs to a hypothesis requires background assumptions. Evidence statements are not categorical statements about the world, but statements about the relevance of facts to statements. Another way to put this is by noting, as Achinstein himself emphasizes, that an evidential claim is an empirical claim. This means that reasons not included in the evidential claim itself are relevant

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to its assessment. Some of these reasons will constitute evidence; others will constitute assumptions about the equipment and conditions of observation and experimentation; others may rule out alternatives; while still further assumptions may be general theoretical frameworks within which facts of certain types are connected with putative facts of other types. The contextualist wants to emphasize not the incompleteness of an evidence claim, but the dependence of its truth on a context of background assumptions that are themselves empirical in nature, not known to be true, and that might be false. These assumptions provide reasons to think not that some categorical assertion, like the one about the products of muon decay, is true, but that some fact is relevant to the truth of a claim about another fact. Where it matters most, the hypothetical facts for which some d is afﬁrmed to be evidence are not directly accessible and we don’t have direct access to the associations between the hypothetical fact and the datum. Some theoretical background assumption(s) (whose truth we presuppose, but are not in a position to know) tell(s) us that there is some connection such that the factivity of one counts as a reason to believe the factivity of the other. The contextualist, then, is denying that unrelativized statements can ever (well, at least in the cases that matter) be independent of an epistemic context. Achinstein might say, of course, that the relevance of fact to hypothesis is established by the explanatory connection clause in the deﬁnition of evidence. Only if we focus on the ﬁrst clause, requiring that the probability of h on e be greater than one half, does the relevance problem arise. Once the second clause is added, that the probability that there is an explanatory connection between h and e, on h and e, then the relevance of e to h is secured. Does this put the contextualist’s worries to rest? Let us look at an example. While this is still a somewhat fabricated example, it is closer to actual scientiﬁc practice than are lotteries. Consider a question about the causes of depression in young men. Suppose we want to consider how much this might be genetically inﬂuenced. One strategy would be to see if there is a higher frequency of a given gene in young men who are depressed than in young men who are not depressed. Following this strategy, we would ﬁrst identify a population of young men who are depressed, probably generating our sample population from young men receiving treatment for depression, but then administering some standard test for depression. Then we would create a control sample, matched with our original population on a speciﬁed set of traits, but not depressed (using the same test as used on our ﬁrst sample). We take blood samples from all our subjects, subject the samples to molecular analysis, and ﬁnd that a higher percentage (imagine 20%) of those in the ﬁrst group have one or

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two short alleles of the serotonin transporter gene (5-HTTLPR) than do those in the second group (say 3%). For what and under what circumstances could this result (let’s call it d) be evidence for a hypothesis? There are several hypotheses for which the result could be evidence, and accordingly several claims in which d could ﬁgure. 1. d is evidence that one or two short alleles at 5-HTTLPR causes depression. (H1c) 2. d is evidence that one or two short alleles at 5-HTTLPR inﬂuences depression. (H1i) 3. d is evidence that one or two short alleles at 5-HTTLPR increases the likelihood of depression. (H1l) Remembering the analysis of evidence claims, these are restateable as 1. i. p(H1c (5-HTTLPR causes depression)/d) > ½ ii. p(that there is an explanatory connection between H1c (5-HTTLPR causes depression) and d/d) > ½ 2. i. p(H1i (5-HTTLPR causes depression)/d) > ½ ii. p (that there is an explanatory connection between H1i (5-HTTLPR inﬂuences depression) and d/d) > ½ 3. i. p(H1l (5-HTTLPR causes depression)/d) > ½ ii. p(that there is an explanatory connection between H1l (carrying 5-HTTLPR increases the likelihood of depression) and d/d) > ½ If any of these evidence claim pairs is true, this would entitle us to take our result d as evidence for whichever of these claims in which we are interested. The question is: what entitles us to assert any of these probabilities? In the lottery case, we know the total number of tickets and the number held by Sylvia. This makes calculating the probability a relatively simple matter. In the gene–depression case, this is much harder. The ﬁrst two hypotheses afﬁrm a causal relation between a genetic conﬁguration and a phenotypic trait. The explanatory connection between h and d in those cases is based on a connection between the genetic structure and the phenotype. The explanatory connection in the third case could be understood as that of a common cause of the genetic structure and the phenotype, through linkage of the genetic structure with another genetic structure, which has the causal relation to the phenotype. It would enable prediction, but not intervention. Surely knowing that the probability that a hypothesis is true is greater than one half if some experimental result has a certain value is more than half the struggle in the process of inquiry. One can say the same for knowing that the probability that there is an explanatory connection between the hypothesis and the data is greater than one half. Carrying

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out the study is relatively simple compared to ascertaining its evidential import. We need to know the base rates both of the three types of allelic pairing and of the base rate of depression in the population in order that the associations in the study be taken to indicate anything about a potential explanatory connection. Moreover, we must be able to rule out that there are other genes that might be more highly represented in the sample population and are the genes inﬂuencing the phenotypic phenomenon. We must also be assuming that there is a causal chain from genetic structures through anatomy and physiology to temperamental phenotypes, that depression constitutes an identiﬁable phenotype related to endophenotypic (e.g., neurophysiological) structures and processes, and that the incidence of short alleles in the non-depressed control population can be accounted for. These kinds of assumptions are what concern the “new-age relativized holist,” who is not a holist but a contextualist. It’s not the entire theory that’s implicated, but a set of quite speciﬁc assumptions. To point out the web of assumptions against the background of which a datum will count as evidence is not to dismiss the analysis or the objectivity of the concept. One might say that the value of Achinstein’s analysis of evidence is that it forces one (the researcher, the community of scientists who assess the researcher, the lay public who wish to know whether to act on the basis of some hypothesis) who is in the position of having to evaluate the evidential support for some hypothesis to consider whether the datum confers the requisite probabilities on the hypothesis. And this consideration requires knowing what additional information to include in order to raise the probability to something greater than one half. In some cases, this will be empirical information, like information about base rates that can be obtained relatively readily. In other cases, what is missing will not be empirical information that helps to complete the evidence statement, but assurance of the truth of some fundamental framing assumptions, like assumptions that there is a causal pathway from the genetic structures in question to high-level behavioral and/or temperamental phenotypes or to the endophenotypes that underlie them. From the contextualist’s point of view, these assumptions are part of the Epistemic Situation of contemporary geneticists. They proceed on the assumption that there exist such causal pathways, and see it as their task to identify endpoints of a complex process: genetic structure and phenotype. The assumption that there is a causal pathway between the end points is not part of the evidence (how could it be when we do not know whether it is true?), but the background against which it makes sense to pursue genetic investigation at all. Achinstein’s positive relevance account shows that it is necessary to spell out both the additional empirical information

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and the background assumptions. To that extent it is of potential value to scientists. But it does not give us or them a principled way to determine what should go into the evidence statement and what should remain among the assumptions in light of which the results in question would count as evidence at all. To that extent, the account is incomplete. For an additional example, consider the case to which Achinstein devotes an entire chapter, Perrin’s experiments with Brownian motion that were rewarded by a Nobel prize. There can be some disagreement as what precisely these experiments were relevant to: the reality of molecules or that the structure of matter is particulate rather than continuous. The former interpretation is stressed by philosophers using this example as part of an argument for realism. The latter arguably makes more sense of the historical situation and Perrin’s own statements about his accomplishments. The point, however, is that the observed behavior of resin droplets (painstakingly produced as analogs to unobservable molecules just over the threshold of visibility) in different gases (that could slow their motion sufﬁciently that it could be measured) and the comparisons of measurements of droplets in different gases yields, with a lot of additional assumptions, a value for the number of molecules in a gram weight of the gas close enough to Avogadro’s number to be thought to coincide with it. Those assumptions, hard won during the physics of the nineteenth century, were necessary in order that Perrin even conceive his experiments. Once he was able to generate an empirical measurement that yielded Avogadro’s number, many other parametric measurements fell into place, entitling physicists and philosophers to consider the kinetic theory of gases as empirically grounded. It’s quite possible to reconstruct Perrin’s reasoning to see how he took the behavior of his analogs as evidence (of a kind that satisﬁes Achinstein’s criteria), but he was in a particular epistemic situation, one in which we remain.6

4. CONCLUSION So, how is the positive relevance account of evidence of use to scientists? What good is an objective account of evidence? To say that it is objective is to say that the connection afﬁrmed by the attribution to some data of evidential relevance to a hypothesis is a real connection. Thus, it is, in an ontological sense, independent of what any individual may believe about it. As a criterion of evidential status, the positive relevance account offers a standard of reference by which to evaluate any claim of the evidential relevance of a datum, or set of data, to a hypothesis. But ontological objectivity does not entail epistemological a-contextualism. Applying

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the standard in any case more interesting and complicated than closed lottery situations is likely to reveal the need for additional information. Depending on how widely shared assumptions are in a given scientiﬁc community, application will also reveal the dependence of evidential status on assumptions framing the general research approach within which the datum has or data have been generated. If fully shared, the dependence is likely to remain unnoticed. But unnoticed does not equal nonexistent. In any case, adoption of such a standard is useful in guiding scientists to further research, research that might lead to discharging some of the assumptions. Certainly, if there were a principled way to determine which assumptions could or should be discharged and which should remain as assumptions, the account would be more useful, but that fact does not diminish the utility I have identiﬁed. Of course, the scientiﬁc community has to agree that this is the standard to which they wish to hold themselves. Does this account lay holism, or contextualism, to rest? I don’t see that Achinstein has offered a satisfactory argument against the contextualists’ claim. The contextualists are not claiming that whether some fact has evidential relevance is relative to individuals’ beliefs nor are they claiming that any empirical claim must include its grounds in order to be perspicuous or meaningful. The contextualists are claiming that empirical claims about evidential import (generally, and in the kinds of cases scientists are interested in) presuppose the truth of assumptions we are generally not in a position to ascertain. This assertion is supported by analyzing cases that are now or have in the past been of interest. The contextualists claim that we are always in an epistemic situation, and that, in the cases worth worrying about, we always have, at best, ES evidence. Since we don’t know what we don’t know, the trick lies in identifying just what our epistemic situation is. REFERENCES Achinstein, P. 2001. The Book of Evidence. New York: Oxford University Press. Longino, H. 2009. Perilous Thoughts: Comment on van Fraassen. Philosophical Studies 143 (1): 25–32. ——— . 1990. Science as Social Knowledge. Princeton: Princeton University Press. Van Fraassen, B. 2009. Perils of Perrin. Philosophical Studies 143 (1): 1–24.

NOTES 1. Provision i is absorbable into ii, as the truth of ii requires the truth of i. But, although the shorter deﬁnition is more elegant, it is more perspicuous for my purposes to articulate both probability provisions.

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2. There are alternative ways of expressing this relation that can transform i into an a priori statement, but these can be disregarded. 3. Achinstein’s example concerns taking frequencies in a sample of a population as evidence of frequency in the general population. 4. Achinstein does not consider cases where there might be, instead of two hypotheses, h and not-h, three or four, say, hi, hii,, and hiii. Presumably such cases can be addressed by altering the probability threshold. 5. Thus bearing at least a family resemblance to the contextual empiricism I have elsewhere defended (Longino 1990). 6. See van Fraassen 2009, and my comment (Longino 2009) for an elaboration.

11 The Objective Epistemic Probabilist and the Severe Tester Deborah G. Mayo

1. INTRODUCTION In 1998, Peter Achinstein participated in a PSA Symposium I organized, the goal of which was to promote philosophical accounts of evidence as relevant to scientiﬁc practice.1 I was therefore somewhat jarred that Achinstein titled his presentation “Why Philosophical Theories of Evidence Are (and Ought To Be) Ignored by Scientists” (Achinstein 2000). But it turns out we were entirely in sync as regards the reasons for his lament: the problem with philosophical accounts is (1) they are far too weak to give scientists what they want from evidence, and (2) they make the evidential relationship a priori whereas establishing claims of evidence requires empirical investigation. From this agreement it became clear that we share fundamental theses about evidence. As Achinstein has recently noted, we concur “that whether e, if true, is evidence that h, in the most important sense of ‘evidence,’ is an objective fact, not a subjective one of the sort many Bayesians have in mind. We agree further that it is an empirical fact, not an a priori one of the sort Carnap has in mind” (Achinstein 2010, 170). In fact, Achinstein is to be credited as being one of the only philosophers of science to explicitly incorporate the need for empirical checks of evidence in his account. In addition, we are of like mind in insisting on a “threshold” concept for warranted evidence—if data x do little to warrant H, then to infer H is unwarranted, by dint of x. (Although he would put this in terms of beliefs, the idea is the same.) Nevertheless, Achinstein alleges that he and I disagree on the fundamental role of probability in an adequate account of evidence. Achinstein’s (objective) epistemic probabilist holds a variation on the view that probability enters to quantify how reasonable it is to believe in H, given data x; in the view I advance, probability arises to quantify how well, or how severely, H

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is tested by means of x. Where Achinstein’s threshold for evidence for H requires the posterior (objective epistemic) probability for H to be sufﬁciently high (at least greater than 0.5), mine requires H to have passed a test that is sufﬁciently probative or severe. Not only is severity not based on a Bayesian calculation of posterior probabilities in hypotheses, it can even happen, Achinstein argues, that H passes with high severity while the posterior probability of H is low. If, as Achinstein holds, high posterior probability is necessary (though not sufﬁcient) for warranted belief, then it appears the severe tester would countenance warranting H in cases where Achinstein advises withholding warranted belief. Conversely, it can happen that Achinstein’s epistemic probabilist assigns a high degree of reasonableness to belief in H when the severe tester withholds inferring H. This “Achinstein–Mayo conﬂict” may be dubbed the “highly probable vs. highly probed” conﬂict (Mayo 2005), and it is the focus of this paper. Whether the conﬂict constitutes a problem for the severe tester or for the epistemic probabilist turns on which measure more adequately captures the evidential warrant for the hypotheses in the “counterexamples” raised. Achinstein and I have had several exchanges over the years revolving around this conﬂict (Achinstein 2000, 2005, 2010, and Mayo 2000, 2005, 2010), and I am grateful to have the opportunity to revisit the issue once more. For I am increasingly convinced, especially given our most recent (2010) exchange, that the severity account is actually in sync with the goals and special features of Achinstein’s objective epistemic probabilist (although I will only be able to discuss some of the reasons for this here). When it comes to objective evidence—the only account I will be considering—Achinstein breaks ranks with the typical Bayesian account of conﬁrmation in several respects: ﬁrst, the prior probabilities (in an exhaustive set of hypotheses) are to be neither measures of subjective degree of belief nor a priori logical measures (either of the Carnapian or more modern “reference” or information-theoretic Bayesian varieties); second, he denies that it is necessary or sufﬁcient for conﬁrmation that x increase the probability of H, although the posterior probability of H must reach a threshold for reasonable belief (at least 0.5); and third, it is required that there be some kind of (“non-Bayesian”?) explanatory connection between x and H (either x explains H, H explains x, or there is a third factor explanatorily connected to both). According to Achinstein, objective epistemic probabilists “are committed to saying the inference is justiﬁed only if the objective epistemic probability (the posterior probability) of the inductive conclusion” is sufﬁciently high (Achinstein 2010, 179). This assertion is uncontroversial if he is merely playing on the fact that, in ordinary English, we may use “H is probably true” to express that there is good evidence for claim H. Indeed I had

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earlier assumed that Achinstein intended “high epistemic probability” as a formal way to abbreviate something like “high inductive evidential warrant.” Consider, too, Achinstein’s additional requirement that: P(there is an explanatory connection between H and e|e) > 0.5.

Is this just an abbreviation for something like: “there is good evidence for an explanatory connection between H and e”? If it is left as a qualitative sum-up of empirical background information, then it would seem we already must be in possession of some non-Bayesian way to appraise evidence for such explanatory claims. And if “probability” can live here merely as an abbreviation for how good the evidence is for an explanatory connection, then why not also in the after-data sum-up of the warrant for H? Achinstein (2010) makes it clear that he intends high objective epistemic probability in hypothesis H to be a posterior probability in H, as computed using conditional probability (or Bayes’s theorem). True, this assumption is often regarded (by philosophers at least) as obvious or at least innocuous. I argue that it is neither, even when probability is used merely as a metaconcept for philosophical discussion.2 To begin with, there are the obstacles to arriving at the ingredients required for the Bayesian computation along with the challenge to show why the numbers thereby obtained may be interpreted as some kind of objective weight of evidence or belief. Moreover, probability logic seems to inadequately capture the reasoning appropriate to inductive inference in science, or so I argue (Mayo 2010). The examples that arise in illustrating posterior probability-severity conﬂicts involve dichotomous hypotheses that I label as H0 and H1, so I restrict my discussion to these.

2. EVIDENCE AS PASSING A SEVERE TEST Even though I intend to give a very general account of evidence, I use the notion of “testing” to emphasize a kind of standpoint or “burden of proof” that the severe tester demands. Clearly, evidence is not being taken seriously in appraising hypothesis H if it is predetermined that a way would be found to either obtain or interpret data as in agreement with (or as “passing”) hypothesis H, regardless of the evidence. Here is one of many ways to state this: Severity Requirement (weakest): An agreement between data x and H fails to count as evidence for a hypothesis or claim H if the test would (almost certainly) yield so good an agreement even if H is false.

Because such a test procedure had little or no ability to ﬁnd ﬂaws in H, ﬁnding none scarcely counts in H’s favor.

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The weak severity requirement can be substantiated in terms of the goals of learning. To ﬂout it would be tantamount to ignoring evidence and would permit being wrong with maximal probability. The onus is on the person claiming to have evidence for H to show their procedure is not guilty of so egregious a lack of severity. Although one can get considerable mileage even stopping with the weak severity requirement, I am prepared to accept the converse as well: Severity Principle (full): Data x provide a good indication of or evidence for hypothesis H (just) to the extent that test T severely passes H with x.

(1) Examples: blowout preventers and college readiness Example 1: testing the BOP on the Deepwater Horizon rig Although the blowout preventer (BOP) on the Deepwater Horizon drilling rig passed the required government tests, the question arises: did those passing results provide ample evidence that H1: the BOP on the Deepwater Horizon rig would perform adequately (to prevent a blowout in the Macondo well)?

Not if the government tests, conducted approximately every 2 weeks, are performed under conditions that render it easy for H1 to pass, even if H1 is false, that is, even if H0: the BOP would not perform adequately (either the “blind sheer ram” would be unable to cut the actual pipe, and/or it would malfunction in the conditions of extreme pressure and temperature that would be encountered).

Passing the government tests shows H1 “agrees with” data x (H1 might even logically entail passing results x). But if there is only a small probability, say 0.1, that the rig fails the government tests even if H1 is false (H0 is true), then H1 is very poorly corroborated; that is, the severity is ~ 0.1. So the error probability associated with the inference to H1 would be 0.9—clearly high.3 Using this rule would, in the long run, very often erroneously afﬁrm H1—that is one thing entailed by the high error probability. But that is not the reason we deny that x warrants H1. We deny this because of what the data fail to indicate in the case at hand. As with scientiﬁc instruments more generally, the reported error probabilities (when computed correctly) inform us of the general capability of tools (in this case, it is a testing tool). The capability we care about here is the tests’ abilities to alert us to errors in reasoning. For example, hypothesis H1 would more realistically be framed in terms of quantities or parameters: the minimum thickness of

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the pipe the BOP would need to cut, and at what minimal pressure. High error probabilities in the government tests, when well speciﬁed,4 inform us if the simulated conditions are inadequately demanding as regards either requirement needed for H1. Severity assessments may arise from formal statistical models, but in the strongest cases, they are built on entirely informal grounds. The next example speciﬁcally arose in relation to the Achinstein–Mayo conﬂict (Howson 1997a, 1997, Mayo 1997b, 1997c, 2003a, 2005, 2010, 192–5).

Example 2: Isaac and his college readiness A student, Isaac, is given a wide variety of tests designed to check that he has sufﬁcient mastery of high school material in order to be ready for work in a four-year college, that is, to check what is called “college readiness.” We are told that Isaac has scored nearly perfect grades on rigorous standardized tests covering science, history, literature, mathematics, and so on. We are further told that obtaining such high scores would be extremely improbable were Isaac not college ready. (We would prefer to consider degrees of readiness, but the critic’s example requires just the dichotomous hypotheses.) Reasoning that it is practically impossible for a student who lacked readiness to have consistently scored so well on a wide variety of tests—barring cheating—we infer the test results are evidence of his college readiness. I come back to “barring cheating” shortly. I ﬁrst make a few points about severity that emerge from these examples.

(2) Features of severity reasoning For this it helps to have an abbreviation: We can abbreviate “the severity with which test T with outcome x passes hypothesis H1” as SEV(H1, test T, x),

where it should be understood in what follows that the test T would delineate the kind of experiment, the mode of data collection and data model, and the possible outcomes and hypotheses. The “logic” of SEV is not probability logic. In example 1, we had SEV(H1, test T, x) = 0.1

Although the severity for H1 is low, it does not follow that its denial H0 has passed a severe test. In fact, apparently the passing results of the Deepwater Horizon on April 20, 2010, warranted neither H1 nor H0. This is one of the

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reasons that an error probability (associated with a test and an inference) is not well captured by the logic of probability. Neither hypothesis has reached the threshold for evidence. At the same time there is no danger of falling into the situation Achinstein rightly wants to avoid, namely, allowing both a hypothesis and its denial to be warranted by x. That is because if SEV(H, test T, x ) is high, then SEV(~H, test T, x) is low.

However, the converse does not hold: If the SEV(H, test T, x ) is low, the severity for ~H will in some cases be low, in other cases high. Severity is relative to a hypothesis and a set of data. It is crucially important to recognize that a severity assessment is always relative to (i) a hypothesis (or set of hypotheses) being considered for inference, and (ii) a speciﬁc set of data. Since it was so easy to pass H1: BOP erroneously, the passing result x fails to provide good evidence for H1. But suppose instead that a different result occurred, call it y, and that with result y test T passes H0: the BOP is inadequate. The very fact that test T sets such a low bar for the BOP being declared adequate (H1) gives all the more grounds for inferring its inadequacy (H0) when the results are y, that is, SEV(H0, test T, y) = high. So, in this account, it is not possible to assess a test’s severity without specifying the data and the speciﬁc inference being entertained in claiming to have evidence for H. The relativity of severity enables the account to smoothly handle familiar problems. In example 2, for instance, Isaac’s scores pass with severity the hypothesis of college readiness: H1(I) Isaac is college ready,

but they do not severely pass claims about the cause of his readiness (e.g., that Isaac was ﬁrst-born). Nor would his scores severely pass claims resulting from “tacking on” irrelevant conjuncts to hypothesis H1(I) (e.g., the BOP on the Deepwater Horizon is adequate). His college exam results did nothing to probe or rule out errors regarding the cause of his readiness, or the inadequacy of the BOP. Any test rule that would regard Isaac’s test scores as evidence for these other hypotheses would violate the weak severity principle. This is the basis for getting around classic problems with both probabilistic and hypothetico-deductive accounts, discussed elsewhere (Mayo 1996; Mayo and Spanos 2010).

3. WHAT’S IN A TEST? Without restricting the account to formal contexts, statistical tests provide some general elements that help to illuminate the posterior probability-severity conﬂict. In those examples, there are two (exhaustive) hypotheses H0 and H1; so, while over-simple, I stick with such cases.

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(A) Hypotheses: H is typically a claim about some aspect of the process that generated the data, data x0 = (x1, . . . , xn): so the two (exhaustive) hypotheses H0 and H1 make rival claims about the aspect of interest. Probabilities of various outcomes are to be “computed under the supposition that Hi is correct” (about the generating mechanism), and that is the way to read: P(x; Hi).

Note that this is not a conditional probability, since that would assume there is a prior probability for Hi. Since it is less restrictive, we can use this notation and still entertain contexts where a Bayesian calculation is being considered. (B) Distance Function: a function of the data, d(X ), the test statistic, reﬂects how well or poorly the data x0 = (x1, . . . , xn) ﬁt the hypothesis H0—the larger the value of d(x0), the farther the outcome is from what is expected under H0 in the direction of alternative H1, with respect to the particular question being asked. (Note: X is a random variable, and x0 is a ﬁxed value of X; bolding the random variable indicates it is a vector.)

Suppose in our college-ready example, the data d(X ) is the average of 6 different standardized college-readiness tests, each with 800 as its maximum score; and say the test infers evidence of readiness so long as d(X ) is at least 750. (C) Test Rule T: infer that x is evidence that H1(x): x is college ready iff {d(X) > 750}.

This refers to a generic rule. Once x0 is in hand, the rule infers H1(x0). For example, if the student is Isaac, the inference would be H1(I): Isaac is college ready. (D) Error Probability: Applications of an inductive test rule can be “in error” as regards the data generation mechanism, so long as the data are limited. The probability of {d(X ) > 750} under the assumption that H0, is the probability of erroneously inferring a student is college ready. That is, P({d(X ) > d*};H0(x)-not college ready)

is an error probability. It is given by the probability distribution of d(X )—called its sampling distribution (computed under one or another hypothesis). The sampling distribution characterizes the capability of the inferential rule to unearth ﬂaws and distinguish hypotheses. What makes an account “error statistical” is its consideration of these error probabilities. I am belaboring this because the confusion between the distribution of d(X) and the distribution of hypotheses is ubiquitous. Suppose Isaac’s average yields 770, so x agrees with H1 (and disagrees with H0). From the givens of the example, the probability in (D) equals some very low value p.

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Therefore, H1 passes with high severity, 1 – p, and we infer that x is evidence that Isaac is college ready. (E) Empirical Assumptions: Quite a lot of empirical background knowledge goes into implementing these computations. We can place them into two groups of questions:

1 How probative would the test be if its assumptions were approximately satisﬁed? 2 Are its assumptions approximately satisﬁed? Answering question #1 turns on a yes answer to question #2. For instance, in the college-readiness test, the judgment (1) that it is practically impossible for a student to do so well if she were not college ready is based on assuming (2) that the tests are “working” in the case at hand, for example, that the students are not cheating, but achieving their scores as a result of their academic knowledge.5 The task of checking such assumptions calls for its own discussion, which I do not have space to consider here. The main thing to note is that both the severity and the posterior probability calculation require satisfying the assumptions in question #2, and any alleged posterior probability-severity conﬂict must already assume a yes answer to #2.

4. POSTERIOR PROBABILITY-SEVERITY CONFLICTS Note that the test ingredients in Section 3 do not include any assessment of the probabilities of the hypotheses themselves. The severe tester is keen to assess quantitatively “how false” or “how true” hypotheses are, but that is very different from assigning them a probability. The claims Hi(x0) are either correct or incorrect as regards the mechanism generating the data x0, and I take it Achinstein would agree. Insofar as we are interested in using data to make inferences about what generated this data, in this world, and insofar as we are keeping to a frequentist account of probability, Achinstein rightly observes that it would make no sense to speak of the probability of Hi, as if universes were as plenty as blackberries from which we randomly selected this one universe (as Peirce would say).6 By contrast, Achinstein is prepared to obtain his epistemic probabilities by a kind of straight rule: Achinstein’s Straight Rule for Objective Epistemic Probabilities: If xi is randomly selected from a population where p% have property C, then the objective epistemic probability that xi has C equals p.

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(1) Modifications. Before turning to the Bayesian computation, two of the modiﬁcations called for in order to bring the Bayesian calculation into the frequentist error-statistical fold should be noted, to avoid misunderstanding how the conﬂict can even arise. Turning error probabilities into likelihoods There is often confusion about likelihoods, so let me explain by means of a particular case, example 2. A single application of the six exams gives one outcome x0 (where x0 = the observed six scores) leading to one average score d(x0). Suppose Isaac’s average scores are d(x0) = 770. Once x0 is ﬁxed, we can consider the probability of x0 under the various Hi. This is the likelihood of Hi given data x0.7 But the error probability in Section 3(D) is not a likelihood for the experiment being considered. It refers to average test scores other than the particular d(x0) observed, in particular, to all scores as great as or greater than 750. But Bayesians use likelihoods, not error probabilities. To bring the error probability into the Bayesian realm, the critic lumps together outcomes so that there are only two, call them success: s, or failure: ~s. An outcome is called a success (s), in relation to our college readiness example, if the observed scores are at least 750, else it is a failure (~s). By condensing outcomes, the likelihood that enters the Bayesian computation—for example, P(s|Hi)—is the same as the error probability, for example, P(d(X ) > d(x0); Hi). Turning events into hypotheses Second, to make out a posterior probability-severity conﬂict the critic considers “hypotheses” to which a frequentist might seem willing to assign a probability, in other words, the hypotheses are what we would normally consider speciﬁc events: that a sample possesses a characteristic such as “being able to prevent a blowout” or “being college ready.” (Hi(x) is like a one-place predicate, which does not have a truth value until x is replaced by a constant x0.) But we also want hypotheses to assign probabilities to outcomes. So, to help the critic’s example, let us stipulate that, once a particular name, Deepwater Horizon or Isaac, replaces x, the resulting hypotheses assign probabilities to the outcomes s and ~s. But what shall we say about the priors?

(2) Ready or not? The posterior probability-severity conﬂict in the case of poor Isaac goes like this: The severe tester takes the outcome s “success” as evidence of

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Isaac’s readiness H1(I). Certainly she would deny s is evidence of his unreadiness (H0(I) doesn’t even “ﬁt” the very high scores, s). But now imagine, says our critic, that Isaac was randomly selected from a population—call it Fewready Town—where the relative frequency of college-ready students is some very small number, say one out of ten thousand. The critic, applying Achinstein’s straight rule for priors, infers that the prior probability P(H1(I)) is small (e.g., 0.0001). But then, the critic continues, the posterior probability that Isaac is college-ready H1(I), given his high test results, would be very low (though the posterior probability has increased from the prior).8 There are two questions that arise: First, would frequentists accept the straight rule for assigning probabilities to hypotheses? Second, even if a frequentist would regard such a rule as fallacious, does the posterior thereby obtained yield the more intuitively adequate degree of evidential warrant? We say no to both. Fallacy of probabilistic instantiation Although the probability of randomly selecting a particular student from the population of high schoolers from Fewready Town is small, say 0.0001, it does not follow that Isaac, the one we happened to select, has a probability of 0.0001 of being college ready. To suppose it does is to commit what may be called a fallacy of probabilistic instantiation (Mayo 1997a, 1997b, 2003b, 2005, 117). Suppose the experiment is to randomly select a member of Fewready Town. To infer from the premises P(H1(x)) = very low (e.g., 0.0001) and x 0 = I (i.e., Isaac) to the inference:(*) P(H1(I)) = 0.0001.

is a fallacious instantiation that can easily give rise to contradictions. But Achinstein, in his recent update, grants this, so we turn to the second question that might be raised.9 The charge of committing a fallacy of probabilistic instantiation, he now allows, would be true if the probabilities in question were construed as relative frequencies. However, . . . I am concerned with epistemic probability. If all we know is that Isaac was chosen at random from a very disadvantaged population, very few of whose members are college ready . . . then we would be justiﬁed in believing that it is very [improbable] that Isaac is college ready [i.e., p(H1) is very low and hence p(H1/s) is very low; I replace his symbols with mine]. (Achinstein 2010, 187)

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Hence, (*) would give a legitimate objective epistemic prior. But does it yield a relevant degree of warrant for H1? Even confronted with Isaac’s high test scores, s, Achinstein’s probabilist is justiﬁed in denying that the scores are good evidence for H1(I). Rather, they are evidence for believing H0(I)—that Isaac is not college ready. Whether Achinstein merely denies evidence for readiness or also goes on to make the stronger claim, that the high scores s are evidence for H0 non-readiness, there is still the conﬂict he wishes to describe. (In the Stand and Deliver clariﬁcation he seems clearly to be making the stronger claim. See Section 3 of this essay.) But is this a problem for the epistemic probabilist or the severe tester? Severe testers always evaluate an inferential report, regardless of the procedure that generated it, by considering its relevant error probabilities, without which they cannot assess severity. Given a Bayesian report of a high posterior degree of belief, say 0.95, in a hypothesis H1(I), a severe tester asks: how often would such a high assignment occur even if H is false? The example has only two outcomes: success and failure—s or ~s. Clearly getting ~s, the lower average grades, gives even less evidence of readiness; that is, P(H0(I)|~s) > P(H0(I)|s). Therefore, whether Isaac scored as high as s or lower, it appears that Achinstein’s epistemic probabilist denies there is evidence of readiness. The probability of Achinstein ﬁnding evidence of Isaac’s readiness even if in fact he is ready is minimal, if not zero, thereby violating the weak severity requirement! If a procedure would very often instruct us to infer or believe in H, even if H is false, then its inferring H does not seem to provide an objective warrant for the truth of H. To take this example further: Suppose in fact Isaac was selected randomly, not from Fewready Town, but from a population where college readiness is common, Fewdeﬁcient Town. The same average score s now warrants a strong objective epistemic belief in Isaac’s readiness. So students from Fewready High would need to score quite a bit higher on these same tests to have their scores be regarded as evidence for college readiness (than would students selected from Fewdeﬁcient High). The concern here, of course, is not the political implications of such “reverse discrimination” but the way this consequence brings out the shortcomings of using the recommended posterior probability as a measure of what Isaac’s scores tell us about Isaac.

(3) Achinstein and Stand and Deliver Achinstein illuminates his analysis by reminding us of the movie Stand and Deliver where students in a poor area with a lot of student dropouts

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pass the advanced placement tests in math with ﬂying colors, having been drilled by a caring high school math teacher (I never saw the movie). Ofﬁcials from the Educational Testing Service are suspicious, and insist that the students retake the test “under the watchful eyes of their own representatives.” Says Achinstein, [G]iven that all they knew were the test results and the background of the students, were the ofﬁcials from the E.T.S. justiﬁed in believing that, despite the high test results, it is unlikely10 that the students have a good knowledge of basic calculus? I think that this is a reasonable epistemic attitude. They assigned a very low prior epistemic probability to the hypothesis that these students know calculus, and hence a low posterior probability to this hypothesis given the ﬁrst test results. We may suppose that after the results of the second test, conducted under more stringent testing conditions, the posterior probability of the hypothesis was signiﬁcantly high. (Achinstein 2010, 187–8, my emphasis)

There are two key points that Achinstein obviously intends as relevant to his position on our college-readiness exchange, even though here H1 refers to the (math) ability of a group of students. Yet they seem deeply puzzling. First, to raise the possibility of cheating would be to question the assumption on which the posterior probability-severity conﬂict is based. It is given in the college-readiness example that “the test is severe in the sense that passing it is very difﬁcult to do if one is not ready for college” (Achinstein 2010, 186). The example we are supposed to entertain just is the second test (where assumptions hold). Second, to suppose that the results of the second test now yield a high posterior probability to the group’s ability sidesteps the issue at hand. For however small the likelihood for readiness is with the second test’s super high scores, s*, the critic adduces a small enough prior for readiness so as to yield a low posterior. Then, the original question that Achinstein asks the severe tester would be re-asked of him: Are you prepared to take s* as evidence of H1 even though the posterior epistemic probability of H1 (given s*) is low? Is Achinstein now intimating that he is leaning against the low posterior probability to H1(I) given the very high scores s*, even given that Isaac was randomly selected from what we might call Veryfewready Town? Might he even agree, further, that the very high scores s* are evidence for rejecting the prior as a relevant measure of evidence? When we move from hypotheses like “Isaac is college ready” to more realistic generalizations, the problem of obtaining priors by means of something like Achinstein’s straight rule is even more pronounced, but there is no space to describe them here (see Mayo 1997a, 1997b, 2010, 194–99).

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5. MILL AS SEVERE TESTER Perhaps the most interesting feature of Achinstein’s most recent discussion is to be found in his defense of Mill’s account of induction: Although “one of Mill’s deﬁnitions of an inductive inference [is] one in which ‘we conclude that what is true of certain individuals of a class is true of the whole class’ . . . he does not say, and indeed he explicitly denies, that any induction so deﬁned is justiﬁed. . . .” Achinstein (2010, 173). He quotes Mill: When a fact has been observed a certain number of times to be true, and is not in any instance known to be false; if we at once afﬁrm that fact as an universal truth or law of nature, without ever testing it by any of the four methods of induction [Mill’s famous methods for establishing causal laws], or deducing it from other known laws, we shall in general err grossly. (Mill 1888, 373)

To avoid erring grossly, it is necessary to run empirical checks of “different sorts of ‘fallacies’ or mistakes in reasoning, including failure to look for negative instances and making the generalization broader than the evidence allows” (Mill 1888, 373). Whether such ﬂaws and fallacies are avoided “depends on non-formal empirical facts regarding the sample, the sampling, and the properties being generalized. I would take Mill to be espousing at least some version of the idea of ‘severe testing’ ” (Achinstein 2010, 174). So would I. But what about the central point on which Achinstein and I are said to disagree? To my surprise, Achinstein declares, speaking about both Mill and Newton, that Neither in their abstract formulations of inductive generalizations . . . nor in their examples of particular inductions to general conclusions of the form "all A’s are B’s," does the term "probability" occur. Both write that from certain speciﬁc facts we can conclude general ones—not that we can conclude general propositions with probability, or that general propositions have a probability, or that they have a probability conditional on the speciﬁc facts. From the inductive premises we simply conclude that the generalization is true, or . . . "very nearly true," by which [Newton] appears to mean not "probably true," but "approximately true." (Achinstein 2010, 176)

Now I am certainly no Mill scholar, and I am glad Achinstein has set out “to give Mill a better run for his money.”11 Adhering to Achinstein’s description of Mill, there is no inclination to foist a posterior probability on inductive generalization H. Background considerations enter not to assign prior probabilities to an exhaustive list of hypotheses (e.g., about the proportion of A’s that are B’s in a population). Rather, there is an

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appeal to empirical considerations both to avoid as well as to check, a set of classic ﬂaws and foibles that, if committed and not compensated for, would invalidate the inductive move. Far from wishing to justify the familiar inductive “straight rule,” Mill appears to be saying that an induction following this pattern would be warranted just when the test did a good job of ruling out the ways we can “err grossly” in going from the sample correlation to the population. Contemporary experimenters have a more sophisticated set of tools at their disposal, but the overarching reasoning is the same. From Achinstein’s own enlightening depiction, I too “would take Mill to be espousing at least some version of the idea of ‘severe testing.’ ” Having done a plum job giving evidence of this, however, Achinstein promptly discards the evidence, and instead converts Mill into an epistemic probabilist of the Bayesian kind. I will not get into the acrobatics required for Achinstein to convert Mill’s remarks about probabilities of events so that Mill may be seen as assigning probabilities to inductive hypotheses. What reason is there to convert Mill thus, aside from insisting that a way would be found to interpret Mill as ﬁtting a certain Bayesian philosophy (thereby violating the minimal severity principle)?

6. CONCLUDING REMARKS Achinstein is critical of the severity account because it is possible for H to pass severely even though the posterior probability of H might be low. I argue that the priors involved in such “posterior probability-severity” conﬂicts are not kosher for a frequentist. Further, in no case where this conﬂict occurs does the posterior probability seem to get the intuitively correct appraisal of reasonableness to believe. Where severity disagrees with a posterior, it is more reasonable to regard the evidence as grounds to reject the prior probability (or one of the test assumptions). In defending Mill, Achinstein gives further evidence that I am not entirely alone in viewing inductive inference as nonBayesian.

REFERENCES Achinstein, P. 2010. Mill’s Sins or Mayo’s Errors? In Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science, ed. D. Mayo and A. Spanos. Cambridge: Cambridge University Press.

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——— , ed. 2005. Scientiﬁc Evidence: Philosophical Theories and Applications. Baltimore, Md.: Johns Hopkins University Press. ——— . 2000. Why Philosophical Theories of Evidence Are (and Ought To Be) Ignored by Scientists. Philosophy of Science 67 (3): 180–92. Howson, P. 1997a. A Logic of Induction. Philosophy of Science 64 (2): 268–90. ——— . 1997b. Error Probabilities in Error. Philosophy of Science 64 (4): 185–94. Kass, R. and L. Wasserman. 1996. The Selection of Prior Distributions by Formal Rules. Journal of the American Statistical Association 91 (435): 1343–70. Mayo, D. G. 2010. Sins of the Epistemic Probabilist: Exchanges with Peter Achinstein. In Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science, ed. D. Mayo and A. Spanos. Cambridge: Cambridge University Press. ———. 2008. How to Discount Double-Counting when It Counts: Some Clariﬁcations. British Journal for the Philosophy of Science 59 (4): 857–79. ——— . 2005. Evidence as Passing Severe Tests: Highly Probed vs. Highly Proved. In Scientiﬁc Evidence: Philosophical Theories and Applications, ed. P. Achinstein. Baltimore, Md.: Johns Hopkins University Press. ——— . 2003a. Could Fisher, Jeffreys, and Neyman Have Agreed on Testing? Commentary on J. Berger’s Fisher Address. Statistical Science 18 (203): 19–24. ——— . 2003b. Severe Testing as a Guide for Inductive Learning. In Probability Is the Very Guide in Life, ed. H. Kyburg. Chicago: Open Court. ——— . 2000. Experimental Practice and an Error Statistical Account of Evidence. Philosophy of Science 67 (3): 193–207. ——— . 1997a. Duhem’s Problem, The Bayesian Way, and Error Statistics, or “What’s Belief Got To Do with It?” Philosophy of Science 64 (2): 223–44. ——— . 1997b. Error Statistics and Learning from Error: Making a Virtue of Necessity. In Philosophy of Science 64 (PSA Symposia Proceedings), ed. L. Darden. Chicago: University of Chicago Press. ——— . 1997c. Response to Howson and Laudan. Philosophy of Science 64 (2): 323–33. ——— . 1996. Error and the Growth of Experimental Knowledge. Chicago: University of Chicago Press. Mayo, D. G. and D. R. Cox. 2010. Objectivity and Conditionality in Frequentist Inference. In Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science, ed. D. Mayo and A. Spanos. Cambridge: Cambridge University Press. Mayo, D. G. and A. Spanos. 2006. Severe Testing as a Basic Concept in a Neyman– Pearson Philosophy of Induction. British Journal for the Philosophy of Science 57 (2): 323–57. ——— , eds. 2010. Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science. Cambridge: Cambridge University Press. Mill, J. S. 1888. A System of Logic, 8th edition. New York: Harper and Bros. Peirce, C. S. 1931–1935. Collected Papers, ed. C. Hartshorne and P. Weiss. Cambridge, Mass: Harvard University Press. Woodward, J. 2000. Data, Phenomena, and Reliability. Philosophy of Science 67 (3): 163–97.

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NOTES 1. The other participant in this Symposium was Jim Woodward (see Woodward 2000). 2. In the most sophisticated accounts now in use, the prior probability assignments are based on information-theoretical systems, and are speciﬁcally not intended to represent degrees of belief, or even probabilities. See Kass and Wasserman 1996 and Mayo and Cox 2010. 3. It does not matter which we make H0 and which H1 in this account. I choose to make H0 the hypothesis of “inadequacy” or “unreadiness” in both examples 1 and 2, respectively, for ease in reading. They must, of course, be denials of each other. 4. For a discussion of the relevance of error probabilities, see Mayo and Cox 2010 and Mayo 2008. 5. The testers might qualify “college-readiness” to mean simply mastery of high school material, to put to one side any controversy about whether such mastery is a valid indication of “college-readiness.” 6. Except for very special cases. 7. Likelihoods do not obey the probability axioms; for example, the sum of the likelihoods of a hypothesis and its denial is not one. 8. There will not always be such an increase in the examples used in this type of criticism! In classic examples, statistically signiﬁcant results against a null hypothesis H0 are shown to correspond to results accorded a high Bayesian posterior; moreover, the posterior exceeds the prior. 9. To clarify, consider a case where a legitimate frequentist prior might be possible. Conceivably, various genetic factors might allow computing that the (frequentist) probability that Isaac would have brown hair is, say, 0.6. Compare that to an experiment of randomly selecting from a population where 10% have brown hair, and drawing Isaac. The probability is 0.1 of drawing a student with brown hair. But the (frequentist) probability that the student we drew— Isaac—has brown hair is 0.6. 10. The use of “unlikely” here means “improbable.” 11. It would follow that C. S. Peirce was incorrect to accuse Mill of omitting the two key rules of inductive inference: predesignation and random sampling (Peirce 1931–1935, 1.95 N).

12 Achinstein and Whewell on Theoretical Coherence Gregory J. Morgan

1. INTRODUCTION In Particles and Waves, Peter Achinstein gives a precise probabilistic version of theoretical coherence inspired by William Whewell’s somewhat vague notion of coherence (Achinstein 2010). Whewell believed that as theoretical science proceeds, it becomes more coherent and rejects false incoherent theories. Achinstein offers a challenge: try to make Whewell’s idea more precise while maintaining the properties that Whewell claimed coherence to have. I will argue (1) that Achinstein’s probabilistic rendition of coherence fails to capture Whewell’s notion, since the probabilistic rendition of coherence is not an a priori sign of truth, and (2) that Achinstein’s approach is better seen as a critique of Whewell’s central methodological claims than as an interpretation of Whewell’s ideas.

2. WHEWELL ON COHERENT COHERENCE William Whewell, in his classic Philosophy of the Inductive Sciences, analyzes the progress of science: . . . we have to notice a distinction which is found to prevail in the progress of true and false theories. In the former class all the additional suppositions tend to simplicity and harmony; the new suppositions resolve themselves into the old ones, or at least require only some easy modiﬁcation of the hypothesis ﬁrst assumed: the system becomes more coherent as it is further extended. The elements which we require for explaining a new class of facts are already contained in our system. Different members of the theory run together, and we have thus a constant convergence to unity. In false theories, the contrary is the case. (Whewell 1847, 233, my emphasis)

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While Whewell illustrates his claim with numerous episodes in the history of science, he believes that one can know a priori that coherence is a sign of truth. “Truth may give rise to such a coincidence; falsehood cannot” (71). For Whewell, truth is coherent and simple (72). False hypotheses cannot explain all phenomena, whereas true hypotheses can (62). For him, the true philosopher, if successful, “binds together” otherwise incoherent facts like stringing a set of pearls, to use his simile. In a claim that arguably conﬂates psychological inability and logical impossibility, Whewell goes so far as to say that once a system of facts have been bound together, it is often impossible to see the facts as “incoherent and detached” (52). Robert Butts claims that Whewell views facts thus bound together as necessary and known by intuition (Butts 1968, 16). Indeed, consistent with his neo-Kantianism, Whewell sees the connection between coherence and truth as necessary and a knowable a priori. Whewell’s notion of coherence is closely related to his better-known notion of consilience. For Whewell, a consilient theory correctly predicts unobserved phenomena of a kind different than it was designed to explain. In so doing, a consilient theory uniﬁes different classes of phenomena (Whewell 1847, 230). Let us make his idea more precise. Assume there are two classes of observable phenomena, O1, . . . On and On+1, . . . On+m. Imagine scientist S constructs a theory T1 that entails O1, . . . On and On+1, . . . On+m, but does not believe that On+1, . . . On+m are relevant in formulating her theory. In this case, T1 would be a consilient theory. Whewell’s notion of consilience has both an objective dimension and a subjective dimension. If observable phenomena O1, . . . On and On+1, . . . On+m are different kinds of phenomena, then this fact does not depend on whether anyone believes that this is the case. On the other hand, whether S considers or contemplates certain phenomena in formulating her theory depends trivially on the propositional attitudes of S, and thus Whewell incorporates a subjective component into his notion of consilience. A theory is coherent if, as new kinds of phenomena are observed, the theory explains them without having to introduce ad hoc assumptions, that is, if it repetitively uniﬁes new kinds of phenomena with little or no modiﬁcation. Thus coherence, like consilience, depends on the historical development of the theory in question. If a theory has a history of successful consilience, then it is coherent.

3. ACHINSTEIN’S SANITIZED VERSION OF COHERENCE Achinstein (1991), in attempting to make Whewell’s notion more precise, removes the subjective component from coherence giving what I call

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a sanitized version of coherence. First, he stipulates that a theory T consists of a set of hypotheses, h1, h2, . . . , hm. He then deﬁnes what it is for a hypothesis h1 to be coherent with the remaining hypotheses. h1 is coherent with h2, . . . , hm on B, if and only if p(h1/h2, . . . hm & B) > k, and p(h1/h2, . . . , hm & B) > p(h1/B) (Achinstein 1991, 130).

Then he introduces the notion of coherence for the set of hypotheses. A set of hypotheses h1, . . . , hm is coherent, on B, if and only if each hypothesis is coherent with the other members of the set on B (130).

Finally, Achinstein deﬁnes coherence for a theory: theory T is coherent if and only if the set of hypotheses, h1, . . . , hm is coherent. Let us call the person who claims, like Whewell, that coherence is a sign of truth a coherentist. This central question of this chapter is whether one can adopt Achinstein’s sanitized version of coherence and also be a coherentist.

4. TWO CONCEPTIONS OF SIGN OF TRUTH As it is commonly used, the notion “sign of truth” is ambiguous and vague. Restricting our focus to usage in theoretical science, let me distinguish two distinct senses: one usage of the term suggests that possession of a sign of truth at least makes a theory (T) likely and another usage suggests that possession of a sign of truth makes a theory more likely. First there is an absolute notion or threshold sign of truth that I will call a sign1 of truth: If coherence is a sign1 of truth, then, ∀T, p(T/T is coherent) > k, where k ³ 0.5.

The consequent is not a sufﬁcient condition since it could be the case that p(T/~(T is coherent)) = p(T/T is coherent) > k, in which case coherence is irrelevant to the probability of a theory, but T is nonetheless likely. Presumably, adding the condition p(T/~(T is coherent)) £ k to the above necessary condition would generate necessary and sufﬁcient conditions for coherence being a sign1 of truth. One weakness of the necessary condition is that it is undeﬁned when p(T is coherent) = 0. Notice that the existence of refuted coherent theories do not necessarily undermine the coherentist’s claim as in that case one is often considering a different conditional probability, that is, p(T/T is coherent and there is signiﬁcation evidence against T) < k. If coherence were an infallible sign1 of truth, the value of k would be 1. To be charitable, I will consider cases where coherence is not an infallible sign of truth, that is, cases where k<1. Since Achinstein is concerned with

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what one should believe, I will consider this type of sign when k ³ 0.5. If k < 0.5, then it is more reasonable to believe ~T than to believe T. There is also a weaker notion of a sign of truth. While sign1 of truth is absolute, the second notion of sign of truth, which I call a sign2 of truth, is relative: Coherence is a sign2 of truth if and only if, given two theories that are identical in all epistemic properties except that T1 is coherent and T2 is not, then p(T1) > p(T2).

The idea here is that, by possessing coherence, a theory’s probability is increased. There can be relative signs that are not threshold signs. For example, a sign could increase the probability of ﬁnding the truth without reaching the threshold k.

5. FOUR DISTINCT POSITIONS One can use the empirical/ a priori distinction to create four distinct positions that coherentists might occupy. To illustrate these positions, let us consider a sign1 of truth, although similar considerations also apply to a sign2 of truth. The core inference that a coherentist endorses for a particular coherent theory T1 is the following: Premise A: ∀T, If T is coherent, then there is a reason to believe that it is true. Premise B: Theory T1 is coherent. Conclusion: Therefore, there is a reason to believe that T1 is true.

For each of the premises, one may ask the question: is it an empirical or an a priori claim? A given coherentist’s answers to these questions classiﬁes her into one of four positions. Position 1: Both premises A and B can be known a priori. A particular sanitized interpretation of William Whewell puts him in the rationalist coherentist camp. On this view of Whewell, it is an a priori truth that there is a connection between coherence and truth and one can tell a priori whether a given theory is coherent. Position 2: Premise A expresses an a priori truth, but whether a particular theory is coherent or not is an empirical matter. A more orthodox interpretation of William Whewell puts him in this camp. Position 3: Premise A is empirical, but it is an a priori matter whether a particular theory is coherent. As with Position 1, on this view one need not perform any worldly investigation to determine if a given theory is coherent.

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Position 4: Both premises A and B are empirical claims. Those who hold that the general principle is empirical (Positions 3 and 4) often justify their belief inductively. For example, if coherent theories in the past have been likely, then they argue we have some reason to think that current coherent theories are likely.

6. IS COHERENCE A SIGN 1 OF TRUTH? The ardent coherentist claims that coherence is a sign1 of truth, a necessary condition of which is that p(T/T is coherent) > 0.5. If coherence were a sign1 of truth and a theory’s coherence were determinable without empirical inquiry, then it would be possible to justify a belief in a coherent theory without testing it experimentally. This would be a signiﬁcant achievement, but I will argue it is a mirage. Satisfying the necessary condition of a sign1 of truth is a tall order. Consider a competing theory T*, such that ~(T & T*). If T* is also coherent, then it cannot be the case that p(T/T & T* are coherent) > 0.5 and p(T*/T & T* are coherent) > 0.5 since the probability of mutually exclusive theories cannot sum to greater than 1. In some cases, we can construct a competing T* from the components of a coherent T. Assume that T (= {h1, h2. . . . hm}) is coherent. From Achinstein’s deﬁnitions it follows that p(h1/h2, . . . , hm & B) > p(h1/B). Whewell claims that falsity cannot exhibit coherence. However, consider the theory T* that consists of {~h1, ~(h2 &, . . . , hm)}. Given plausible assumptions, T* is also coherent. (See Appendix 1.) At least one of T and T* must be false. In particular, even if T is as coherent as possible, that is, k = 1, then an incompatible competing theory is coherent also. The coherentist might argue that useful judgments of a theory’s probability are not made in a vacuum, but rather are made in the context of additional evidence and consequently one should consider the effect of coherence and the additional evidence. This complaint voices a legitimate point. The goal of using signs of truth is to learn what one should believe; any such judgment would likely be made on the basis of more evidence than merely the coherence of T. No one, to my knowledge, advocates that scientists use the internal coherence of a theory as the sole criterion of theory acceptance. To make the coherentist’s position as cogent as possible, let us consider the role of coherence in the belief in empirically adequate theories. I will assume that T is empirically adequate with respect to evidence E if and only if T entails E. It follows that, for any T, if T is empirically adequate with respect to E, then p(T/E & T is coherent) ³ p(T/T is coherent). If one can show that even in cases of empirically adequate theories, p(T/E & T is coherent) ³ 0.5

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for some T and E, then it follows that there exists a T such that p(T/T is coherent) < 0.5, that is, that coherence is not a sign1 of truth. This result should not be too surprising, since if coherence does not render an empirically adequate theory rationally believable, then it is implausible that it renders an empirically inadequate theory rationally believable.

(1) The problem of coherent rival theories The coherentist faces an uphill battle to show that coherence is a sign1 of truth. John Earman has presented what might be called the problem of rival theories (Earman 1994). He shows that if we assume that there exists a rival theory T* that has at least as high prior probability as T, p(T*/B) ³ p(T/B), then no matter how many more conﬁrming observations we make (in the sense that both T and T* individually entail O1 & O2, . . . ,On), then p(T/O1 & O2, . . . ,On & B) £ 0.5 (where B stands for “background knowledge,” and Oi stands for the ith observation). Thus, we cannot infer a likely theory from the observable phenomena unless we “load the dice” against rival theories, to use Earman’s phrase. Actually, the situation is even worse. One can generalize Earman’s result: if we assume in addition to T, m-1 mutually incompatible theories that exhaust all the remaining possibilities, and if these theories also save all the phenomena, then p(T/O1 & O2, . . . ,On & B) ≤ 1/m (See Appendix 2). Are the dice loaded against incoherent theories? It is a popular proposal to claim that if non-empirical factors play a role in theory conﬁrmation, they inﬂuence the prior probability. Wesley Salmon, for example, claims that simplicity and symmetry have a “signiﬁcant bearing” on the prior probability of a theory (Salmon 1996, 283). A coherentist might suggest that an empirically adequate theory with the most coherence has a higher probability than its less coherent rivals. Does this suggestion work? Unfortunately one can construct a variant of Earman’s argument that I call the problem of coherent rival theories. There is no reason to think that a theory with the most coherence will be unique. Nothing about coherence requires that there is only one most coherent theory. There could be multiple theories with the maximal amount of coherence. Given this possibility, there is good reason to think that an a priori proof of uniqueness is impossible. If there is a rival theory T* that also saves the phenomena and is equally coherent, then by analogous argument, p(T/B) = p(T*/B) and p(T/B) £ 0.5, since T and T* are incompatible. At this point the coherentist might shift gears. Perhaps she concedes that Earman’s theorem suggests that in the long run the coherence of a theory cannot guarantee that its probability will not converge to a number above 0.5. However, echoing John Maynard Keynes, she might suggest

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that what happens in the long run is irrelevant to what one should believe now, given current evidence. It still could be the case that current evidence is such that it is now rational to believe that coherent theories are likely. It is to this question that I now turn. In its simplest form, Bayes’s Theorem shows the three components of a theory’s probability: p(T/E) = p(T)× p(E/T)/p(E) = prior probability× likelihood/expectedness

A slightly more complicated version of the theorem includes a term for background knowledge B. To consider the role of the coherence of T, consider background knowledge B that includes “T is coherent.” p(T/E&B) = p(T/B) p(E/T&B)/p(E/B)

The probability of a theory depends on three things: the prior probability, the probability of the evidence given the theory (that is, the likelihood), and the probability of the evidence. The denominator, the probability of the evidence, p(E/B), sometimes called the expectedness of the evidence, depends upon E and B and is the same for all theories competing to account for the same phenomena regardless of whether they are coherent. If the coherence of a theory has any effect upon the theory’s plausibility, it must either affect the prior probability or the likelihood.

(2) Does coherence influence the likelihood of a theory? What then of likelihood, the probability of the evidence given background knowledge and that the theory is true, that is, p(E/T&B)? Often this expression is taken as one measure of the explanatory power of the theory. The problem with linking coherence to likelihood is that we can conceive of incoherent theories having a high likelihood. An incoherent theory may even entail the evidence E, in which case the likelihood p(E/T&B) = 1. Indeed, if we frame the problem confronting the theoretician to be a choice among empirically adequate theories as we did earlier, then the likelihood is set to 1 for all candidates, coherent or not.

(3) Does coherence influence the prior probability of a theory? Given their name, one might think that all prior probabilities are determined a priori. However, we should distinguish between two types of priors: (1) empirical priors and (2) a priori priors. A priori priors, symbolized p(T), are not conditional on any contingent background knowledge.

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Because of the lack of empirical constraint, some, with good reason, argue that a priori priors are often undeﬁned. The coherentist could argue that coherence provides the needed constraint. I am suspicious of this suggestion. Empirical prior probabilities, symbolized p(T/B), are typically conditional upon the background knowledge B and consequently will depend upon the nature of the background knowledge. As the saying goes, today’s priors were yesterday’s posteriors. Given the empirical nature of these prior probabilities, it is difﬁcult to assign values from the philosopher’s armchair. Here I think the burden is on the coherentist to show that there are features of the background knowledge that would determine that the prior probabilities of coherent theories are high enough to guarantee that the posterior probabilities are greater than 0.5. The underlying intuition behind the coherentist’s assignment of probability is that a coherent theory has a higher probability than an incoherent theory. I have serious reservations about this intuition. Consider a logically weakened version of T1, called T1°, that is, assume T1 entails T1°, but T1° does not entail T1. If T1 is coherent or more coherent than T2 it does not follow that T1° is coherent or more coherent than T2. For example, T1° might contain only the probabilistically independent components of T1. The coherentist might be inclined to argue that if T1 is more coherent than T1°, then p(T1) > p(T1°). However, this claim violates the probability calculus since if T1 entails T1°, then by the axioms of probability p(T1) £ p(T1°). Is the procedure of assigning coherent theories (or more coherent theories) higher prior probabilities rational? It is not clear that any standards of rationality apply here. Normal ways of constraining rational belief, such as Dutch book arguments, do not dictate that coherent theories have higher probabilities than incoherent theories. Practically any assignment of prior probability, as long as the probabilities of mutually exclusive and exhaustive theories sum to one, is allowed. Perhaps one might claim that the coherentist’s strategy is rational in the sense that it violates neither deductive logic nor the probability calculus. But this claim is weak. There is no good sense in which the coherentist’s strategy of assigning prior probability is more rational than an innumerable number of alternative assignments. To see this point, consider a competing strategy, that of the anti-coherentist. The anti-coherentist thinks that less coherent theories should have higher prior probabilities than more coherent ones. He repudiates every relative assignment of prior probability that the coherentist makes. If T1 is more coherent than T2 and the coherentist asserts that p(T1) > p(T2), then the anti-coherentist asserts that p(T1) > p(T2). There is no a priori reason to privilege one approach over the other. The ardent

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coherentists disagree, but on what basis can they argue for a difference between the two symmetrical positions? It cannot be from experience, since we are considering a priori priors. This leaves some non-empirical means. There are additional reasons to think that coherence is irrelevant to the prior probability of a theory. Consider the following: let T = {h1, h2, h3}, p(h1) = p(h2) = p(h3) = c < k <1, and p(T) = p(h1 & h2 & h3) = c3. Let us assume that h1, h2, and h3 are mutually statistically independent of each other and consequently T is not coherent. Consider another theory T* = {h1*, h2*, h3*} where h1* = h1 & h2, h2*= h2 & h3, and h3* = h3 & h1. In this case p(h1*/h2* & h3*) = p(h2*/h1* & h3*) = p(h3*/h1* & h2*) = 1 > k. Therefore, T* is coherent. Is p(T*) > p(T)? No, the two theories actually express the same propositions—the only real difference between them is that T* is coherent and T is not. This type of counterexample can be extended to more complicated cases in which each hypothesis is not entailed by the conjunction of the rest. To generalize, coherence appears to be a property of the way the theory is represented, not a property of the content of a theory, and so can vary when we vary the way of representing the same facts. If the coherentists could provide an a priori proof of their principle, they would be convincing, but no proof is forthcoming. To bias our a priori probabilities in favor of coherence is at best a metaphysical article of faith, which either unjustiﬁably biases our beliefs in favor of coherence or divorces probability assignments from belief. That we must privilege the a priori priors of coherent theories is not a methodological necessity either. On could argue that science progresses as efﬁciently, or perhaps even more efﬁciently, without a bias toward coherence. If I am correct, this leaves the coherentist’s defense of the epistemic role of coherence in a precarious position and no more rational than competing approaches. Whether the coherentist strategy works for empirical prior probabilities is an open question.

7. IS COHERENCE A SIGN 2 OF TRUTH? If the previous argument was successful, then the coherentist cannot successfully defend the view that the coherence of a theory is a sign1 of truth without appeal to empirical evidence that philosophers are ill suited to garner. At this point in the debate, the coherentist might retreat to the weaker position that coherence is a sign2 of truth. I will argue that the coherentist cannot successfully defend this weaker position on a priori grounds either.

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Consider two competing mutually exclusive and empirically adequate theories T1 and T2 that are comparable on all epistemic respects, except that T1 is coherent and T2 is not. If coherence is a sign2 of truth, then p(T1/E&B) > p(T2/E&B). If one can show that the inequality does not hold then by modus tollens, coherence is not a sign2 of truth. One advantage of this comparative approach is that we no longer need to consider the expectedness of the evidence p(E/B). From Bayes’s theorem it follows from the consequent that p(T1/B) p(E/T1&B)/p(E/B) > p(T2/B) p(E/T2&B)/p(E/B). The denominators cancel, leaving the following inequality that the coherentist must prove: p(T1/B) p(E/T1&B) > p(T2/B) p(E/T2&B). Rearranging we get P(T1/B)/P(T2/B) > p(E/T2&B)/p(E/T1&B).

Thus it is the relative value of the ratios of priors and likelihoods of the two theories that determine the truth of the coherentist’s claim. There are four ways in which this inequality could be true. (1) Driven by the priors: The coherence of T1 increases the prior probability of T1 over T2 to the degree that differences in the likelihood are irrelevant. (2) Driven by the likelihoods: The coherence of T1 increases the likelihood of T1 over T2 to the degree that differences in the priors are irrelevant. (3) Driven by the priors and likelihoods: the coherence of the theory increases both the prior and likelihoods. Possession of coherence increases both the priors and the likelihoods. (4) Coherence has no systematic effect on the priors or likelihoods individually, but nonetheless p(T1/B) p(E/T1&B) > p(T2/B) p(E/T2&B). I will deal with the four cases in reverse order, ending with the most plausible case. The fourth case is the least likely to occur. For it to obtain, when the prior probability T1 is less than T2, the likelihood of T1 must be greater than T2 by a greater amount than T1 is less than T2. Furthermore, where the prior probability of T1 is greater than T2, the likelihood of T1 cannot be even greater than the likelihood of T2. That this is the case is implausible and I can think of no mechanism that would guarantee that these relations exist. The mechanism would have to increase a coherent theory’s priors when it decreases the likelihoods and vice versa. Arguments against case 3 will be similar to arguments against cases 1 and 2. If any of my arguments against case 1 and 2 are successful, they will also be successful arguments against case 3.

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Case 2 concerns signs2 of truth that inﬂuence the posterior probability of a theory by increasing the likelihood of the coherent theory, p(E/T1&B), over a rival, p(E/T2&B), without the alleged sign of truth. Similar remarks apply to consideration of likelihoods as those mentioned in Section 5.2. First, if we are considering empirically adequate theories, T1 and T2, then the likelihoods are equal to 1 and consequently they are equal for the theory with the alleged sign of truth and the theory without it. Second, if we have a conception of coherence that necessarily involves making the evidence less surprising, then the notion of coherence risks becoming relativized to a set of evidence. Theories can be coherent without accounting for the evidence and judgments of a theory’s coherence, and do not depend upon which evidence one considers. I see no good reason to assume that coherence systematically increases the likelihoods of a theory. Case 1 is the most interesting of the four cases. As mentioned above, the prior probability of the theory is the least implausible component of a theory’s probability where coherence is alleged to have an effect on the probability of a theory. Does a coherent theory have a higher prior probability than a non-coherent one? If so, this fact is either a priori or empirical. In Section 6.3, I have argued that it is not a priori that coherent theories have higher prior probabilities. Not all is lost for the coherentist, however. A more plausible position is to argue that whether a sign2 of truth exists is an a posteriori question to be settled with empirical evidence. If this is the case, then scientists and historians of science would more easily provide the appropriate evidence, if it exists, than philosophers of science.

8. CONCLUSION What should one say about the relation between coherence and truth? On my view, a general probabilistic connection between coherence and truth (or falsity) would be a contingent connection. Here I disagree with Whewell. Discovering this connection would be an empirical discovery. If this general fact were part of the background knowledge, and if T1 is a coherent theory, then the general connection is relevant to the probability of T1. If it is knowable a priori that T1 is coherent, then adding that T1 is coherent to the background knowledge does not increase the probability of T1. In an important sense, the background knowledge already contains this (and all other) a priori facts. However, even in this case, it does not follow that coherence is irrelevant to the believability of theories since whether there is a general empirical connection between coherence and truth is relevant. Consider the general claim that most coherent theories

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are true. Whether this is part of the background knowledge does affect the probability of the theory: p(T1/B & most coherent theories are true) > p(T1/B & most coherent theories are false). If the coherence of a theory is determinable a priori, coherence is not a sign2 of truth, but it is possible that coherence is relevant to a theory’s probability. Whether it is relevant, that is, whether there is a general connection between coherence and truth, is an empirical question—one better answered by an empirical survey than conceptual analysis. Achinstein’s sanitized version of coherence fails to capture Whewell’s notion since the probabilistic rendition of coherence is not an a priori sign of truth. His approach is better seen as a critique of Whewell’s central methodological claims than as an interpretation of Whewell’s ideas.

APPENDIX 1 Part of the proof is straightforward: we can show that ~h1 is coherent with ~(h2, . . . hm) on B. Here is the proof: p(h1/h2, . . . , hm & B) > p(h1/B) by assumption p(h2, . . . , & hm/h1 & B) > p(h2, . . . , & hm/B) by Bayes’s theorem 1 - p(h2, . . . , & hm/h1 & B) > 1 - p(h2, . . . , & hm/B) p(~(h2, . . . , & hm)/h1 & B) > p(~(h2, . . . , & hm)/B) p(h1/~(h2, . . . , & hm) & B) > p (h1/B) by Bayes’s theorem 1 - p(h1/~(h2, . . . , & hm) & B) > 1 - p (h1/B) p(~h1/~(h2, . . . , & hm) & B) > p (~h1/B) To complete the proof of ~h1 is coherent with ~(h2, . . . , & hm) on B, we need to show that p(~h1/~(h2, . . . , & hm) & B) > k. I cannot offer a proof of this claim, but using Bayes’s theorem again one can show that p(~h1/~(h2, . . . , & hm) &B) > [p(~h1/B) – p(~(h2, . . . , & hm)/B) - kp (~(h2, . . . , & hm)/B)]/p(~h1/B) follows from the coherence of T. As k ® 1, then [p(~h1/B) – p(~(h2, . . . , & hm)/B) + kp(~(h2, . . . , & hm)/B)]/p(~h1/B) ® 1 and p(~h1/~(h2, . . . , & hm) &B) ® 1. Thus it is possible that, if T is coherent on B, then ~h1 is coherent with ~(h2, . . . , & hm) on B. Next we must consider the second part of Achinstein’s deﬁnition. One needs to show that ~(h2, . . . ,&hm) is coherent with ~h1 on B. Using an analogous argument it is possible that p(~(h2, . . . , &hm)/~h1) >k. Finally, one must show that p(~(h2, . . . , &hm)/~h1 & B) > p(~(h2, . . . , hm)/B) and thus show that ~(h2, . . . ,&hm) is coherent with ~h1 satisfying the second part of Achinstein’s deﬁnition. The last step follows deductively:

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p(~h1/~(h2, . . . ,&hm) &B) > p(~h1/B) p(~h1/B)p(~(h2, . . . , &hm)/~h1 & B)/p(~(h2, . . . , hm/B) > p(~h1/B) by Bayes’s Theorem p(~(h2, . . . , &hm)/~h1 & B) > p(~(h2, . . . , hm)/B)

APPENDIX 2 Proof: let a theory T exist, which in conjunction with background knowledge B entail O1, O2, . . . , On. Claim: assume that p(T/B) < 1/m. If (i) T1, . . . ,Tm–1 also entail O1, . . . On, and (ii) B entails ¬ (Ti & Tj) where i ¹ j, and (iii) ∀i (p(Ti/B) ³ p(T/B)) and (iv) p(T Ú T1 Ú T2 Ú . . . Ú Tm–1/B) = 1, then for any n, no matter how large p(T/O1 & O2, . . . , & On & B) £ 1/m. From Bayes’ theorem and (i) one can derive the following equality p(T / O1 & On & B) p(T / B) = p(T1 ∨ T2 ∨ Tm −1 / O1 & On & B) p(T1 ∨ T2 ∨ Tm −1 / B)

Now we know p(T/B) < 1/m, by assumption, and by (iv) p(T1 Ú T2 Ú ...Ú Tm–1/B) ³ (m–1)/m. Assume that the claim is false, i.e., p(T/O1 & O2, . . . & On & B) > 1/m, then p(T1 Ú T2 Ú . . . Ú Tm–1/O1 & O2, . . . & On & B) < (m–1)/m, and the above equality cannot hold. REFERENCES Achinstein P. 1991. Particles and Waves: Historical Essays in the Philosophy of Science. New York: Oxford University Press. Butts, R. 1968. William Whewell’s Theory of Scientiﬁc Method. Pittsburgh: University of Pittsburgh Press. Earman, J. 1994. Concepts of Projectibility and the Problem of Induction. In Grue!, ed. D. Stalker. Chicago: Open Court. Salmon, W. C. 1996. Tom Kuhn meets Tom Bayes. In The Philosophy of Science, ed. D. Papineau. Oxford: Oxford University Press. Whewell, W. 1847. The Philosophy of the Inductive Sciences. London: John W. Parker.

13 Observationally Indistinguishable Spacetimes: A Challenge for Any Inductivist John D. Norton

1. INTRODUCTION For several years, through the “material theory of induction,” I have urged that inductive inferences are not licensed by universal schemas, but by material facts that hold only locally (Norton 2003; 2005). My goal has been to defend inductive inference against inductive skeptics by demonstrating how inductive inferences are properly made. Since I have always admired Peter Achinstein as a staunch defender of induction, it was a surprise when Peter identiﬁed me as one of the skeptical enemies in “The War on Induction” (Achinstein 2010). Peter reproached me for “taking on” his inductive heroes, Newton and Mill, and their celebrated rules of inductive inference. That my project could lead me to become a foe of induction was unimaginable. Or it was, until I began an analysis of a problem in philosophy of physics, whose elaboration is the purpose of this note. I wanted to endorse certain inductive inferences whose cogency seems unassailable: we have never seen certain pathologies in spacetime, so inductive inference should assure us that we never will. However I was unable to display the facts that license these inferences. After some reﬂection, I believe this problem shows that induction has less reach than we thought. There are problems we expect inductive inference to solve but that it cannot solve. This admission is no failure of the material theory of induction. No other approach to inductive inference fares any better with them. I will argue below that attempts to ground the inductive inferences in universal inductive principles founder on both the vagueness of the principles and the tendency of the applicable principles to contradict each other. While

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Peter has identiﬁed me as a foe of induction, I doubt that his analysis will help these principled approaches. Contrary to my expectations, Peter’s recently published book chapter (Enter John Norton) does not mount a full-blown defense of Newton’s and Mill’s rules as a priori, even though he ﬁnds the rules to codify “a type of reasoning that is crucial to empirical science.” (Achinstein 2010) Rather, he agrees with me that empirical considerations do determine whether an inductive inference is good. An inference that merely has the familiar inductive form “that A is B, so all A’s are B” may fail to be good if the underlying facts are inhospitable. Indeed, the analysis of the problem presented here is a success for the material theory of induction, provided one is prepared to limit the reach of inductive inference in this and similar cases. For the material theory enables us to delineate which inductive problems are tractable and which are not. That decision reduces to whether we can identify appropriate warranting facts. Theories of inductive inference based on universal principles are unable to make the corresponding discrimination, for their universal principles must hold everywhere. A failure of inductive inference is for them inexplicable. The problem at issue concerns observationally indistinguishable spacetimes, described in the following section. In them, deductive inference cannot determine which spacetime is ours, no matter how extensive a portion of the spacetime is observed. In Section 3, I will argue that these results do not illustrate an underdetermination of theory by evidence, since they make no decision between competing theories, and they make little contact with the inductive considerations that must ground such a decision. Rather, in Section 4, I will describe how they exemplify a different sort of failure manifested by physical theories, a form of generic indeterminism in general relativity. In it, a speciﬁcation of the observable past always fails to ﬁx the remainder of a spacetime. While we may have no means to distinguish deductively among different cosmic futures in the cases considered in this literature, I will urge in Section 5 that we can pick among them with quite familiar sorts of inductive arguments whose cogency seems unassailable. Nonetheless, in Section 6, I will urge that these inductions are troubling in that they are what I shall call “opaque.” That is, we cannot see through the inductive inferences to an unproblematic warrant, whether it be in matters of principle or fact.

2. OBSERVATIONALLY INDISTINGUISHABLE SPACETIMES The existence of observationally indistinguishable spacetimes in general relativity was brought to the attention of philosophy of science by Clark Glymour (1977) and David Malament (1977). An observer at any event

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in a spacetime is depicted as having full knowledge of everything in the temporal past of that event. The temporal past is that set of events from which ordinary processes, propagating at less than the speed of light, may reach the observer’s event. It may happen that exactly the same observable past arises somewhere in a second spacetime. The ﬁrst spacetime of the observer is observationally indistinguishable from the second, if this ﬁnding is assured no matter where the observer may be in the ﬁrst spacetime. Manchak (2009) proved that any well-behaved1 spacetime always has many geometrically distinct, nemesis spacetimes from which it is observationally indistinguishable. Moreover the nemesis spacetimes will be “locally” the same as the observer’s spacetime. In the ﬁrst spacetime, one might have a condition that holds at each event, such as the Einstein gravitational ﬁeld equations; or, more simply, a different condition that just asserts everywhere vanishing geometric curvature. The locality clause of the theorem assures us that the nemesis spacetimes will satisfy these same conditions. The theorem and its proof involve some sophisticated spacetime geometry. But the basic idea is simple. A loose analogy, shown in Figure 13.1, illustrates it. Imagine an ant on an inﬁnite, ﬂat (Euclidean) sheet of paper who can survey only the surrounding 10,000 square foot patch. No matter where the ant may be, it cannot distinguish its sheet from a nemesis sheet, which consists of a copy of the original sheet of paper rolled into a cylinder with a circumference of one mile.

Fig. 13.1. Ant on a sheet of paper

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3. WHAT THE SIGNIFICANCE IS NOT: UNDERDETERMINATION OF THEORY The thesis of the underdetermination of theory by evidence, in its strong and interesting form, asserts that all evidence necessarily fails inductively to ﬁx theory.2 The similarity in the terms “observationally equivalent theories” and “observationally indistinguishable spacetimes” requires some thought.3 Are the observationally indistinguishable spacetimes illustrations of the thesis of the underdetermination of theory by evidence? I will argue that they are not. I agree with the opening remarks of Manchak (2009). He notes the distinctness of his result from the skeptical thesis that acceptance of some particular scientiﬁc claim can be resisted in the face of all evidence by revision to background theories. The assurance of observationally indistinguishable spacetimes in general relativity fails to bear on the thesis on the underdetermination of theory by evidence in two ways. First, the indistinguishability does not pertain to theory. We are not presented, for example, with general relativity and some competitor theory, indistinguishable from it. Rather, what we cannot distinguish is whether this spacetime is the one of our observations or whether it is that one.4 Second, the indistinguishability asserts a failure of deductive inference, whereas the thesis of the underdetermination of theory by evidence asserts a failure of inductive inference. Many spacetimes are logically compatible with the fragment of spacetime that we observe. So deductive inference does not allow us to ﬁx which of them is our spacetime. This failure is no failure of inductive inference, which routinely fares better with such problems. Deductive inference cannot assure us that our spacetime will continue to manifest the conservation of electric charge, even though it has been observed to do so without exception. The simplest inductive inferences can give us that assurance. Manchak’s theorem, however, is stronger. It does preclude particular sorts of inductive inferences from distinguishing the spacetimes. Our observable spacetime is four-dimensional and has a Lorentz signature metrical structure. We are allowed the inductive inference that this will persist in the unobserved part. More generally, we are allowed to infer inductively to the persistence of any local condition, such as the obtaining of the Einstein gravitational ﬁeld equations, in both the observer’s and the nemesis spacetimes. These inductive inferences, the theorem shows, will still not enable us to separate the spacetimes, for both will agree on them. What is not shown, however, is whether other inductive inferences would enable us to separate the two spacetimes. It is essential to the

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theorem that the observer’s spacetime and its nemesis are factually distinct. What needs to be shown is that these factual differences cannot be exploited by an inductive inference that can separate the two spacetimes. I will suggest below in Section 5 that apparently routine inductive inferences are capable of exploiting these factual differences to discriminate a spacetime from its nemesis. In Section 6, however, I will urge that this routine appearance is deceptive in that the warrants of these inductive inferences are unclear.

4. WHAT THE SIGNIFICANCE IS: A FORM OF INDETERMINISM The results on observationally indistinguishable spacetimes amount to this: we ﬁx some part of the spacetime and, within the context of some physical theory like general relativity, the rest of the spacetime remains undetermined. This result is a form of indeterminism. Indeterminism in physical theories arises whenever the full speciﬁcation of the present fails to ﬁx the future. Indeterminism is routine in standard, collapsed versions of quantum theory. The full speciﬁcation of the present state of a radioactive atom does not determine when it will decay in the future. Determinism arises commonly in the spacetimes of general relativity. For example, in the Robertson-Walker spacetimes of relativistic cosmology, selecting a single moment of cosmic time identiﬁes a three dimensional surface in the four-dimensional spacetime that has the special property of being a "Cauchy surface." Having this property entails that, if we ﬁx the spacetime geometry and matter ﬁelds of the universe on this surface, they are ﬁxed by the theory for all times. The failure of determinism in quantum theory in the 1920s was shocking, since it implied a profound limit on what we could know about the future. It told us that no matter how much we knew about the present state of some suitably chosen quantum system, we could not know assuredly what it would do in the future. This kind of principled epistemic limit on what we can know is not captured well by seeking to implement determinism in terms of the Cauchy surface “nows” of cosmic time in relativistic spacetimes. For no observer can observe the entirety of one of these surfaces. Rather, what an observer can know at one moment is delimited better by the observer’s temporal past, even though it represents an excessively optimistic assessment of our observational abilities. Then the results on observationally indistinguishable spacetimes place powerful constraints on just

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what can be inferred directly from our spacetime theories about the remaining unobserved parts of our spacetime. They tell us that, even with the assistance of local spacetime theories, we can never assuredly ﬁx a unique extension to the portion we have observed. In this regard these results are the appropriate analog of the indeterminism of quantum theory.5 However, there is a strong disanalogy to the indeterminism of quantum theory. Both forms of indeterminism express an impossibility of the past deductively determining the future. They differ markedly when we consider the possibility of inductive determination of the future. While inductive discrimination is possible in both cases, as we shall see below, they employ different sorts of inductive inferences.

5. SOME COSMIC INDUCTIONS Inductive inferences can discriminate a spacetime from an observationally indistinguishable nemesis arising in the results on observationally indistinguishable spacetimes. A simple example illustrates the types of induction required. Consider a Minkowski spacetime. It is observationally indistinguishable from a “half Minkowski spacetime”; that is a Minkowski spacetime in which half has simply been excised. This excised half is the “t = 0” hypersurface, in a standard coordinate system, and all events to its future. The observational indistinguishability depends on the fact that every observer’s past in either spacetime is identical to every other observer’s past in either spacetime; they are all geometric clones of one another, as illustrated in Figure 13.2. Consider the timelike curves of any inertial observer in either spacetime. No such observer would ever detect a failure of the observer’s world line to extend by a millisecond of proper time.6 Every observer would have repeatedly done the experiment of waiting a millisecond and found always that their worldline was extended by a millisecond, as shown in Figure 13.3. The natural inductive inference is that all future terminated inertial worldlines can be extended by one millisecond of proper time. But that condition can only be met in the full Minkowski spacetime. Hence, even though the two spacetimes are observationally indistinguishable as far as deductive discriminations are concerned, this induction indicates in favor of the full Minkowski spacetime. This last example uses a peculiar spacetime, an extendable half Minkowski spacetime. These extendable spacetimes are only a little more peculiar than the constructions used to generate indistinguishable spacetimes. Where the nemesis of a Minkowski spacetime was created by

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observer

observer time

observer’s temporal past

observer’s temporal past

space

Minkowski spacetime

Half Minkowski spacetime

Fig.13.2. Minkowski and half Minkowski spacetimes

t=0

1 millisecond

1 millisecond time

space

Minkowski spacetime

Half Minkowski spacetime

Fig. 13.3. Millisecond extensions of inertial observers’ worldlines

subtracting spacetime structure, more common examples in the literature create nemeses by adding. The ingenious chain construction of Manchak’s proof requires us to build an inﬁnity of duplicate spacetimes and then stitch them together in an inﬁnite chain by what amounts to wormholes. In the case of a full Minkowski spacetime, observers would never detect the wormholes in the portions of spacetime they observe. Thus must remain forever unsure of whether such a wormhole link to the duplicated Minkowski spacetimes will eventually enter the growing portion that they can observe. Deduction cannot rule out the possibility. Induction can: these odd structures have never been seen, so one expects never to see them. There are more examples in which spacetime structure is added. A familiar case is a two-dimensional de Sitter spacetime and versions of it

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time Original de Sitter spacetime

Doubled de Sitter spacetime

Tripled de Sitter spacetime

space

Fig. 13.4. Two dimensional de Sitter spacetimes

spatially unrolled into larger spacetimes of twice, thrice, etc. the spatial size of the original spacetime.7 This de Sitter spacetime can be pictured as a two-dimensional hyperboloid in a three-dimensional Minkowski spacetime. Its spatial slices are circles and the unrolling just consists of replacing them with larger circles of twice, thrice, etc., the circumference. The original and unrolled versions are depicted in Figure 13.4.8 The unrolled versions have the curious property of harboring space-time regions that are duplicated twice, thrice, etc. according to the extent of the unrolling. This property is illustrated in the ﬁgure by the presence of a single observer’s temporal past in the original de Sitter spacetime, then two copies of it in the doubled de Sitter spacetime, followed by three copies in the tripled de Sitter spacetime. A spacetime with no duplications and a spacetime with 27 duplications of the observer’s past will be observationally indistinguishable by deductive means. However, Occam’s razor motivates an inductive inference to the ﬁrst spacetime.

6. THE OPACITY OF COSMIC INDUCTIONS While we can discriminate inductively among possible futures in both cases, the indeterminism arising through observationally indistinguishable spacetimes is more troubling than the indeterminism of quantum theory. In the case of quantum theory, the warrant for the inductive inferences is quite clear and unproblematic. In the spacetime case, it is hard to see through the inductions to the warrant that lies behind them. Insofar as warrants can be found, they are suspect. I will call these latter inductions “opaque.” In the case of quantum theory, the theory supplies physical chances to help us pick among the possible futures. Take the radioactive decay of an atom. We are equally sure that the atom will or will not decay over a

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single half-life; both outcomes have the same physical chance of 1/2. We can be very sure, inductively, that decay will have happened if we wait ten half-lives; the physical chance of decay is then 1– (1/2)10 = 0.999. These inferences from the known past to the unknown future are grounded by the physical chances of the quantum theory itself. We can see through these inductions to the physical theory that grounds them; in this sense, they are “transparent.” The inductions arising in observationally indistinguishable spacetimes are of a different kind.9 Relativity theory provides no physical chances to weight the different spacetime extensions that it allows for our temporal past. The theory itself merely declares that the various alternatives are possible and nothing more. It leaves to us the task of determining if one or other of them is somehow preferred. We must look outside the physical principles of cosmology to decide this question. This is a natural project for inductive inference. However, the examples of Section 5 above reveal no single, principled inductive approach that can be applied across the many cases of indeterminism. Rather, we must consider each on a case-by-case basis and hope that we can ﬁnd principled grounds in each. Take the extrapolation of the extendability of observed spacetime curves to all spacetime curves. Can it be grounded in an inductive principle that asserts that what has always been so, will always be so? Such a universal principle is untenable. It can only apply to some things that have been so, otherwise we rule out the possibility of any novel changes in the future. It must be modiﬁed so some future novelty is possible. But what could these modiﬁcations be, if we are to secure a universal inductive principle applicable beyond the one case? The danger is that we reduce the principle to a blatant circularity, in which we solemnly declare that it applies except when it does not. Worse, we must also be able to overrule the principle if further facts demand it. In a cosmology with a future “big crunch” singularity, we will have the same records of assured millisecond extensions, yet our inertial trajectories will not be indeﬁnitely extendable. That failure can be deduced from present facts through the singularity theorems of general relativity. We face similar problems when we try to rule out the funhouse mirror duplications of the unrolled de Sitter spacetimes or the extravagantly duplicated spacetimes connected by wormholes. We would like to ground the inductive inference in a principle like Occam’s razor. However, the idea behind it, that simplicity is often accompanied by truth, is more a convenient and fallible rule of thumb than a guarantee. These problems are deepened by an absence of any clear rules as to just what counts as simple.10 I have long harbored dissatisfaction with the evident failure of any universal inductive principle such as the ones just listed. My solution has

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been to propose that we abandon the search for universal, formal approaches to inductive inference. In a material theory of induction, I urge (Norton 2003; 2005) that inductive inferences are not warranted by general principles, but by facts. A ﬁtting application of this material approach is to the inductive inferences just seen on radioactive decay. The laws of quantum theory are the facts that warrant them. What is troublesome from the material perspective is the absence of warranting facts for the inductions in the spacetime case. It seems natural to infer inductively to the fully extended Minkowski spacetime rather than the extendable half Minkowski spacetime, or to avoid admitting holed spacetimes that are created from other spacetimes by excising even quite small parts. However it is very hard to specify just what facts ground the inference. That we have never seen holes in spacetime does not settle the matter. By their construction, there cannot be an observable trace of holes. That remains true even if our world tubes pass directly through the hole. We would cease to be for the portion of our world tubes coinciding with the excision. However, the portion of our world tubes in the future of the hole would be reconstituted with all the memories and other traces of the excised spacetime. If observed facts do not ground the inductive inference, what of physical laws? We could cite the common postulate in relativity texts that spacetimes are inextendable. However, that postulate is merely the supposition of precisely what is at issue, and is distinctive in that it is dispensable from a physical perspective. It is present for mathematical convenience. In his unpublished manuscript, Manchak reports the justiﬁcations usually given for assuming inextendability (Manchak 2009a). They amount to invoking Leibniz’s principle of plenitude. Manchak quotes from the writings of the mathematical physicist Robert Geroch as a typical justiﬁcation: “Why, after all, would Nature stop building our universe . . . when she could just as well have carried on?” One cannot help but be struck by how tenuous the grounding has become. We are now to secure our inductions in abstract metaphysics. The principle of plenitude itself is sufﬁciently implausible that we need to prop it up with anthropomorphic metaphors. We are to imagine a personiﬁed Nature in the act of creating spacetime, much as I might be painting my fence on the weekend. Just as I might not want to stop when there is one board remaining unpainted, so Nature is supposedly loath to halt with a cubic mile-year of spacetime still uncreated. If the complete arbitrariness of the principle of plenitude is not already clear, we might pause to apply it elsewhere. We are supposed to prefer spacetimes without duplications by virtue of a metaphysics of simplicity. Yet surely the metaphysics of plenitude would direct the opposite result.

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Why would Nature, guided by the slogan “make all you can make,” eschew yet another duplication of the spacetime if it is possible? All these inductive inferences are opaque in that we cannot see through them to their warrants. If we seek to justify them by means of general inductive principles, we resort to principles that are clearly false, or, if not, so hedged as to be inapplicable. If we seek to justify them materially in facts, we arrive almost immediately in the dubious, abstract metaphysics of plenitude and simplicity. This circumstance is to be contrasted with the transparent inductive inferences in the quantum context. Their grounding is found directly in the laws of quantum theory; we can in turn satisfy ourselves of those laws by tracing back further warrants in the experimental and theoretical foundations of quantum theory. In sum, we have what appears to me to be an intractable problem.11 On the one hand, it seems completely unjustiﬁed to presume that wormholes we have never seen in our past spacetime will appear in the future. It seems completely unjustiﬁed to presume that processes we observe here are duplicated many times over in an unrolled spacetime, when those duplications are by construction, necessarily invisible to us. It seems completely unjustiﬁed to assume that there are holes in spacetime, when the spacetime would, by construction, look identical to us if there were no holes. Indeed, even if our world tubes had no past, we would have memories of a past that never was. The inductive inference from those memories to the reality of the past seems irresistible, as do the inductive inferences that reject spatial duplications and future wormholes to new universes. To deny these inductive inferences would, in other contexts, be denounced as delusional. We routinely dismiss as desperate zealots those who tell us our universe was created last Wednesday complete with all records of an ancient past. Yet, when we try to display the proper warrant of those inductive inferences we favor, whether the warrant is in general principles or material facts, the ground crumbles around our feet.

ACKNOWLEDGMENTS It is a pleasure to present this essay in honor of Peter Achinstein, with gratitude for his scholarship and dedication to philosophy of science. I thank him for his thoughtful discussion in Achinstein (2010) and also for correspondence, in which he clariﬁed his views and made suggestions for editing this note. I also thank Claus Beisbart and John Manchak for helpful discussion on an earlier draft.

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REFERENCES Achinstein, P. 2010. Evidence, Explanation, and Realism. New York, Oxford University Press. Beisbart, C. and T. Jung. 2006. Privileged, Typical, or Not Even That? Our Place in the World According to the Copernican and the Cosmological Principles. Journal for General Philosophy of Science 37 (2): 225–56. Glymour, C. 1977. Indistinguishable Space-Times and the Fundamental Group. In Foundations of Space-Time Theories: Minnesota Studies in the Philosophy of Science, vol. 7, ed. J. Earman, C. Glymour, and J. Stachel. Minneapolis: University of Minnesota Press. Magnus, P. D. 2005. Reckoning the Shape of Everything: Underdetermination and Cosmotopology. British Journal for the Philosophy of Science 56 (3): 541–57. Malament, D. 1977. Observationally Indistinguishable Spacetimes. In Foundations of Space-Time Theories: Minnesota Studies in the Philosophy of Science, vol. 7, ed. J. Earman, C. Glymour and J. Stachel. Minneapolis: University of Minnesota Press. Manchak, J. 2009. Can We Know the Global Structure of Spacetime? Studies in History and Philosophy of Modern Physics 40 (1): 53–6. ——— . (2009a) “What is a ‘Physically Reasonable’ Spacetime?” URL: http:// philsci-archive.pitt.edu/id/eprint/4506Spacetime? Norton, J. D. 2008. Must Theory Underdetermine Evidence? In The Challenge of the Social and the Pressure of Practice: Science and Values Revisited, ed. M. Carrier, D. Howard, and J. Kourany. Pittsburgh, Pa.: University of Pittsburgh Press. ——— . 2006. The Formal Equivalence of Grue and Green and How It Undoes the New Riddle of Induction. Synthese 150 (2): 185–207. ——— . 2005. A Little Survey of Induction. In Scientiﬁc Evidence: Philosophical Theories and Applications, ed. P. Achinstein. Baltimore, Md.: Johns Hopkins University Press. ——— . 2003. A Material Theory of Induction. Philosophy of Science 70 (4): 647–70.

NOTES 1. The theorem excludes spacetimes in which the entire spacetime is observable from one event. They are “bizarre,” because they include closed timelike curves, which permit time travel. 2. In a recent paper, I urge that the thesis is groundless (Norton 2008). For further analysis of the relation of these examples to the underdetermination thesis and the possibility that the observationally indistinguishable spacetimes may just be variant presentations of the same facts, see Magnus 2005. 3. It requires more thought than I gave it in writing footnote 13 of Norton 2008. 4. There is an ambiguity in the use of the term “theory.” One might conceive an individual spacetime as a theory in its own right. The geometry of Minkowski spacetime is the special theory of relativity. However this use is unnatural in general relativity, in which the particular spacetimes are models of the general theory.

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5. Claus Beisbart has pointed out to me that, aside from Manchak’s result, there is a familiar expectation of this sort of indeterminism. Fixing one’s temporal past leaves open the possibility of inﬂuences propagating to one’s future from the region of spacetime outside one’s past light cone. 6. In the half Minkowski spacetime, some worldlines will not extend by a millisecond, when the observer’s worldline runs into the non-existent t = 0 excision. That observer ceases to exist and there is no detection or record of the failure. 7. This spacetime has only one spatial dimension. The spatial duplications described are harder to implement with three-dimensional spaces. The simplest case arises with a topologically toroidal Euclidean space. It is created by taking a cube of Euclidean space and identifying opposite faces. The space can be unrolled by connecting its faces to duplicate cubes of Euclidean space. 8. The ﬁgures are misleading insofar as it appears that the doubling is achieved by a uniform expansion of the spacetime. That would alter the spacetime curvature at every point of the spacetime, so that the temporal pasts in the two spacetimes would no longer be isometric. Rather the doubling is effected by a cutting and pasting that leaves local spacetime structure unaffected. Take a de Sitter spacetime “1” and copy of it, de Sitter spacetime “2.” Cut each spacetime along a timelike geodesic that then exposes edges “1L” and “1R” in spacetime 1 and “2L” and “2R” in a spacetime 2. Glue 1L to 2R and 1R to 2L to form the doubled de Sitter spacetime. 9. The problem has been long discussed in the context of justifying the cosmological principle. Its justiﬁcation requires an inductive inference from the large scale, spatial homogeneity, and isotropy of the observed part of spacetime to all spacetime. For a recent discussion, see Beisbart and Jung 2006. 10. I set aside Bayesian analyses. All they will do is take something like these principles and use them to determine prior probabilities and likelihoods. The resulting analysis will be no more secure than the principles used to set these quantities, although this will be harder to see because of the complications of the computational machinery. 11. Peter Achinstein has urged me to explain how this problem differs from another notorious intractability in induction, “grue.” In Norton 2006, I argue that grue only provides a novel inductive challenge if we grue-ify our total science. However, then the standard and grue-iﬁed alternatives are isomorphic, so we cannot rule out the possibility that they are merely notational variants of the same facts. Hence, we should not expect an inductive logic to separate them. A variation on this approach may assist us in the case of spacetimes with excisions. Since no experience will ever enable us to learn whether ours is the fully extended or mutilated spacetime, strict empiricist leanings may incline us to say that the two do not really differ factually. However, this sort of thinking cannot help us if we are choosing among spacetimes that may have wormholes in our future. These wormholes will eventually manifest in our observations.

14 Making Contact with Molecules: On Perrin and Achinstein Stathis Psillos

1. INTRODUCTION In his essay, “Philosophy in France in 1912,” André Lalande made the following observation. M. Perrin, professor of physics at the Sorbonne, has described in Les Atomes, with his usual lucidity and vigor, the recent experiments (in which he has taken so considerable a part) which prove conclusively that the atoms are physical realities and not symbolical conceptions as people have for a long time been fond of calling them. By giving precise and concordant measures for their weights and dimensions, it is proved that bodies actually exist which, though invisible, are analogous at all points to those which we see and touch. An old philosophical question thus receives a positive solution. (Lalande 1913, 366–7)

This brief and matter-of-fact announcement expressed a rather widely shared sentiment on the European continent that Jean Perrin’s experimental work had clinched the issue of the reality of atoms. Indeed, it is now obvious that between roughly 1908 and 1912, there was a massive shift in the scientiﬁc community in favor of the atomic hypothesis. It is also obvious that Perrin’s experimental work on the causes of Brownian motion played a major role in this shift. When Perrin received the Nobel Prize for physics in 1926, it was noted in the presentation speech by Professor C. W. Oseen that he “put a deﬁnite end to the long struggle regarding the real existence of molecules.” Peter Achinstein has offered one of the most systematic expositions and reconstructions of Perrin’s argument, aiming (a) to show how his own theory of evidence best accounts for the signiﬁcance of Perrin’s results; and (b) how Perrin has offered a local and experimental argument for scientiﬁc realism. After some detailed presentation of Perrin’s

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argument, I will offer my own reconstruction of it and will show why it is superior to Achinstein’s. Finally, I will try to draw some lessons for scientiﬁc realism.1

2. ENTER PERRIN Over time, Perrin seems to have shifted from a neutral position, with friendly gestures to atomism, to a full endorsement of the atomic theory. In his textbook of 1903, he contrasted two methods of doing science: the inductive, which proceeds by analogy and generalization, and the intuitivedeductive, which consists “in imagining a priori matter to have a structure that still escapes our imperfect senses, such that its knowledge permits deductive predictions about the sensible properties of the universe” (Perrin 1903, viii). The latter method fosters “the illusion of a satisfactory explanation . . . [of] the visible in terms of the invisible, even when [it does not] lead to the discovery of new facts” (viii). Though he notes that in that book he will adopt the inductive method, he nonetheless claims he will not aim to condemn “en bloc” the molecular theories, but rather to submit them to a critical scrutiny in such a way that their essential elements are preserved. Perrin was sensitive to the fact that for many (notably Duhem and perhaps Ostwald and Mach), the atomic hypothesis was a venture into metaphysics. Surprisingly, he added: “I do not forget that the sensation is the only reality.” This would seem to condemn the atomic hypothesis from the start. Yet, Perrin added two important caveats. The ﬁrst is that “[sensation] is the only reality, on the condition that to the actual sensations all possible sensations are added.” This is important because he thought that the atomic hypothesis could, in the end, be rooted in sensations. How this could be is illustrated by his second caveat, in which he drew an analogy between molecules and microbes—the latter did become the object of “possible sensation” via the microscope. Here is how he put it. One would certainly have been able, without the aid of the microscope, to arrive at the thought that contagious diseases were due to the multiplication of very small living beings. One, guided by these ideas a priori, would have been able to discover almost all of the Pasteurian technique. One would have thus followed deductive science and cured the contagious diseases, but following a way condemned by the supporters solely of the inductive method, until the very day in which the microscope had proved that the microbe hypothesis expressed several possible sensations. Here then is an indisputable example of a structure which could escape our senses and the knowledge of which allows anticipation of certain properties which are [to our senses] directly accessible. (Perrin 1903, ix–x)

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The point is that a hypothetico-deductive account of scientiﬁc method won’t provide strong grounds for accepting the reality of the explanatory posits—more is needed, and this more comes, in the end, from experimental conﬁrmation and, in particular, from placing the hypothesized entities into a causal network that ends up in certain observational trails. By the time he wrote his Les Atomes, he had become an ardent defender of the intuitive-deductive method. In the preface, he noted, To divine in this way the existence and properties of objects that still lie outside our ken, to explain the complications of the visible in terms of invisible simplicity is the function of the intuitive intelligence which, thanks to men such as Dalton and Boltzmann, has given us the doctrine of Atoms. This book aims at giving an exposition of that doctrine. (Perrin 1916, vii)

However, even then, he very much hoped that there would be some day in which atoms would be “as easy to observe as are microbes today,” though for him the use of a microscope is within the “realm of experimental reality” (1916, x). The point that needs to be appreciated is that for Perrin science should proceed by refusing to limit itself “to the part of the universe we actually see,” and that the best way to achieve this is to aim at explanation-by-postulation, that is by aiming to explain the visible in terms of the invisible (1916, xii). Perrin’s more technical work is collected in his Brownian Movement and Molecular Reality, which appeared in French in 1909 and was translated into English in 1910. In this book, Perrin makes almost no methodological remarks, but I shall attempt to reconstruct the structure of his argument for the reality of molecules in a way that his methodology is clearly brought out. The key point of his strategy is this: “Instead of taking this hypothesis [the atomic hypothesis] ready made and seeing how it renders account of the Brownian movement, it appears preferable to me to show that, possibly, it is logically suggested by this phenomenon alone, and this is what I propose to try” (1910, 7). Perrin takes it that the atomic hypothesis is an already given plausible hypothesis, its plausibility being grounded in the fact that it remains the only serious admissible explanation of Brownian movement. Reviewing the work of Léon Gouy and others, Perrin suggests that several potential causes of the movement can be safely eliminated and that, in particular, the cause of the movement is internal and not external (cf. 1901, 6). This kind of eliminative approach paves the way for rendering the standard atomic explanation of Brownian movement “by the incessant movements of the molecules of the ﬂuid” the only serious admissible explanation. This is not enough to render it true or probable; and yet, by the end of his reasoning, Perrin does think that it is probable and true. This happens

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because Perrin succeeds in showing that Brownian movement is itself an instance of molecular movement and hence that it obeys the laws of the molecular movement. Hence, it can be used to (a) determine Avogadro’s number and (b) specify the individuating properties of atoms. To see all this, let us follow his steps in some detail. Perrin’s theoretical schema proceeds as follows. Let us suppose we have a uniform emulsion (all granules are identical) in equilibrium that ﬁlls a vertical cylinder of cross section s. Consider a horizontal slice contained between the levels , where this slice is enclosed between two semi-permeable pistons—they are permeable to the molecules of water but impermeable to the granules. Each piston is subjected to osmotic pressure. This slice of granules does not fall; hence there must be an equilibrium between the force that tends to move it upward (viz., the difference of the osmotic pressures) and the force that tends to move it downward (viz., the total weight of the granules less the buoyancy of the liquid). Having estimated both forces, Perrin arrives at the equation of the distribution of the emulsion 2/3Wlog(n0/n) = j(D−d )gh

(1)

where W is the mean granular energy, j the volume of each granule, D its density, d the density of the intergranular liquid and n and n0 respectively the concentrations of the granules at the two levels separated by height h. The task then is to measure all magnitudes other than W; hence, to determine W (cf. 1910, 24). The important assumption that Perrin makes is that the mean granular energy W of the particles in Brownian motion is equal to mean molecular energy W¢. In other words, he argues that the Brownian particles behave as large molecules and hence obey the laws of the gases (see also 1916, 89, 92). Indeed, the ﬁrst few sections of his 1910 work aim to motivate this claim. The mean kinetic energy W¢ of the molecules of a gram-molecule of a gas is a function of Avogadro’s number N. It is equal to (3R/2N)T, where T is the absolute temperature of the gas and R is the constant of the perfect gases (cf. 1910, 19). Hence, W¢ = (3R/2N)T

(2)

Perrin relies on van’t Hoff’s proof that the invariability of energy (viz., that the mean kinetic energy is the same for all gases at the same temperature) holds also for the molecules of dilute solutions and generalized it further to all ﬂuids, including emulsions. The claim that “the mean energy of translation of a molecule [is] equal to that possessed by the granules of an emulsion”—that is that W = W¢—is crucial. It paved the way for an experimentum crucis: either W = W¢ or W

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¹ W¢ and given that both W and W¢ could be calculated, we might have “the right to regard the molecular theory of this movement as established” (1910, 21). Being an extremely skillful experimenter, Perrin managed to prepare suitable emulsions of gamboge and mastic, with spherical granules of radius a. (1) thus becomes 2/3Wlog(n0/n) = 4/3pα3(D−d )gh.

(1¢)

Here again, all magnitudes but W are measurable. Determining the ratio (n0/n) was quite demanding, but Perrin used the microscope to take instantaneous snapshots of the emulsion. Determining the value a of the radius was even more demanding, but Perrin used three distinct methods to achieve this, one relying on Stokes’s equation (capturing the movement of a sphere in a viscous ﬂuid), and two without applying this equation (using, instead, a camera lucida). These calculations were in impressive agreement, which led Perrin to conclude, among other things, that the otherwise controversial application of Stokes’s equation (because it was meant to apply to continuous ﬂuids) was indeed legitimate. When all was said and done, Perrin was able to calculate the granular energy W (which is independent of the emulsion chosen). If W = W’ (if, that is, the Brownian particles do behave as heavy molecules and hence if the laws of the gases do hold for them too), there is a direct prediction of Avogadro’s number N from (1¢) and (2), that is, (RT/N)log(n0/n) = 4/3pa3(D−d)gh

and N = 3RTlog(n0/n)/4pa3(D−d)gh.

(1²)

This prediction could then be compared with known calculations of N based on the kinetic theory of gases, for example, that by van der Waals’s (N = 6×1023) (cf. 1910, 44). Perrin made a number of experiments and concomitant calculations and the agreement was always impressive. As he put it, “It is manifest that these values agree with that which we have foreseen for the molecular energy. The mean departure does not exceed 15 percent and the number given by the equation of van der Waals does not allow for this degree of accuracy” (Perrin 1910, 46). Perrin became immediately convinced that “this agreement can leave no doubt as to the origin of Brownian movement” (1910, 46). “[A]t the same time,” he said, “it becomes very difﬁcult to deny the objective reality of molecules” (1916, 105). What convinced him, he says, was that on any other hypothesis (better, on the negation of the atomic hypothesis), the expected

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value of N from the study of the movement of granules suspended in a liquid would be either inﬁnite or zero—it would be inﬁnite if all granules actually fell to the bottom of the vessel, and zero if the fall of the granules was negligible. Hence, on the hypothesis that matter has not molecular structure, the probability that the predicted value of N would be the speciﬁc one observed would be zero; on the contrary, this probability is high given the atomic hypothesis. This, Perrin noted, “cannot be considered as the result of chance.” Perrin takes another step. He stresses that the determination of Avogadro’s number by (1²) affords a determination of the properties of molecules that can be calculated on its basis. Moreover, this determination of N is now “capable of unlimited precision,” since all magnitudes in (1²) other than N can be determined “to whatever degree of precision desired.” Hence, Perrin went on to calculate N and to conclude that its value is N=7×1023. From this, he calculated the weight and the dimensions of molecules. He also reported on a number of other calculations of Avogadro’s number, including: the measurement of the coefﬁcient of diffusion; the mobility of ions; the blue color of the sky (the diffraction of the sunlight by the atmospheric molecules); the charge of ions; radioactive bodies; and the infrared part of the spectrum of the black-body radiation. Though all these calculations were less accurate than his own, Perrin took them to prove molecular reality (cf. 1910, 90), since they are in considerable agreement, showing that this number is “essentially invariant” (1910, 74). Here is his conclusion: I think it impossible that a mind, free from all preconception, can reﬂect upon the extreme diversity of the phenomena which thus converge to the same result, without experiencing a very strong impression, and I think it will henceforth be difﬁcult to defend by rational arguments a hostile attitude to molecular hypotheses, which, one after another, carry conviction, and to which at least as much conﬁdence will be accorded as to the principles of energetics (1910, 91).

What then is the logical structure of Perrin’s argument? Recall his claim that he was after a crucial experiment for the reality of atoms. Of course, there are no crucial experiments in the strict sense of the expression, viz., in the sense of disproving a hypothesis or of proving a hypothesis. But as Poincaré has put it, an experiment can condemn a hypothesis, even if it does not—strictly speaking—falsify it. Perrin’s argument was precisely meant to condemn the denial of the atomic hypothesis—which, of course, is not to say that he intended to condemn energetics. As we have just seen, he did think (and he had already noted this in his 1903 work) that energetics need not imply the denial of the atomic hypothesis, namely, that matter is continuous.

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The way, then, I think Perrin’s argument should be reconstructed is as follows. With the argument sketched above, Perrin has made available two important probabilities, namely, Prob (n=N/AH) = very high Prob(n=N/-AH) = very low

That is, the probability that the number of molecules in a gram-molecule of a gas (including an emulsion, which does behave as a gas) is equal to Avogadro’s number given the atomic hypothesis is very high, while the probability that the number of molecules is equal to Avogadro’s number given the denial of the atomic hypothesis is very low. These two likelihoods can be used to specify the so called Bayes factor f. f= prob(n=N/-AH)/prob(n=N/AH)

Bayes’s theorem states prob(AH/n=N) = prob(n=N/AH)prob(AH)/prob(n=N)

where: prob(n=N) = prob(n=N/AH)prob(AH)+prob(n=N/−AH)prob(−AH).

Using the Bayes factor, Bayses’s theorem becomes: prob(AH/n=N) = prob(AH)/(prob(AH) + f prob(-AH)).

Perrin’s argument then can be put thus: 1. f is very small. 2. N = n is the case. 3. prob(AH) is not very low. Therefore, prob(AH/n=N) is high. Now, premise 1 (that f is very small) is established by the body of Perrin’s demonstration, which shows that given the denial of the atomic hypothesis, it is extremely unlikely that Avogadro’s number has the speciﬁc value it does. Premise 2 is established by a series of experiments involving different methods and different domains. Premise 3 is crucial, since it is required for the probabilistic validity of Perrin’s argument. It speciﬁes the prior probability of the atomic hypothesis and without the prior probability the argument noted above would commit the base-rate fallacy. Perrin’s preparatory eliminative work has aimed to show that, by eliminating several alternative potential explanations of Brownian movement,

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the atomic hypothesis has gained at least some initial plausibility which is reﬂected in its having some prior probability of being true. Actually, the following might be added. There is a rare case in which the prior probability of a hypothesis does not matter, and this is when the Bayes factor is zero. This happens when just one theory can explain the evidence. Then, we can dispense with the priors. If the Bayes factor is zero, no matter what prob(AH) is, the posterior probability prob(AH/ n=N) is unity. And the Bayes factor is zero if prob(n=N/-AH) is zero. Recall Perrin’s wording: “That, in the immense interval [0, inﬁnity] which a priori seems possible for N, the number should fall precisely on a value so near to the value predicted, certainly cannot be considered as the result of chance” (1910, 46; cf. 1916, 105). This is almost tantamount to saying that his experiments established that prob(n=N/-AH) = 0. This kind of claim would (and does) explain Perrin’s conﬁdence that the atomic hypothesis has been “established”; that he has offered “a decisive proof” of it (1916, 104). Admittedly, there is room for manoeuver here, since it might be argued that prob(n=N/-AH) has, after all, a small ﬁnite value. In that case, some reliance on the prior probability prob(AH) is inevitable and the usual philosophical dialogue would kick off: How are the priors ﬁxed? Are they objective? If not, is the case for the reality of atoms strong? I do not want to follow this dialogue now (except to note that I agree with Achinstein that prior probabilities need not be subjective or idiosyncratic degrees of belief). I want to stress, however, that it seems to me that the major role Perrin’s work has had in persuading scientists to adopt the atomic hypothesis lies mostly in its presenting a rare but very important case in which the posterior probability of the atomic hypothesis becomes (almost) unity—given, of course, that it is assigned a non-zero prior, which it seems everybody but Duhem did. A chief point that Perrin makes is precisely that size does not matter, but causal role does! Like microbes, molecules do end up being the objects of possible sensation—in the broad sense in which Perrin understands this, namely, to include detection through the microscope. Hence Perrin, like Pasteur before him, places the atoms ﬁrmly within the laboratory, grounding their causal role and offering experimental means for their detection and the speciﬁcation of their properties. This is of great signiﬁcance because it becomes clear that Perrin’s argument should be compelling for anyone who does not take it that strict naked-eye observability is a necessary condition for accepting the reality of an entity. It should also be compelling for anyone who thinks that continuity of causal role is a criterion for accepting the reality of an entity—irrespective of whether some instances of this entity are observable, while others are not.

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By the same token, it becomes clear that the real issue about the so-called theoretical entities is not their unobservability, but rather their accessibility. In this sense, what Ostwald aptly called “the scientiﬁc horizon” is not ﬁxed and immovable; claims that are once below it can move above it. What facilitates this change is not that some suspicious entities become observable, but rather that some suspicious entities enhance their explanatory role: claims about them are highly conﬁrmed by ordinary scientiﬁc methods; their causal role is established experimentally; they become the locus of uniﬁcation of disparate phenomena. Perrin’s case is instructive because it shows vividly that there are points after which resistance to accepting the reality of certain entities becomes dogmatic and mostly motivated by philosophical prejudice (cf. Krips 1986).

3. ENTER ACHINSTEIN The core of Achinstein’s claim is that the calculation of Avogadro’s number by Perrin’s experiments using (a notational variant of) equation (1²) above conﬁrmed Perrin’s core hypothesis, namely that molecules exist and that Avogadro’s number is 6×1023. More speciﬁcally, Achinstein takes proposition T to express the core hypothesis of the atomic theory: T = Chemical substances are composed of molecules, the number N of which in a gram molecular weight of any substance is (approximately) 6 ×1023.

He takes it that this proposition already has had some support from background knowledge b and other evidence. In particular, he rightly claims that T’s plausibility (and in fact its non-zero probability) was based on the application of “causal eliminative” reasoning (Achinstein 2001, 255). Actually, the initial probability that Achinstein assigns (or claims that Perrin assigned) to T, given background knowledge, is Prob(T/b)>1/2. He then claims that Perrin’s experimental result led him to accept the following proposition: C = The calculation of N done by means of Perrin’s experiments on Brownian particles using equation [(1²)] is 6×1023, and this number remains constant [when several parameters in equation (1²) are varied].

Achinstein goes on to claim that C is more probable given the truth of T than without T and to make his crucial point that C conﬁrms T. This is because given (i) prob(C/T&b) > prob(C/b) (ii) prob(T/b)>0 (iii) prob(C/b)>0

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it follows from an application of Bayes’s theorem that (iv) prob(T/C&b)>prob(T/b). Moreover, since he has assumed that prob(T/b)>1/2, it follows that (v) prob(T/C&b)>1/2. Achinstein put this in the service of his own theory of evidence. In broad outline, two statements are the main features of Achinstein’s theory. The ﬁrst is that for something e to be evidence for a hypothesis H, it must be the case that the probability of H given e should be higher than ½. That is, prob(H/e)>1/2. So, Achinstein works with an absolute concept of evidence: e is evidence for H only if e is not evidence for the denial of H. This is meant to capture the view that evidence should provide a good reason to believe. But, second, this absolute conception of evidence (though necessary) is not sufﬁcient for reasonable belief. What is added is that the probability that there is an explanatory connection between H and e, given H and the evidence e, should be more than ½. Call E(H/e) the claim that there is an explanatory connection between H and e. Achinstein’s second feature is that prob(E(H/e)/H&e)>1/2. More accurately, e is evidence (a good reason) for H only if the product of prob(E(H/e)/e&H) with prob(H/e) should be greater than ½. Given this conception, (v) is far more important than (iv) above. Besides, the foregoing requirement that there is an explanatory connection between the hypothesis and the evidence is satisﬁed in Perrin’s case, and Achinstein argues that (vi) prob(E(T/C&b)/T&C&b)>1/2. Of course, there is no guarantee that the product of prob(E(T/C&b)/T&C&b) with prob(T/C&b) is great than ½. The values of the two factors should be chosen by hand such that their product is greater than ½. Achinstein argues that they can be plausibly taken to be sufﬁciently high in Perrin’s case. But this is certainly an extra and defeasible assumption. In any case, Achinstein’s conclusion is that not only did Perrin provide evidence for the reality of molecules, but also that this is best captured by his own theory of evidence. It seems to me this is not right. Achinstein’s reconstruction leads to a weak conclusion vis-à-vis the case at hand. If Perrin just succeeded in establishing that prob(T/C&b)>1/2, it seems there is no explanation of why his achievement was taken (by himself and almost everybody else) to be decisive in establishing the reality of atoms. On Achinstein’s reconstruction, all Perrin achieved was to show that the atomic hypothesis is more likely than not. This is not a mean feat, of course. But it is hardly sufﬁcient to sway the balance in favor of the atomic hypothesis in the way it actually did. There

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is no natural way to increase the posterior probability of T in Achinstein’s account, unless T is given a very high prior probability and the product prob(E(T/C&b)/T&C&b) × prob(T/C&b) is ﬁddled with. My account, on the contrary, does show that AH (which is roughly equivalent to Achinstein’s T) becomes very probable, given Perrin’s experimental results. Besides, my account, unlike Achinstein’s, captures the strength of the evidence. More speciﬁcally, Achinstein notes that his own account of evidence cannot easily explain why some qualities of some piece of evidence (e.g., precision and directness) provide stronger support for a hypothesis than pieces of evidence that lack these qualities (Achinstein 2001, 262). (Achinstein ends up adding these qualities by hand into his theory.) In my account, the precision of the determination of Avogadro’s number and the diversity of means by which this precise determination was achieved makes it all the more improbable that this will be the right number (that is, that n will be equal to N) given the negation of AH. Defending his own theory of evidence against other attempts to reconstruct and explain Perrin’s achievements, Achinstein (2001, 259) notes that his own account (i) is better than Salmon’s (which was based on the common cause principle) because on his own account the molecular hypothesis does get conﬁrmed by the evidence; and (ii) is better than an ordinary hypothetico-deductive reconstruction, since it does not suppose a deductive link between the molecular hypothesis and Perrin’s results. It’s patently the case that my own account fares at least as well as Achinstein’s vis-à-vis the other two stories. Achinstein is very sensitive to the charge that Perrin’s reasoning might be circular, since Perrin seems to assume the reality of the molecules before he tries to prove it (Achinstein 2001, 259). His answer to this charge is that Perrin does not start with an unquestioned assumption that molecules exist, but that he does take this assumption to have some initial probability, based on the causal-eliminative reasoning that preceded his own strategy. I think this is right and is actually brought out by my own account too. Hence, my account offered in the previous section has all the strengths and none of the weaknesses of Achinstein’s.

4. LESSONS FOR SCIENTIFIC REALISM Perrin’s case highlights a claim that lately I tend to ﬁnd all the more forceful, namely, that commitment to the reality of speciﬁc explanatory posits is a matter that depends on the context. This is so because, as I have argued in Knowing the Structure of Nature (Psillos 2009), there are two types of evidence that are brought to bear on the truth of scientiﬁc hypotheses

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(and which inform judgments of prior probability and of conﬁrmation). The ﬁrst type is ﬁrst-order evidence and is related to whatever evidence scientists have in favor of a hypothesis. In Perrin’s case, this evidence includes the several methods of determination of Avogadro’s number, the evidence that goes into ﬁxing a non-zero prior probability to the atomic hypothesis (e.g., the evidence that the cause of Brownian movement is internal to the ﬂuid), and so on. The second type of evidence, what I call second-order evidence, comes from the track record of scientiﬁc theories and/or meta-theoretical (philosophical) considerations that have to do with the reliability of scientiﬁc methodology. This, for instance, is evidence that many past explanatory hypotheses have been abandoned, that there have been alternative potential explanations of some phenomena that came to be accepted later on, and so on. This kind of (historical-philosophical) evidence does not concern particular scientiﬁc theories but science as a whole. It is the kind of evidence that, for instance, motivates the pessimistic induction. I have argued that the proper philosophical task is to balance these two kinds of evidence and that this balancing is context-dependent (Psillos 2009). Perrin’s case is very instructive precisely because it shows that the context can settle issues of balance. For instance, it is clear that Perrin’s case is so strong that the ﬁrst-order evidence for the reality of molecules takes precedent over the second-order evidence there might be for being skeptical about explanatory posits. The fact that other explanatory hypotheses have failed in the past is trumped—in this context—by the strength of the ﬁrst-order evidence. It would be folly, however, to think that considerations concerning the second-order evidence should be totally wiped out—or worse, that these are considerations to which working scientists are blind. These are meta-theoretical or philosophical considerations that do get into the evidential balance sheet nonetheless. Achinstein seems to imply that these considerations are almost irrelevant to the issue of the reality of explanatory posits (Achinstein 2002, 495). They are not. Achinstein (2002) is right in stressing that the proper battleground for scientiﬁc realism is made of speciﬁc arguments in favor of the reality of speciﬁc unobservable entities. Given the key role that explanatory considerations play in specifying the prior probabilities of certain hypotheses (e.g., the atomic hypothesis), it is an exaggeration to call the proper argument for realism “experimental.” Better put, the proper argument for realism is explanatory-experimental, the latter component meaning to stress that causal contact with the explanatory posits enhances the claim to their reality. But Achinstein (2002) seems to want to draw the further conclusion that the realism debate as it has been conducted so far is independent of the kind of argument for realism you get from Perrin. This is wrong.

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I will conﬁne myself to two points. First, Perrin already works within what I have elsewhere (Psillos forthcoming [a]) called “the realist framework.” Simply put, Perrin already works within the framework that seeks explanation of the manifest behavior of bodies while positing typically unobservable entities; hence he adopts a framework that allows for the assignment of prior probabilities to “invisible” entities. This is not something that evidence or a priori reasoning forces on anyone. To see this, just think of die-hard opponents of realism (Duhem? van Fraassen?) who refuse to adopt this framework; and hence, who refuse to assign nonzero (Duhem) or anything-but-vague (van Fraassen) prior probabilities to speciﬁc explanatory posits—such as the molecules. To put the point somewhat crudely, Perrin’s argument does not amount to an argument for scientiﬁc realism in general (as opposed to an argument for the reality of certain entities) because it is launched within the realist framework. Hence, the debate about the realist framework itself is alive and well. My second point concerns the relation between Perrin’s argument and the so-called “no miracles” argument (NMA) for realism. Achinstein intends to distance Perrin’s argument from NMA (Achinstein 2002, 486). But he does not have to do so. The relation between Perrin’s argument and NMA is precisely the one anticipated by realists like Boyd and myself (Psillos 1999), namely, Perrin’s argument is one of the very many ﬁrst-order instances of inference to the best explanation (IBE), which feed the premises of the realist argument that IBE is reliable. And this is precisely what the NMA aims to do, namely, to defend the reliability of IBE. I have defended all this in a forthcoming paper (Psillos forthcoming [b]). What Perrin’s case has taught me, among other things, is that the ﬁrst-order IBEtype of reasoning that leads to commitment to the reality of certain explanatory posits has a ﬁne structure and a strength that is shaped, by and large, by the context.

REFERENCES Achinstein, P. 2002. Is There a Valid Experimental Argument for Scientiﬁc Realism? Journal of Philosophy 99 (9): 470–95. ——— . 2001. The Book of Evidence. New York: Oxford University Press. Krips, H. 1986. Atomism, Poincaré and Planck. Studies in History and Philosophy of Science 17 (1): 43–63. Lalande, A. 1913. Philosophy in France in 1912. Philosophical Review 22 (4): 357–74. Perrin, J. 1916. Atoms, trans. D. L. Hammick. London: Constable & Company Ltd. ——— . 1910. Brownian Movement and Molecular Reality, trans. F. Soddy. London: Taylor and Francis. ——— . 1903. Traité de Chimie Physique: Les Principes. Paris: Gauthier-Villars.

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Psillos, S. Forthcoming (a). Choosing the Realist Framework. Synthese, DOI 10.1007/s11229-009-9606-9. ——— . Forthcoming (b). The Scope and Limits of the No-Miracles Argument. In The Philosophy of Science in a European Perspective, vol. II, ed. F. Stadler et al. Springer. ——— . 2009. Knowing the Sructure of Nature. London: MacMillan-Palgrave. ——— . 1999. Scientiﬁc Realism: How Science Tracks Truth. London & New York: Routledge.

NOTES 1. I dedicate this essay to Peter, who has taught me (and us, I hope) how important it is to combine philosophical rigor with historical sensitivity.

15 Achinstein and the Evidence for Evolution Richard A. Richards

1. INTRODUCTION Peter Achinstein begins his Book of Evidence with the striking claim that “standard philosophical theories about evidence are (and ought to be) ignored by scientists” (Achinstein 2001, 3). The problem with standard theories of evidence, according to Achinstein, is that they “are based on assumptions incompatible with ones scientists make when they speak of, and offer, evidence for hypotheses” (3). Achinstein is right as far as he goes, but he could have gone even further. For historians of science, as well as scientists, the standard philosophical ways of conceiving evidence are of little use, and may in fact be counterproductive in the efforts to think clearly about what counts as evidence for a scientiﬁc hypothesis. In his Book of Evidence, Achinstein lays out what would be required for a concept of evidence to be useful for scientists. First, it must be strong enough to warrant belief in a hypothesis—not merely raise its probability (Achinstein 2001, 8–9). Second, it must be empirical—not a priori, semantic, or merely mathematical (Achinstein 2001, 5, 26, 28). In other words, scientists assume that evidence provides a good reason to believe a hypothesis—not just some reason, and on the basis of the empirical facts, and not just logical or formal relations either. I endorse Achinstein’s criticism of standard philosophical theories of evidence and both of his conditions of adequacy, relative to the assumptions of scientists. But we can also ask about the adequacy of a concept of evidence for historians of science, who try to understand the actual acceptance and rejection of hypotheses on the basis of evidence. For historians, a concept of evidence must help us understand not just what should count as evidence for a hypothesis in general, that is, what constitutes a good reason for anyone to believe, but what in fact did count as evidence, that is, what caused belief in a hypothesis. This is not to say that historians never care about what should count as evidence. But sometimes this concern is contextual, and is

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about what a scientist should believe, given what he or she knows, or is in a position to know. Historians might, for instance, ask if Galileo was justiﬁed in believing the heliocentric model of the cosmos rather than the geocentric, given what he knew at the time or was in a position to know. There are then two main tasks for a historically adequate theory of evidence: ﬁrst, a prescriptive task to provide conditions for having a good reason to believe a hypothesis; second, a descriptive task to provide conditions for having an actual reason to believe. And for historians both tasks must be sensitive to context. As we shall see, while standard philosophical theories of evidence are inadequate relative to these tasks, Achinstein’s framework provides the conceptual resources to carry out both tasks and with sufﬁcient sensitivity to context. To see more precisely what a historically adequate theory of evidence requires, we shall ﬁrst look at a puzzling case in the history of science: Charles Darwin’s belief in branching evolution prior to his acceptance of a mechanism (natural selection), and his seemingly inconsistent views about whether he was justiﬁed in doing so. Second, we will look at standard philosophical theories of evidence, to see how they are inadequate for understanding the details of Darwin’s ambivalence. Third, we shall see how Achinstein’s framework can help us understand the complexities here. In particular, his concepts of subjective and epistemic situation evidence will be of value in understanding the details of Darwin’s views about evidence and evolution. Subjective evidence gives us a descriptive framework, while the idea of an epistemic situation gives us the resources to think about the prescriptive question relative to a variety of contexts.

2. A DARWINIAN PUZZLE After Darwin’s return from the ﬁve-year Beagle voyage at the end of 1836, he turned his attention to the “mystery of mysteries,” the origin of species. During this time, and before his discovery in 1838 of natural selection, he began speculating about the possibility of branching evolution: the formation of new species by branching and modiﬁcation. (His ﬁrst branching diagram appeared in the middle of 1837 in his “B” notebook.) Two decades later in the Origin, he told us that his belief in branching evolution was on the basis of what the historian of science Mary Winsor calls the “taxonomic facts,” which include the hierarchical groupings of organisms generated by similarities and differences (Winsor 2009). It is a truly wonderful fact—the wonder of which we are apt to overlook from familiarity—that all animals and all plants throughout all time and space should be related to each other in group subordinate to group, in the

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manner which we everywhere behold—namely, varieties of the same species most closely related together, species of the same genus less closely and unequally related together, forming sections and sub-genera, families, orders, sub-classes, and classes. (Darwin 1964, 128)

At the end of the Origin, Darwin ﬁrst claimed that he believed in branching evolution on the basis of these taxonomic facts. Then he claimed that he “should without hesitation” adopt this hypothesis about branching evolution on the basis of just these facts. . . .The several classes of facts in this chapter seem to me to proclaim so plainly that the innumerable species, genera, and families of organic beings, with which this world is peopled, have all descended, each within its own class or group, from common parents, and have all been modiﬁed in the course of descent, that I should without hesitation adopt this view, even if it were unsupported by other facts or arguments. (Darwin 1964, 457–8, my emphasis)

But earlier in the Origin, Darwin seemed inclined in another direction, toward the view that the taxonomic facts were not sufﬁcient to justify belief in branching evolution. . . . [A] naturalist . . . might come to the conclusion that each species . . . had descended from other species. Nevertheless, such a conclusion, even if well founded, would be unsatisfactory, until it could be shown how the innumerable species inhabiting this world had been modified. (Darwin 1964, 3, my emphasis)

Here he seems to have claimed instead that the taxonomic facts were by themselves insufﬁcient. Also required was a suitable mechanism of change, natural selection. Darwin’s views about whether the taxonomic facts were evidence for branching evolution are complicated and puzzling in several ways. First, he seems to have claimed that he in fact came to believe in branching evolution based on the taxonomic facts. Second, he seems to have claimed that he should believe in branching evolution just on the basis of the taxonomic facts. But third, he also seems to have claimed that something more was required—mechanism. The ﬁrst claim seems to be descriptive, about what actually caused him to believe in branching evolution. The second claim seems to be prescriptive, about what he would be justiﬁed in believing. The third claim seems to be prescriptive, not about his own belief, but the belief of “a naturalist”—some abstract naturalist, or perhaps his fellow naturalists of the time. But why would he be justiﬁed in believing in branching evolution on the basis of taxonomic facts, if others were not? Shouldn’t the same facts that justiﬁed his belief also justify the beliefs of his fellow naturalists or some abstract naturalist? To fully understand

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Darwin’s views here, we need some way of assessing both descriptive and prescriptive claims about evidence relative to Darwin, and relative to either some abstract naturalist, or his contemporary naturalists. An adequate concept of evidence should render situations like this explicable. But standard philosophical theories of evidence do not seem up to this task.

3. STANDARD PHILOSOPHICAL THEORIES OF EVIDENCE There have been theories of scientiﬁc evidence as long as there has been something we can reasonably call science. Some of the standard philosophical theories go back to the beginnings of modern science in the views of Francis Bacon, René Descartes, and Isaac Newton. More recent theories originated in the nineteenth century in the work of John Herschel, William Whewell, John Stuart Mill, and Charles Peirce. The twentieth century has given us the theories of Carl Hempel, Rudolf Carnap, Karl Popper, and more. I cannot address the full variety and complexity of these theories here, but we can think about them in more general and schematic terms. John Norton has done so, arguing that there are really three main families of theories of evidence: inductive generalization, hypothetical induction, and probabilistic. In each of these families, the concept of evidence is prescriptive, and the evidential relation is formalized in distinctive ways, relative to a distinctive inductive schemata. The ﬁrst family of theories of evidence is inductive generalization, and is based on the principle that “an instance conﬁrms a generalization” (Norton 2003, 652). This can be from the very simple enumerative induction where “an instance of an A that is B conﬁrms the generalization that all A’s are B’s” (652). But it also includes more complex principles such as Mill’s joint method of agreement and disagreement. The important idea here is that there is some formal schema that gives the evidential requirements for whether an observation should count as evidence for a hypothesis. For instance, is the observation of some black ravens evidence for the hypothesis that all ravens are black? If it satisﬁes the formal schema, the answer is “yes.” The second family of theories of evidence, according to Norton, is hypothetical induction, and is based on the idea “that the ability of a theory, possibly with auxiliary assumptions, to entail the evidence is a mark of its truth” (Norton 2003, 653). This is the familiar hypothetico-deductive method, whereby a hypothesis is conﬁrmed to some degree when its predictions are veriﬁed by observation. The abstract, formal schema here goes something like: “if hypothesis h, then some observation o; if o, therefore

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probably h.” Because this requirement is widely seen as too weak, a variety of restrictions have been proposed based on the requirements that the prediction be unlikely if the hypothesis is false, that the hypothesis be simple or parsimonious, or that the hypothesis be the best explanation. Here, as in the case of inductive generalization, these are prescriptive theories, giving the conditions of adequacy for when we are justiﬁed in taking some observation to be evidence for a hypothesis, and based on some schematic formalization that lays out the proper form of reasoning. The third family of theories of evidence is probabilistic and based on the idea that the evidential relation conforms to the demands of some “deﬁnite calculus, usually the probability calculus” (Norton 2003, 659). This family is most at home when stochastic processes are involved. These theories sometimes also assert that “degrees of belief should correspond to the same calculus as governs stochastic processes in the physical world” (660). Here, as in the two other families of theories, the claim is prescriptive, about what should count as evidence, and it is based on some formal schematization, typically the probability calculus and Bayes’s theorem. There are well-known problems with each of these theories of evidence, as we have seen in the historical debates about Hume’s problem of induction, the Raven paradox, and the strange predicate “grue.” My focus here, however, is not on these problems with induction, but with the inadequacy of these standard theories for understanding the history of science. The ﬁrst and most obvious problem is that all three families of theories of evidence are prescriptive rather than descriptive; they give the conditions of adequacy for what should count as evidence, not what in fact has counted as evidence. Newton gave us his rules of reason to tell us how we should reason, not to describe actual reasoning—even if he thought his own reasoning conformed to his Rules. Bacon, Descartes, Herschel, Whewell, Mill, and Peirce similarly gave guidance on what should count as evidence, not what has in fact counted as evidence. Contemporary philosophical accounts of evidence follow in this tradition. Elliott Sober, for instance, at the beginning of his Evidence and Evolution, seems to endorse this tradition, telling us that “historians and sociologists study science as it is, whereas philosophers of science study science as it ought to be. Philosophy of science is a normative discipline” (Sober 2008, xv). Sober then gives an extended analysis of prescriptive thinking about evidence. But to understand the Darwin case, we need to know whether or not Darwin did in fact believe in branching evolution on the basis of the taxonomic facts, not just about whether he should have believed. If philosophical theories of evidence are going to be useful to historians of science, they must provide the resources suitable for thinking about the

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historical facts—what actually counted as evidence for scientists in context, not just the prescriptive ideal. But even the prescriptive question poses problems for standard theories of evidence. How do we determine what Darwin or anyone else should have believed? The second problem with standard philosophical theories of evidence, that they are not empirical, arises because these theories typically give formal, a priori criteria for what should count as evidence. On the simplest enumerative version of inductive generalization, something counts as evidence for a hypothesis because it satisﬁes the hypothesis. Any observed A that is also B satisﬁes the hypothesis “all A’s are B’s,” and can therefore serve as evidence for that hypothesis. Since this is a formal theory, it applies whenever the formal relations are satisﬁed— whenever the schema is instantiated. Because it is formal, it is also a priori, in that the “satisfaction” requirement does not depend on empirical facts, but on the logical relation between “A is a B” and “all A’s are B’s.” We see a similar formalization in Mill’s methods, and those theories of evidence based on the probability calculus and Bayes’s theorem. In each case, since the prescriptive criteria are formal, they are a priori. As Achinstein argues, however, the concept of evidence used by scientists is not a priori. It is empirical in that it relies on empirical assumptions. For example, whether an instance of an “A that is a B” counts as evidence for the generalization that “all A’s are B’s” depends on empirical facts about the A’s and B’s. On an a priori theory of evidence, by contrast, the fact that a sample of water has a particular melting point is evidence for the hypothesis that all samples of water have that melting point, and the fact that a piece of wax has a particular melting point is evidence that all samples of wax have that melting point. This is because both inferences satisfy the general, formal schema. But we know that water and wax are different in important ways; instances of water are uniform in ways that instances of wax are not. We can therefore make generalizations about water that we cannot make about wax. In particular, the melting points of water are uniform in the ways that the melting points of wax are not. Consequently, the empirical facts justify a generalization about the melting point of water, but not one about the melting point of wax. Knowledge of these differences will surely be relevant to the justiﬁcation of the belief in a particular hypothesis about melting points (Norton 2003, 649). Because standard philosophical theories of evidence are formal and a priori, they render the evidential relation insensitive to the empirical facts. This has implications for the history of science. When historians ask what Darwin or anyone else should have believed, they may want to know what he should have believed irrespective of anything else. But they may

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also want to know what he should have believed given his historical context—what he was in position to know or believe about the empirical facts. To answer such contextual questions, an adequate theory of prescriptive evidence must be able to take context into account. As we shall see, Achinstein’s framework provides the necessary resources.

4. ACHINSTEIN ON EVIDENCE The most basic, and perhaps most important feature of Achinstein’s theory of evidence is its recognition of multiple concepts of evidence. Achinstein introduces these concepts by reference to Heinrich Hertz’s famous experiments with cathode rays in 1883. Hertz wanted to know if cathode rays were electrically charged—if they “gave rise to electrostatic forces” (Achinstein 2001, 14). To answer this question, Hertz constructed an experimental apparatus whereby cathode rays would be sent through a glass tube that had an electrometer attached to measure any electrostatic effect. The results of this experiment were negative, and Hertz concluded that “cathode rays are electrically indifferent” (15). A later experiment by J. J. Thomson in 1897, however, arrived at a different outcome, suggesting that cathode rays were in fact electrically charged. Thomson achieved this outcome, in part, by better evacuating the air from the glass tube (17). Were the negative results from the 1883 experiment evidence for the hypothesis that cathode rays are electrically indifferent? Achinstein argues that we can answer this question in different ways. We could answer by saying that given what Hertz knew in 1883, the experiment did indeed provide evidence for the hypothesis. Or we could answer that between 1883 and 1897 the experiment provided evidence, but not after 1897. Or we could answer that the experiment never was evidence for the hypothesis, even though Hertz believed it was. These three ways of answering the question about evidence, according to Achinstein, reﬂect the use of different concepts. Using one concept we might answer in one way, but using another concept we might answer in another way. Achinstein identiﬁes four fundamental concepts of evidence: subjective, epistemic situation, potential, and veridical. The subjective concept of evidence, according to Achinstein, would be focused on what Hertz actually believed, based on everything else he believed or knew. The basic idea is that the outcome of the experiment e is evidence for the hypothesis h that cathode rays are electrically inert, if and only if Hertz believed that e was evidence for h, he believed that h was true, and his reason for believing that h was true is e (Achinstein 2001, 25). This is a subjective concept in that it depends on what a

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particular subject, Hertz, believed and why he believed it. It is also a descriptive concept in that it tells us about what actually served as evidence, not what should have served as evidence. Epistemic situation evidence, according to Achinstein, is objective in that it does not depend on the actual beliefs of individuals, but it is relativized to an epistemic situation at a particular time. [An epistemic situation] is an abstract type of situation in which, among other things, one knows or believes certain propositions are true, one is not in a position to know or believe that others are, and one knows(or does not know) how to reason from the former to the hypothesis of interest, even if such a situation does not in fact obtain for any persons. (Achinstein 2001, 20)

Using this concept of evidence, we could ask what Hertz was in a position to know or believe, or not know or believe in 1883 (regardless of what he actually knew or believed), and how that might provide a good reason to believe that cathode rays were electrically inert. This concept of evidence is prescriptive in that it focuses on what can justiﬁably be inferred, not what was actually inferred. Alternatively, we could ask instead whether Hertz’s experiment in 1883 was evidence for the hypothesis that cathode rays are electrically inert, regardless of what anyone knows or believes. And we could ask whether Thomson’s experiment in 1897 was evidence for this hypothesis, regardless of what anyone knows or believes. This way of framing the evidential question does not require reference to any actual beliefs, nor does it invoke an epistemic situation. It is, in effect, asking whether the experiments were really evidence. Or, as Achinstein puts it, whether they were a “sign” of the truth of the hypothesis. There are two versions of this way of thinking about evidence. The ﬁrst, weaker version, potential evidence, does not presuppose the truth of the hypothesis. “Some fact e can be evidence that h . . . and hence be a good reason to believe h . . . even if h is false” (Achinstein 2001, 28). On the stronger version, veridical evidence, “if e is a good reason to believe h, then h is true” (26). According to Achinstein, it is this last version of evidence that scientists want. They want e to really be evidence for h, regardless of what anybody knows or believes, and they want h to really be true—and they sometimes think they have this kind of strong evidence. I suspect that Achinstein is right about what scientists want, and I agree that standard philosophical theories of evidence are too weak—they don’t give good reasons to believe. But my concern here is with the value of philosophical theories of evidence to understanding the history of science, and in particular in understanding the Darwin case. As we shall see, the ﬁrst two concepts of evidence outlined here, subjective and epistemic situation evidence, will be most helpful.

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5. THE DARWIN CASE As we have seen, Darwin had seemingly conﬂicting views about whether the taxonomic facts were sufﬁcient evidence to believe in branching evolution. First, he believed that the taxonomic facts were sufﬁcient for him to believe in branching evolution and that he came to believe on the basis of these facts. Second, he seemed to think that he should believe on just these grounds—that he would be justiﬁed in his belief. But third, he seemed to think that these same taxonomic facts were insufﬁcient for others to believe; something else, a mechanism, was required. Standard philosophical theories of evidence, as we have also seen, are inadequate to help us understand these three historical facts because, ﬁrst, they are prescriptive and to understand the ﬁrst fact, we need a descriptive concept. Second, they are abstract and a priori, and don’t seem to be able to take into account differences in what individuals believe or know. What counts as evidence for one person should therefore count as evidence for another. On this way of thinking about evidence, it is paradoxical that Darwin would think something would justiﬁably be evidence for himself but not for others. Darwin’s descriptive claim about evidence, that he did in fact come to believe in branching evolution on the basis of the taxonomic facts, is easily explained and understandable in terms of Achinstein’s subjective evidence. There are, as outlined by Achinstein, three conditions to be met for something to count as subjective evidence. First, Darwin must have believed that the taxonomic facts were evidence for branching evolution; second, he must have believed that branching evolution were true; and third, his reason for believing in branching evolution must have been the taxonomic facts. If we want to know the historical fact—about whether the taxonomic facts were evidence for Darwin for branching evolution, we simply answer these questions using the standard methods of historical reconstruction. So while standard theories of evidence don’t even seem to be applicable to this descriptive task, Achinstein’s framework gives straightforward guidance about how to proceed. Darwin’s prescriptive claims about whether belief in branching evolution was justiﬁed are more complicated, but can be easily understood by reference to epistemic situation evidence. Darwin thought that he should believe in branching evolution on the basis of the taxonomic facts, but he seemed to suggest that others should not believe, because for them something else would be required—a mechanism. This fact is inexplicable by any philosophical theory of evidence that is abstract and a priori. On the inductive generalization theories, for instance, either the facts satisfy the hypothesis or they don’t. If an “A is a B,” then it is evidence for “all A’s

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are B’s.” Similarly, on the hypothetical induction theories, if an observed fact is a deductive consequence of the hypothesis, then it is evidence (given the appropriate additional assumptions about simplicity, etc.). If not, it is not. In these cases, what someone knew or believed, or was in a position to know or believe, is irrelevant. But we can see how the epistemic situation concept of evidence can straightforwardly take individual differences into account. On this concept, as we have already seen, evidence is relativized to an epistemic situation—what a person or persons is in the position to know or believe and how to reason from what is known or believed. In this formulation, the epistemic situation is an abstraction, but it can be abstracted in various ways. First, we can abstract an epistemic situation relative to a single, concrete individual. We can conceptualize Darwin’s epistemic situation at a particular time in terms of what he actually knew or believed and how he thought he could reason from what he knew and believed. In this case, we evaluate his actual beliefs on the basis of his other beliefs and knowledge and his views about what constitutes correct reasoning. And we can evaluate his actual reasoning on the basis of his set of actual beliefs and knowledge, relative to objective standards of reasoning. In some sense then, this abstracted epistemic situation has a concrete basis, in that it contains only the actual beliefs and knowledge of an actual person at a particular time. But it is also abstract in that we are then considering the epistemic situation itself, as a set of beliefs, and independently of the person whose views constitute the epistemic situation. Because it is abstract, we can evaluate the reasoning and beliefs of the person who formed the basis of the epistemic situation. This, however, is only one way to think about evidence in prescriptive terms. Second, we could adopt a more abstract conception of epistemic situation as what some particular person is in a position to know or believe and how he or she could reason from this. This is abstract because it doesn’t rely on actual knowledge and beliefs, or views about correct reasoning. It is also prescriptive in the sense that we can identify what conclusion can be legitimately drawn, including conclusions about a particular hypothesis. Just as we can decide whether Hertz was justiﬁed in believing that cathode rays were electrically inert in 1883, we can decide whether Darwin was justiﬁed in believing in branching evolution in 1837. In both cases, this would be on the basis of what they were in a position to know or believe, not in terms of what they actually knew or believed. Third, we can adopt a yet more abstract epistemic situation in that it is not relativized to what a particular person would be in a position to believe or know, but to what some person or other was in the position to know at a particular time and in a particular cultural or social context.

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So just as we could ask what a German physicist might be in a position to know or believe in 1883, and an English physicist in 1897, we could ask what a naturalist in England might be in a position to know or believe in 1837. This sense of epistemic situation evidence is relativized not to a particular person, but what someone of a particular group might be in a position to know or believe. It might include more than an epistemic situation relativized to a particular person, because more of what is known and believed is typically available to some person or other of a group than to any single person in the group. But it might also include less. A particular person may be in the position to know more than the group of which he or she is a member. It might be the case, for instance, that in 1837 and because of his Beagle voyage, Darwin was in a position to know and believe things that his fellow English naturalists were not. We could continue this process of abstraction by considering epistemic situations that are not localized geographically or culturally, but only temporally. What beliefs and knowledge were available in 1837, independent of location? This epistemic situation would include beliefs and knowledge not available everywhere, so a person in Great Britain may not, strictly speaking, have access to what was available in Germany, and vice versa. Furthermore, we can relativize the epistemic situation to various counterfactuals. What would someone be in a position to know and believe in 1837, if they also knew something about the mechanisms of heredity? The value of this epistemic situation will depend on what questions are being asked. It may not be of broad interest, but nonetheless it is potentially a useful abstraction for thinking about prescriptive questions of evidence within various historical contexts. Here then is how we might understand Darwin’s seemingly conﬂicting views about what was necessary for justiﬁed belief in branching evolution. When he claimed that he was justiﬁed in his own belief in branching evidence, and on the mere basis of the taxonomic facts, he can be understood in terms of his own concrete epistemic situation. Given his concrete set of beliefs, knowledge, and views about correct reasoning, he thought he was justiﬁed in believing in branching evolution. He did not need anything more. But when he was considering the beliefs and knowledge of his fellow naturalists, he was thinking about a different epistemic situation— one that was not constituted in precisely the same way. His fellow naturalists, for instance, were not acquainted with the biogeography of the Galapagos and Falkland islands, and hence did not have that as part of their epistemic situation. Furthermore, they may not have had the same views about what constitutes good and correct reasoning. If this is correct, then Darwin’s seemingly contradictory views are easily explained by his

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consideration of the different epistemic situations. What was justiﬁed in one epistemic situation was not necessarily justiﬁed in another.

6. CONCLUSION An idea implicit in Achinstein’s thinking about evidence is that an adequate theory of evidence must help us understand the actual reasoning of scientists. Standard philosophical theories of evidence fail here, according to Achinstein, because they don’t reﬂect the fact that for scientists, evidence is strong—it must provide a good reason to believe. A philosophical concept of evidence that is too weak will not help us understand the actual reasoning of scientists. Similarly, I argue here, a theory of evidence must make sense of the reasoning of historians of science. To do so, it must have the resources to answer descriptive questions about what individuals actually took to be evidence. Achinstein’s subjective evidence provides the resources to do this. An adequate theory must also be able to help us think prescriptively about what was justiﬁed, and in a way that can account for differences in context, individual knowledge, and belief. Otherwise, it is not clear how we can understand situations like Darwin’s, where he was seemingly contradicting himself about the evidential adequacy of the taxonomic facts. Achinstein’s epistemic situation evidence provides the resources to make sense of this and similar cases. In a passage quoted earlier in this essay, Elliott Sober claims that the philosophy of science is a normative discipline, telling us what science should be like. That may be true, but that fact does not require that philosophy of science ignore the descriptive and contextual. An adequate philosophy of science must be able to help us understand the complexities of the history of science, as scientists came to believe their hypotheses on the basis of empirical facts, and in light of what they were in a position to know or believe. REFERENCES Achinstein, P. 2001. The Book of Evidence. New York: Oxford University Press. Norton, J. 2003. A Material Theory of Induction. Philosophy of Science 70 (4): 647–70. Sober, E. 2008. Evidence and Evolution: The Logic Behind the Science. Cambridge: Cambridge University Press. Winsor, M. P. 2009. Taxonomy was the Foundation of Darwin’s Evolution. Taxon 58 (1): 43–9.

16 The Place of Artificial Selection in Charles Darwin’s Theory of Evolution through Natural Selection Michael Ruse

1. INTRODUCTION Anyone taking up the philosophy of science around 1960, as I did, was bound—in Britain and America at least—to be immersed in the school known as “logical empiricism.” Headed then by people like Richard Braithwaite (1953) in England and Carl Hempel (1965) and Ernest Nagel (1961) in America, there was a great emphasis on explicating the underlying logical structure of scientiﬁc arguments and how they relate to evidence. Thus, in the case of theories, the popular analysis was in terms of so-called “hypothetico-deductive systems,” where one had axiom systems with high-level hypotheses (often referring to unseen, so-called “theoretical entities”) and then from these, lower-level empirical laws could be deduced. Physics of course was the usual science of choice from which illustrative examples could be drawn. Because this philosophy was ﬁrmly committed to the distinction between the context of discovery and the context of justiﬁcation, with only the latter really of concern to the philosopher, there was not much interest in heuristic analogies or like things. However, there was a theory of so-called “models.” These were things that were linked by being different interpretations of the same formal system, the same “calculus.” You have a theory and then you have a different interpretation, a model. It was okay, we learned, to use models, particularly for the cause of understanding—a solar system for the hydrogen atom, for instance—but you had to be very careful. Don’t think that what is going on in the model necessarily holds in the theory. I still remember the dire warning: “The price of the employment of models is eternal vigilance” (Braithwaite 1953, 93).

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2. THE IMPORTANCE OF PETER ACHINSTEIN By the mid 1960s, this whole philosophy was under attack. Mainly it came from those who had turned to science and its history, ﬁnding that things are very different—in many respects much messier—than the logical empiricists supposed. People like Stephen Toulmin (1972), Norwood Russell Hanson (1958), and then above all Thomas Kuhn (1962) started to sweep things very much away. I myself was deeply affected by this movement and it has led to a lifetime’s fascination with the history of science, as much as with its philosophy. But it was not only from without but from within that logical empiricism was under attack, and it was from here that I set off on the path that I still follow. I still remember the moment when I realized that there was something wrong with the philosophy I had embraced. It was when reading Peter Achinstein’s ﬁrst book, Concepts of Science (1968), where he pointed out with devastating clarity that the logical empiricist analysis of models just won’t do. You can have a formal similarity, and yet no one would think of models in such a case. For instance, if you have a ﬂow of liquid through a tube, it is governed by Poiseulle’s law. V=

c (p1−p2) L

(V is the volume of liquid ﬂowing through the tube across a ﬁxed cross section per unit time; c is a constant; L is the length of the pipe; and p1 – p2 is the pressure difference between the ends of the tube.) Formally this law is the same as that governing the expansion of gases, being heated under a constant pressure. W = k (V1−V2) L

(W is work done; P is the pressure of the gas; m is the mass; and V2 – V1 is the volume change.) No one would think of the liquid as a model for the gases. However, the liquid case is also formally the same as the transmission of electricity through a wire, Ohm’s law. I = (v1−v2)

(I is the quantity of charge passing through a ﬁxed cross section of the wire in a unit time; L is the length of the wire; k is a constant; and v1 – v2 the difference in potential between the ends of the wire.) Here we do think in terms of models. But as Achinstein pointed out, it is because we go beyond the formal similarity to physical similarity. In both we are dealing with a long narrow object of length L; in both we are concerned with the quantity of something that passes through a

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special cross-section of this narrow object in unit time; and in both we are concerned with the difference in value of certain quantities between the ends of this narrow object. To draw the analogy one considers not only the formal structure of the equations but also similarities in the designate of the symbols they contain (Achinstein 1968, 245). I cannot begin to tell you what a thrilling shock that was. The logical empiricists were not God. They could be wrong! It took me some time to get a real handle on this—writing your dissertation and your ﬁrst book is not the moment to change underlying philosophies—but as I got more and more seduced by Kuhn and his fellows, that liberating moment from Achinstein stayed with me and I have grown ever more appreciative. I am sure it also had a major role in what has become a lifelong interest in analogical and like reasoning—especially models and metaphors—in science. Appropriately, therefore, it is this interest that fuels this little essay. We are just ﬁnished with the “Darwin Year”—the 200th anniversary celebrations of the birth of Charles Darwin and the related 150th anniversary celebrations of his great book, On the Origin of Species by Means of Natural Selection. Naturally we have been led to think again about the work and its structure and contents, as well as its inﬂuence. In my case this has been particularly so because I wrote the introduction to a new, good book on the Origin, written by (and from the perspective of) one of today’s leading evolutionary biologists (Reznick 2009). As always, I have been struck by the importance in that work of analogies and metaphors, and above all by the example (call it what you will) of artiﬁcial selection, which is the topic of the ﬁrst chapter and the prolegomenon of what is to come after. I want to turn to this topic here, a move made particularly pertinent by the fact that a new book has just appeared, co-authored by the well-known philosopher Jerry Fodor, that takes Darwin to task for the artiﬁcial selection model and argues that this is an irredeemable ﬂaw that ruins the whole work (Fodor and Piattelli-Palmarini 2010). The book built upon an earlier argument made by Fodor: Selection theory is rotten at its core, because of the place of artificial selection. The present worry is that the explication of natural selection by appeal to selective breeding is seriously misleading, and that it thoroughly misled Darwin. Because breeders have minds, there’s a fact of the matter about what traits they breed for; if you want to know, just ask them. Natural selection, by contrast, is mindless; it acts without malice aforethought. That strains the analogy between natural selection and breeding, perhaps to the breaking point. What, then, is the intended interpretation when one speaks of natural selection? The question is wide open as of this writing. (Fodor 2007)

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3. FROM ARTIFICE TO NATURE The discussion in the Origin of artiﬁcial selection, the picking of and breeding from desirable plants and animals by humans, is straightforward and follows Darwin’s usual path of mixing the fact of change with the mechanism of change. Picking the rock pigeon as his example, Darwin argues that all of the different varieties and forms, wonderful though they may be, are in fact descended from the same root stock. Altogether at least a score of pigeons might be chosen, which if shown to an ornithologist, and he were told that they were wild birds, would certainly, I think, be ranked by him as well-defined species. Moreover, I do not believe that any ornithologist would place the English carrier, the short-faced tumbler, the runt, the barb, pouter, and fantail in the same genus; more especially as in each of these breeds several truly inherited sub-breeds, or species as he might have called them, could be shown him. Great as the differences are between the breeds of pigeons, I am fully convinced that the common opinion of naturalists is correct, namely, that all have descended from the rock pigeon (Columba livia), including under this term several geographical races or sub-species, which differ from each other in the most trifling respects. (Darwin 1859, 23)

Darwin argues to this conclusion on the basis of several interrelated facts, particularly that the pigeons of today are all completely interfertile, the strongest mark that we are dealing with one species rather than many. He then goes on to talk about selection. Breeders of animals and plants decide what they want and then they proceed to produce it, picking carefully from the stock and developing new features and variations. Breeders habitually speak of an animal’s organisation as something quite plastic, which they can model almost as they please. If I had space I could quote numerous passages to this effect from highly competent authorities. Youatt, who was probably better acquainted with the works of agriculturalists than almost any other individual, and who was himself a very good judge of an animal, speaks of the principle of selection as “that which enables the agriculturist, not only to modify the character of his ﬂock, but to change it altogether. It is the magician’s wand, by means of which he may summon into life whatever form and mould he pleases.” Lord Somerville, speaking of what breeders have done for sheep, says, “It would seem as if they had chalked out upon a wall a form perfect in itself, and then had given it existence.” That most skilful breeder, Sir John Sebright, used to say, with respect to pigeons, that “he would produce any given feather in three years, but it would take him six years to obtain head and beak.” (Darwin 1859, 31).

He now moves on to the natural world, and having established that there is abundant variation in nature and that there is an ongoing struggle

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for existence (and more importantly for reproduction), he is ready to bring on his mechanism of natural selection. How will the struggle for existence, discussed too brieﬂy in the last chapter, act in regard to variation? Can the principle of selection, which we have seen is so potent in the hands of man, apply in nature? I think we shall see that it can act most effectually. Let it be borne in mind in what an endless number of strange peculiarities our domestic productions, and, in a lesser degree, those under nature, vary; and how strong the hereditary tendency is. Under domestication, it may be truly said that the whole organisation becomes in some degree plastic. Let it be borne in mind how inﬁnitely complex and close-ﬁtting are the mutual relations of all organic beings to each other and to their physical conditions of life. Can it, then, be thought improbable, seeing that variations useful to man have undoubtedly occurred, that other variations, useful in some way to each being in the great and complex battle of life, should sometimes occur in the course of thousands of generations? If such do occur, can we doubt (remembering that many more individuals are born than can possibly survive) that individuals having any advantage, however slight, over others, would have the best chance of surviving and of procreating their kind? On the other hand, we may feel sure that any variation in the least degree injurious would be rigidly destroyed. This preservation of favourable variations and the rejection of injurious variations, I call Natural Selection. (Darwin 1859, 80–1)

Darwin also makes use of the artiﬁcial selection analogy a moment later when he introduces his secondary mechanism, sexual selection, which is the differentiation that comes within a species as organisms compete for mates. He distinguishes two kinds of such selection and in support makes mention explicitly of the human world. First there is male combat, where males ﬁght each other for mates. This brings on adaptations designed to defeat rivals. Sexual selection by always allowing the victor to breed might surely give indomitable courage, length to the spur, and strength to the wing to strike in the spurred leg, as well as the brutal cock-fighter, who knows well that he can improve his breed by careful selection of the best cocks. (Darwin 1859, 88)

Then there is female choice, where beautiful features appear in the males in order to attract the females. It may appear childish to attribute any effect to such apparently weak means: I cannot here enter on the details necessary to support this view; but if man can in a short time give elegant carriage and beauty to his bantams, according to his standard of beauty, I can see no good reason to doubt that female birds, by selecting, during thousands of generations, the most melodious or beautiful males, according to their standard of beauty, might produce a marked effect (89).

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One interesting fact about the Origin is that there are absolutely no examples of natural selection in action today causing change. Darwin gives a pretend example of wolves pursuing two strategies—short and stocky and slow versus light and fast—and suggests that there may be some truth to this, but generally there is no big search or apology. Even when Henry Walter Bates (1862) came up with his brilliant (and experiment-supported) explanation of butterﬂy mimicry, although Darwin was very pleased with the work—praising it generously and getting Bates a job—he only introduced it into later editions of the Origin and then almost at the end of the book. (The fourth edition of 1866 and in the penultimate chapter.) Basically, Darwin did not think that selection could act all that quickly, and so thought the search for evidence of it in action and having an effect was doomed to failure. Ironically, in 1878 an entomologist sent Darwin a letter documenting industrial melanism, the change in color of a moth’s wings toward a darker form due to the camouﬂage advantages brought on by concealment against an ever dirtier background. Apparently he did not reply and there is no evidence that he thought it that signiﬁcant (Hart et al. 2010). However, Darwin was quite willing and eager to use the artiﬁcial selection model throughout the Origin when he wanted to make a point. The best example occurs in the discussion of embryology, where Darwin is arguing that the reason why the embryos of very different adults are often very similar is that the struggle for existence and consequent selection only kicks in as the organisms move towards maturity. In the egg or the womb, they are protected. In support, Darwin turns to the world of the breeder, suggesting that we should ﬁnd something similar. And we do! Some authors who have written on Dogs, maintain that the greyhound and bulldog, though appearing so different, are really varieties most closely allied, and have probably descended from the same wild stock; hence I was curious to see how far their puppies differed from each other: I was told by breeders that they differed just as much as their parents, and this, judging by the eye, seemed almost to be the case; but on actually measuring the old dogs and their six-days old puppies, I found that the puppies had not nearly acquired their full amount of proportional difference. So, again, I was told that the foals of cart and race-horses differed as much as the full-grown animals; and this surprised me greatly, as I think it probable that the difference between these two breeds has been wholly caused by selection under domestication; but having had careful measurements made of the dam and of a three-days old colt of a race and heavy cart-horse, I ﬁnd that the colts have by no means acquired their full amount of proportional difference. (Darwin 1859, 444–5)

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4. PART OF THE THEORY? The question I want to ask now as a philosopher (rather than as a historian) is whether the artiﬁcial selection model/analogy is part of Darwin’s theory proper. Is it an essential piece of the theory of evolution through natural selection as given by Charles Darwin? It occurs between the covers of the Origin of Species, but so then does the title page. Is it really a part of the theory? I am assuming that the background to this question is that a logical empiricist would argue that it is not. It would be agreed that it is there, but it would be dismissed as not central in some way. And actually, going back to history, there is a good reason why one might feel conﬁdent in arguing in this way. The co-discoverer of natural selection, Alfred Russel Wallace, did not introduce the analogy into his little essay that he sent to Darwin. In fact, he argued against the analogy! Dealing with the objection that breeders never make new species—reproductively isolated groups— Wallace wrote, It will be observed that this argument rests entirely on the assumption, that varieties occurring in a state of nature are in all respects analogous to or even identical with those of domestic animals, and are governed by the same laws as regards their permanence or further variation. But it is the object of the present paper to show that this assumption is altogether false, that there is a general principle in nature which will cause many varieties to survive the parent species, and to give rise to successive variations departing further and further from the original type, and which also produces, in domesticated animals, the tendency of varieties to return to the parent form. (Wallace 1858, 54)

Having said this, although they were basically the same, Darwin’s theory was not exactly the same as Wallace’s theory. Darwin always focused on selection working at the individual level, whereas Wallace was always more inclined to see selection working at multi-levels, including producing beneﬁts for the group at the expense of the individual (Ruse 1980). So the history is hardly decisive. Moving back to philosophy, let us ask what it was that Darwin was doing with artiﬁcial selection. Essentially part of his theory or not, what role was it playing in his thinking? A case can be made that there were at least three roles. First, there was the heuristic role. Darwin always claimed that he got to natural selection through the analogy from artiﬁcial selection. My ﬁrst note-book was opened in July 1837. I worked on true Baconian principles, and without any theory collected facts on a wholesale scale, more especially with respect to domesticated productions, by printed enquiries, by conversation with skilful breeders and gardeners, and by extensive reading. When I see the list of books of all kinds which I read and abstracted,

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including whole series of Journals and Transactions, I am surprised at my industry. I soon perceived that selection was the keystone of man’s success in making useful races of animals and plants. (Darwin 1958, 119)

He then tells us that reading Malthus showed exactly how selection could work in nature. In fact, if you look carefully at the selection notebooks to which Darwin is referring, you ﬁnd that the artiﬁcial selection analogy is not as clear as he later suggests. However, there seems little reason to doubt the general recollection that it was the world of the breeders that put Darwin on the route to the big mechanism. So let us agree that there was a heuristic role for Darwin. Invoking the distinction between the context of discovery and that of justiﬁcation, you might complain that this shows precisely that the analogy was not part of Darwin’s theory. Following Kuhn and many others, I am not sure that this distinction is quite as clean cut as the logical empiricists implied. But for the sake of argument, let us for the moment agree that the heuristic role is ancillary to the theory. This however leads us straight on to the second role, namely the pedagogical one. The analogy is used to teach us, to introduce us to the notion of selection in general and to lead us to natural selection. Presenting the analogy and its heuristic role enables the rest of us to follow along and (Darwin hopes) to accept the central mechanism. Remember the already-quoted passage where Darwin does introduce natural selection (taken from the beginning of Chapter Four). We are invited to think about artiﬁcial selection and then go on to natural selection. “Can the principle of selection, which we have seen is so potent in the hands of man, apply in nature? I think we shall see that it can act most effectually” (Darwin 1859, 80).

5. A “VERA CAUSA” Again I suspect that the logical empiricist is going to complain or whine that pedagogy is not part of the theory proper. No one wants to downplay the teaching of the young or uninitiated, but that is not part of real science. Again I suspect that the follower of Kuhn will differ, for one of the most important roles that he saw paradigms as playing was precisely that of bringing students into the ﬁeld and teaching or indoctrinating them. But, again, for the sake of argument, let us give the logical empiricist the case. For now we come to the third role of the analogy, namely that of support. Here I think we can claim deﬁnitely that we have part of the theory proper. Darwin always looked upon the world of the breeders as part of the justiﬁcation for his theory, something made particularly pressing in the light of the (earlier discussed) failure to offer any direct

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justiﬁcation from the natural world. Note that I say “direct” justiﬁcation, for Darwin clearly thought that something like biogeographical distribution justiﬁed his case. In fact, he was very self-conscious about the role that the analogy was playing. In the language of the day, it was for him a proof that natural selection was a vera causa. Following the physicistphilosopher John F. W. Herschel, Darwin looked for a cause that we control as an analogy of a cause that exists naturally. If the analogy of two phenomena be very close and striking, while, at the same time, the cause of one is very obvious, it becomes scarcely possible to refuse to admit the action of an analogous cause in the other, though not so obvious in itself. For instance, when we see a stone whirled around in a sling, describing a circular orbit round the hand, keeping the string stretched, and ﬂying away the moment it breaks, we never hesitate to regard it as retained in its orbit by the tension of the string, that is, by a force directed to the centre; for we feel that we do really exert such a force. We have here the direct perception of the cause. (Herschel 1830, 149)

Note that artiﬁcial selection exactly ﬁts this mold, for here we have a human-caused force doing exactly what a natural-caused force is presumed to do. (See Ruse 1975 for a full discussion of the vera causa principle and the role it played in Darwin’s thinking.) Darwin always stressed the role of artiﬁcial selection when in the years after the Origin he was challenged on his theory. For instance, writing to the botanist George Bentham he says, In fact the belief in natural selection must at present be grounded entirely on general considerations. (1) on its being a vera causa, from the struggle for existence; & the certain geological fact that species do somehow change (2) from the analogy of change under domestication by man’s selection. (3) & chieﬂy from this view connecting under an intelligible point of view a host of facts. (Darwin 1985, vol. 11, 433)

Going back to the embryological discussion for a moment, we see that the breeders’ work is being used quite openly as support for his claims about what happens in nature and why different adults have similar young. “Fanciers select their horses, dogs, and pigeons, for breeding, when they are nearly grown up: they are indifferent whether the desired qualities and structures have been acquired earlier or later in life, if the fullgrown animal possesses them” (Darwin 1859, 446). This is then applied to nature. Now let us apply these facts . . . to species in a state of nature. Let us take a genus of birds, descended on my theory from some one parent-species, and of which the several new species have become modiﬁed through natural selection in accordance with their diverse habits. Then, from the many slight

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successive steps of variation having supervened at a rather late age, and having been inherited at a corresponding age, the young of the new species of our supposed genus will manifestly tend to resemble each other much more closely than do the adults, just as we have seen in the case of pigeons.” (446–7)

I don’t see any way that you could, or really would, want to argue that this is not part of Darwin’s theory. So at some real level, the analogy does belong. And this point I suspect that the logical empiricist will pull the old ploy: “We’ve known this all along!” Inasmuch as the analogy is evidence for the main claims of the theory, it is part of the theory, just as the evidence for Kepler’s laws is part of the Newtonian theory. Or if it is not part of the theory, then it is fully acknowledged support for the theory. Either way, it has a place in the logical empiricist worldview.

The design metaphor Again, I think you have to agree to this, but I think there is (in this case at least) something going on that the logical empiricist picture does rather ignore or downplay. In both the artiﬁcial and the natural selection cases you have a differential reproduction, and one could—indeed population genetics from the 1930s on have—set everything out formally and show we have the same structure, the same calculus. But sensitized by Achinstein we start to look for something more. And there is something more. The artiﬁcial and natural are linked by more than formal similarity. There is if you like a metaphor or physical analogy at the heart of the matter, namely design (Ruse 2003). As Darwin noted, the breeders design the animal or plant that they want and then set about producing it. The same process is supposedly going on in nature. Natural selection does not just bring about change, but change of a particular kind, namely in the direction of designlike features—the eye and the hand and bark and leaves—that are adaptations. This is what makes the whole thing so powerful, and controversial. We have real design in the human world, metaphorical design in nature. In an early version of his theory, Darwin went even further, supposing in imagination that there is a designer. Let us now suppose a Being with penetration sufﬁcient to perceive differences in the outer and innermost organization quite imperceptible to man, and with forethought extending over future centuries to watch with unerring care and select for any object the offspring of an organism produced under the foregoing circumstances; I can see no conceivable reason why he could not form a new race (or several were he to separate the stock of the original organism and work on several islands) adapted to new ends. As we assume his discrimination, and his forethought, and his steadiness of

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object, to be incomparably greater that those qualities in man, so we may suppose the beauty and complications of the adaptations of the new races and their differences from the original stock to be greater than in the domestic races produced by man’s agency: the ground-work of his labours we may aid by supposing that the external conditions of the volcanic island, from its continued emergence and the occasional introduction of new immigrants, vary; and thus to act on the reproductive system of the organism, on which he is at work, and so keep its organization somewhat plastic. With time enough, such a Being might rationally (without some unknown law opposed him) aim at almost any result. (Darwin and Wallace 1958, 114)

It cannot be overly stressed how important this metaphor of design is within the Darwinian system. By thinking of the organic world as if designed, then we can do science. Why does the honeybee build a hexagonal comb? Because that is the strongest and most efﬁcient. Why does the bird have feathers? (Archaeopteryx is introduced into the fourth edition of the Origin.) In order to ﬂy. Why are forelimbs of man, mole, horse, porpoise, and bat so different? To grasp, to dig, to run, to swim, and to ﬂy. It is this (that is to say, things of this sort) that is missed in the logical empiricist account of science, and it is clearly this that has got under the skin of Jerry Fodor. In particular, though there is no end of it in popular accounts of adaptationism, it is a Very Bad Idea to try and save the bacon by indulging in metaphorical anthropomorphisms. It couldn’t, for example, be literally true that the traits selected for are the ones Mother Nature has in mind when she does the selecting; nor can it be literally true that they are the traits one’s selﬁsh genes have in mind when they undertake to reproduce themselves. There is, after all, no Mother Nature, and genes don’t have, or lack, personality defects. Metaphors are ﬁne things; science probably couldn’t be done without them. But they are supposed to be the sort of things that can, in a pinch, be cashed. Lacking a serious and literal construal of “selection for,” adaptationism founders on this methodological truism. (Fodor 2007)

But here’s the rub! Should metaphors be cashed? Some would say that you cannot cash metaphors, even in principle. I won’t go there but I will say that there are very good reasons why you should not always rush to cash metaphors. The fact that not only are there heuristics that might lead you to a theory, but within the theory itself thanks to metaphor there are strengths that lead to new discoveries. Take the stegosaurus, that ungainly dino with funny triangular plates down its back. Why does it have them? This s surely a legitimate question that is quite unanswerable unless you think in terms of design. What is their point? Today, incidentally, this question is usually answered in terms of heat transfer. The plates are just like those found in cooling stations and apparently have the same function (Farlow, Thompson, and Rosner 1976). In Kuhn’s language, because of its

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metaphors, a good paradigm can go on solving new puzzles. (Presumably the example of Wallace shows that you could get to the metaphor of design without the move from artiﬁcial selection, although looking again at the paper that Wallace sent to Darwin, I am not at all sure that he grasped fully the ways in which selection—a term he did not use— could help us to understand the design-like nature of adaptation. Remember that after the paper Wallace never got to develop his thinking independently of Darwin, whose greater importance Wallace always proclaimed.) Finally, is there something particularly offensive about this particular example? Was Darwin wrong to think in terms of design? I don’t see why. It cannot be overemphasized that it was a metaphor and not literal. As it happens, at the time of writing the Origin, Darwin did still believe in a Designer, but one who works at a distance and does not involve Himself in the day-to-day details of evolution. The whole point from that day to this—witness the scorn of contemporary evolutionists for so-called Intelligent Design Theorists—consciousness is kept out of the evolutionary process (qualiﬁcations being made for such things as sexual selection in humans).

6. CONCLUSION The world of the breeders provides a crucial piece of Darwin’s thinking. It offers a model or analogy leading to the central evolutionary force of natural (and its sister sexual) selection. Can it be given a full and adequate analysis by the logical empiricist approach to science? If you stretch and pull and lop—particularly if you lop—you can probably go a long way. But right at the end you miss the most important part of the analogy, the metaphor of design that is at the heart of selection-based evolutionary thinking. What a pity that Jerry Fodor never read Peter Achinstein at the same formative stage as I did! REFERENCES Achinstein, P. 1968. Concepts of Science. Baltimore: Johns Hopkins University Press. Bates, H. W. 1862. Contributions to an Insect Fauna of the Amazon Valley. Transactions of the Linnaean Society of London 23: 495–515. Braithwaite, R. 1953. Scientiﬁc Explanation. Cambridge: Cambridge University Press. Darwin, C. 1985. The Correspondence of Charles Darwin. Cambridge: Cambridge University Press.

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——— . 1958. The Autobiography of Charles Darwin, 1809–1882, ed. N. Barlow. London: Collins. ———. 1859. The Origin of Species. London: John Murray. Darwin, C., and A. R. Wallace. 1958. Evolution by Natural Selection. Cambridge: Cambridge University Press. Farlow, J. O., C. V. Thompson, and D. E. Rosner. 1976. Plates of the Dinosaur Stegosaurus: Forced Convection Heat Loss Fins? Science 192 (4244): 1123–25. Fodor, J. 2007. Why Pigs Don’t Have Wings: The Case against Natural Selection. London Review of Books, October 18. Fodor, J., and M. Piattelli-Palmarini. 2010. What Darwin Got Wrong. New York: Farrar, Straus, and Giroux. Hanson, N. R. 1958. Patterns of Discovery. Cambridge: Cambridge University Press. Hart, A. G., R. Stafford, A. L. Smith, and A. E. Goodenough. 2010. Evidence for Contemporary Evolution during Darwin’s Lifetime. Current Biology 20 (3): R95. Hempel, C. G. 1965. Aspects of Scientiﬁc Explanation. New York: Free Press. Herschel, J. F. W. 1830. Preliminary Discourse on the Study of Natural Philosophy. London: Longman, Rees, Orme, Brown, Green, and Longman. Kuhn, T. 1962. The Structure of Scientiﬁc Revolutions. Chicago: University of Chicago Press. Nagel, E. 1961. The Structure of Science: Problems in the Logic of Scientiﬁc Explanation. New York: Harcourt, Brace, and World. Reznick, D. N. 2009. The “Origin” Then and Now: An Interpretive Guide to the “Origin of Species.” Princeton: Princeton University Press. Ruse, M. 2003. Darwin and Design: Does Evolution Have a Purpose? Cambridge, Mass.: Harvard University Press. ——— . 1980. Charles Darwin and Group Selection. Annals of Science 37 (6): 615–30. ——— . 1975. Darwin’s Debt to Philosophy: An Examination of the Inﬂuence of the Philosophical Ideas of John F.W. Herschel and William Whewell on the Development of Charles Darwin’s Theory of Evolution. Studies in History and Philosophy of Science 6 (2): 159–81. Toulmin, S. 1972. Human Understanding. Oxford: Clarendon Press. Wallace, A. R. 1858. On the Tendency of Varieties to Depart Indeﬁnitely from the Original Type. Journal of the Proceedings of the Linnean Society, Zoology 3 (9): 53–62.

17 Evidence and Justification Kent Staley

1. INTRODUCTION Peter Achinstein has been a persistent advocate of a kind of pluralism about evidence. In different scientiﬁc contexts, distinct evidence concepts come into play. The purpose of the present paper is to advocate a further extension of Achinstein’s pluralism. I will argue that his account should be supplemented with a further concept to more adequately account for the justiﬁcation of scientiﬁc inferences. My proposal does not introduce any new notion of evidence, but articulates instead a relativized, nonprobabilistic notion (the securing of evidence) that helps make sense of certain strategies by which scientists justify their claims about what evidence they have and their inferences from that evidence. That Achinstein’s framework would beneﬁt from such a supplement is a claim needing defense, because that framework already has a concept— called “ES-evidence”—that he says is “based on the idea of providing an epistemic justiﬁcation for belief” (Achinstein 2001, 19), and is thus relativized to particular epistemic situations. In what follows, then, I will be at pains to explain Achinstein’s view of ES-evidence, the relationship ES-evidence bears to Achinstein’s other evidence concepts, and its relationship to this new notion: the securing of evidence.

2. ES-EVIDENCE AND VERIDICAL EVIDENCE Crucially, Achinstein conceives of some kinds of statements that scientists make about evidential relationships between facts and hypotheses as both (1) objective in the sense that statements of those kinds are true or false independently of what anyone believes about the hypotheses and facts in question; and (2) empirical in the sense that ascertaining the truth or falsehood of such statements is (at least sometimes) a matter for investi-

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gation by means of experiment and observation rather than a priori calculation. These features are incorporated into the concepts of “potential evidence” and “veridical evidence.” He proposes the following as necessary and sufﬁcient conditions for the former: (PE) e is potential evidence that h, given b if and only if: 1. p(there is an explanatory connection between h and e/e and b) > ½ 2. e and b are true 3. e does not entail h. (Achinstein 2001, 170). Here e refers to some fact, h is a hypothesis, and b is background information. The probability statement in the ﬁrst condition should be understood in terms of objective epistemic probability, according to which a statement of the form “p(h/e) = r” should be interpreted as asserting that “the degree of reasonableness of believing h, on the assumption of e, is r” (106). Veridical evidence is deﬁned by adding to the conditions speciﬁed in (PE) the further requirement that h is true. Both potential evidence and veridical evidence share a feature that is central to Achinstein’s concerns: if e is evidence that h in either the potential or veridical sense, then e is a good reason to believe that h is true. Moreover, it is a good reason to believe h in a sense that is completely independent of any epistemic situation. An epistemic situation, according to Achinstein, is . . . an abstract type of situation in which, among other things, one knows or believes that certain propositions are true, one is not in a position to know or believe that others are, and one knows (or does not know) how to reason from the former to the hypothesis of interest, even if such a situation does not in fact obtain for any person. (Achinstein 2001, 20)

It is in this sense that the term “epistemic situation” will be used throughout this paper. Potential and veridical evidence are distinguished from ES-evidence, which provides “a justiﬁcation for believing h for anyone in epistemic situation ES” (Achinstein 2001, 174).1 Achinstein deﬁnes the notion thus: (ES) e is ES-evidence that h with respect to an epistemic situation ES if and only if: 1. e is true 2. anyone in ES is justiﬁed in believing that e is (probably) veridical evidence that h. (174) Because veridical evidence satisﬁes the requirement of constituting a good reason to believe the relevant hypothesis and moreover entails that the

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hypothesis in question is true, it captures, according to Achinstein, the aim of scientiﬁc investigation. Scientists, he writes, “are not satisﬁed with providing only a justiﬁcation of belief for those in certain situations, even their own, since the belief might turn out to be false.” Hence ES-evidence does not constitute the aim of scientiﬁc inquiry. And because they “want their hypotheses to be true,” potential evidence also falls short of capturing the aim of scientiﬁc inquiry (34). Achinstein does not deny that scientists seek, in addition to veridical evidence, justiﬁcation in drawing the conclusions that they do. But he treats this as at most a secondary concern. Indeed, when discussing the contexts in which the various evidence concepts come into play, he associates ES-evidence primarily with historical investigations that seek to answer questions about whether a particular scientist was justiﬁed in believing certain hypotheses, given her epistemic situation (Achinstein 2001, 37). This does not mean that a concern with epistemic justiﬁcation (and hence ES-evidence) arises only in historical investigations. “To be sure, when a scientist claims that e is evidence that h, he believes and hopes that, given his knowledge, he is justiﬁed in believing h on the basis of e. But he believes and hopes for something much more”: a good reason for believing h that is independent of any epistemic situation, even his own (Achinstein 2001, 37). Perhaps because he primarily thinks of ES-evidence as coming into play in historical contexts, Achinstein rarely addresses directly the ways in which investigators seek to alter their own epistemic situations with regard to given evidence claims. Even where he does discuss the improvement of an epistemic situation, he considers not the improvement of the investigator’s own situation, but that of his audience. Writing about J. J. Thomson’s experiments on cathode rays yielding evidence that they carry an electric charge, Achinstein notes that, because others might not be able to recognize that his results are a good reason to believe that cathode rays are electrically charged, “What Thomson may need to do, and what a good physics text does, is to set the stage by including sufﬁcient information so that others can be in an appropriate epistemic situation, so that others can become justiﬁed in believing the hypothesis for that reason” (Achinstein 2001, 35). True enough, but how did Thomson himself become justiﬁed in believing that his results are evidence that cathode rays carry an electric charge? I propose that the notion of ES-evidence as Achinstein deﬁnes it does not much help us to answer questions like this. Although ES-evidence acknowledges a role for the notion of epistemic justiﬁcation relative to one’s epistemic situation, it cannot tell us how to understand that con-

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cept. Recall from the above deﬁnition of ES-evidence that for e to be ES-evidence that h relative to some epistemic situation ES, it must be the case that anyone in ES is justiﬁed in believing that e is (probably) veridical evidence that h. Clearly Achinstein here does not even intend, in deﬁning ES-evidence, to give us an account of what it is to be justiﬁed in believing something relative to an epistemic situation, since he has simply moved that concept to the other side of the biconditional. I conclude that his discussion of ES-evidence is meant to acknowledge the role of epistemic justiﬁcation in some uses of evidence-talk in science, and to clarify how such justiﬁcation relates to other evidence concepts, but is not meant to give an account of epistemic justiﬁcation as such. Although there is already a vast literature in general epistemology that seeks to analyze the notion of justiﬁcation, I would contend that such accounts do not help us much to understand justiﬁcation in science. More precisely, I propose shifting the focus of the discussion of justiﬁcation away from analytic epistemology’s concern with specifying necessary and sufﬁcient conditions for the truth of “S is justiﬁed in believing p,” and toward specifying a conceptual framework that serves to explicate justiﬁcatory practices in the sciences. Such a conceptual framework centers on an ideal of justiﬁcation, at which justiﬁcatory practices aim (Staley and Cobb, forthcoming), and thus approaches justiﬁcation by asking what it is that such practices accomplish, and how.

3. SECURING EXPERIMENTAL CONCLUSIONS Consider the following kind of situation: A researcher presents a conclusion from experimental data at a meeting of specialists.2 The decision to present a conclusion indicates the conviction of the researcher and her collaborators that they are prepared to justify their inference in response to whatever challenges they expect to encounter. Their conﬁdence will result from their having already posed many such challenges to themselves. New challenges will emerge from the community of researchers with which they communicate. Such challenges take many forms, depending on the nature of the experiment and conclusions: Are there biases in the sampling procedure? Have confounding variables been taken into account? To what extent have alternative explanations been considered? Are estimates of background reliable? Can the conclusion be reconciled with the results of other experiments? Have instruments been adequately shielded, calibrated, and maintained? To a large extent, such challenges present possible scenarios in which the experimenters have gone wrong in drawing the conclusions that

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they do. Such challenges are not posed arbitrarily. Being logically possible does not sufﬁce, for example, to constitute a challenge that the experimenter is responsible for addressing. Rather, such scenarios are judged signiﬁcant by those in a certain kind of epistemic situation, incorporating relevant disciplinary knowledge; and an appropriate response needs to provide a basis for concluding that the scenario in question is not actual. I propose thinking of practices of justifying an inference as the securing of that inference against scenarios under which it would be invalid (“error scenarios”), where the concept of security is deﬁned as follows: SEC: Let Ω0 be the set of all scenarios that are epistemically possible relative to an epistemic situation K. Suppose that Ω1 Í Ω0. Proposition P is secure throughout Ω1 relative to K iff for every scenario ω Î Ω1, P is true in ω. If P is secure throughout Ω0, then P is fully secure relative to K.

Before proceeding, some explanation of terminology is in order. This deﬁnition employs the notion of epistemic possibility, which can be thought of as the modality employed in such expressions as “For all I know, there might be a third-generation leptoquark with a rest mass of 250 GeV/c2” and “For all I know, I might have left my sunglasses on the train.” Hintikka’s seminal work (1962) takes expressions of the form, “It is possible, for all that S knows, that P,” to have the same meaning as, “It does not follow from what S knows that not-P.”3 I have borrowed the notion of a scenario from David Chalmers for heuristic purposes. He describes a scenario as a “maximally speciﬁc way things might be” (Chalmers, 2011). If there is, relative to one’s epistemic situation, an epistemically possible scenario in which a proposition P is true, that means that, for all one knows, a complete and maximally speciﬁc description of the world entails P. In practice, no one ever considers scenarios as such, of course, but rather focuses on salient differences between one scenario and another. To put this notion more intuitively, then, a proposition is secure for an epistemic agent just insofar as, whatever might be the case for all that the agent knows, that proposition remains true. Applied to an inference from fact e to hypothesis h, an inference from e to h is secure relative to K insofar as the proposition “e is good evidence for h” is secure relative to K. For Achinstein’s account, the relevant way to explicate this might be to say that the conditions for e being potential evidence for h are secure relative to K. Note that the notion of a fully secure inference functions as an ideal for use in articulating an account of justiﬁcation. Second, this account does not suppose that investigators can or should attempt to determine some degree of security of any of their inferences.

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Rather, the value of the concept of security lies in its capacity to conceptualize methods of justiﬁcation encountered in scientiﬁc practice in a systematic way. Indeed, the methodologically signiﬁcant notion is not security per se, but the securing of inferences, that is, the use of methods that serve to increase the relative security of an inference, either by expanding the range of validity of an inference across a ﬁxed space of possible scenarios, or by decreasing the range of possible scenarios in which the inference would be invalid. Using the notion of security to complement Achinstein’s theory of evidence, I propose the following as an ideal of justiﬁcation: JE (Justiﬁed Evidence): An assertion of h as a conclusion inferred from observed fact(s) e is fully justiﬁed relative to epistemic situation K if:

(1) e is potential evidence for h; and (2) the proposition “e is potential evidence for h” is secure throughout all scenarios that are epistemically possible relative to K.4 Note that these conditions are stronger than those for either veridical evidence or ES-evidence. This account articulates a notion of full justiﬁcation as an ideal. The point is that methods of justiﬁcation serve two distinct purposes. First, they aim (fallibly) to create conditions that will render (1) true for the inference at which the investigators arrive. Second, they aim to facilitate the pursuit of (2) by providing investigators with the resources to respond to the challenge of possible error-scenarios and, thus, serve to secure the inference proposed. Though full security may remain an unachieved ideal, the increase in relative security puts investigators in a better epistemic situation, and it is in this sense that methods aimed at securing evidence claims provide justiﬁcation. Two general strategies for the securing of evidence pervade experimental science: In a weakening strategy one replaces a conclusion h with a weaker conclusion h’ that is true across a broader range of epistemically possible scenarios. A strengthening strategy calls for changing one’s epistemic situation ES into a stronger situation ES’ such that error scenarios epistemically possible relative to ES are not possible relative to ES’. To illustrate these strategies and see how the concept of security might complement Achinstein’s account of evidence, let us consider experiments undertaken by Heinrich Hertz, which Achinstein uses to introduce the notion of ES-evidence. As he sees it, Hertz’s experiments provided ES-evidence, relative to Hertz’s epistemic situation, that cathode rays are electrically neutral. However, later experiments by J. J. Thomson showed that Hertz’s results were not veridical or even potential evidence for the neutrality of cathode rays.

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3. HEINRICH HERTZ AND THE JUSTIFICATION OF EVIDENCE FOR THE ELECTRICAL NEUTRALITY OF CATHODE RAYS In his 1883 paper, “Experiments on the Cathode Discharge,” Heinrich Hertz describes a series of experiments carried out in the Physical Institute of the University of Berlin on cathode phenomena. The conclusions that he claims to have “proved” via these experiments include that “cathode rays are only a phenomenon accompanying the discharge, and have nothing directly to do with the path of the current” and that “the electrostatic and electromagnetic properties of the cathode rays are either nil or very feeble” (Hertz 1896, 254).5 Hertz’s research should be understood in the context of the work already undertaken by his Berlin colleague Eugen Goldstein, who regarded the rays as (1) an entirely novel production not readily assimilable to known categories of electrical phenomena, but as (2) consisting of “open currents.” The latter view treated the rays as involving a kind of motion in the ether that propagated through the tube without transferring any material particle; any movement of charge through the tube did not traverse the length of the tube. Instead, rays originate as longitudinal waves at the cathode that terminate when they strike a particle, which in turn becomes the origin of another ray. As Buchwald notes, Goldstein “conﬂated longitudinal waves in the ether with unterminated currents, conceiving that the ether might possess conductivity. For him cathode rays were simultaneously a kind of current and a kind of wave” (Buchwald 1994, 137).

(1) Rays are not currents Hertz found an ingenious way to simultaneously challenge and endorse Goldstein’s claims by attacking (2) in a way that strengthened the support for (1). According to Buchwald’s account, the conception of rays in Geissler tubes as a novel state was central to Goldstein’s view, while the claim that they are open currents was secondary, an interpretation that distinguished the rays from any known electrical phenomenon. By showing that the rays were not any kind of current at all, Hertz could enhance the claim to their ontological distinctness while also establishing his own experimental acumen (Buchwald 1994, 137–41). In one experiment seeking to distinguish between the current in the tube and the rays, he set out to trace the current’s path in the tube by means of its magnetic effect, and to compare that path to the path of the rays through the tube. This involved constructing a tube that was in fact a rectangular frame holding two panes of glass enclosing an evacuated space

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(Figure 17.1). The cathode and anode were inserted just into that space through adjacent sides of the rectangle. A magnetic needle was suspended above the frame such that its deﬂection could be recorded as the frame was moved about. Hertz’s results clearly indicated a distinction between the paths of the current lines as recorded by the magnetic deﬂection and the paths of the cathode rays (Figure 17.2). But, Hertz noted, to justiﬁably regard these results as evidence that the current and rays were distinct one needed to rule out a possibility. If the cathode rays exerted some non-electromagnetic effect on the needle, then one could not use the deﬂection of the needle to map the current, and thus could draw no conclusion about the relationship between the current paths and the ray paths. Hertz performed another experiment to show that “no such effect occurs” (Hertz 1896, 239). In this experiment, Hertz devised a radially symmetric cathode-anode construction. The cathode consisted of a brass disk with a diameter equal to the opening of the tube into which it was inserted. Through a hole in the center of that disk protruded a thermometer tube, through which in turn protruded the anode. Hertz positioned the tube “as near as possible to the magnet, ﬁrst in a position that the magnet would indicate a force tangential to the tube, then radial, and lastly, parallel to the tube.” But he found no deﬂection of the magnet. By contrast, if the anode was placed further down the length of the tube, so that the path from cathode to anode ran parallel to the rays, he did observe “deﬂections of thirty to forty scale divisions” (240). Hertz concluded that the rays had no detectable non-electromagnetic effect on the magnet, since eliminating the electromagnetic effect via a symmetric conﬁguration eliminated any detectable deﬂection. Hertz’s use of a subsidiary experiment here exempliﬁes what I call a “strengthening strategy” for securing his conclusions from the mapping experiment. That is, he added to his knowledge, strengthening his epistemic situation so that some scenarios (those in which cathode rays exert detectable non-electromagnetic effects on the magnetic needle) that were previously epistemically possible and would potentially invalidate any

Fig. 17.1. Hertz’s “tube” turned into a rectangular frame. From Hertz (1896).

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b

a

Fig. 17.2. The lines are equipotential lines (roughly indicating current paths), which are clearly distinct from the cathode light (a) and the positive striae (b). From Hertz (1896).

conclusions drawn from the mapping experiment, became no longer epistemically possible.

(2) Rays lack electrostatic properties Hertz next turned to the question “Have the cathode rays electrostatic properties?” He divides this question into two parts: “Firstly: do the cathode rays give rise to electrostatic forces in their neighbourhood? Secondly: In their course are they affected by external electrostatic forces?” (Hertz 1896, 249). He then described two experiments directed at these two questions respectively. In the ﬁrst, as depicted in Figure 17.3, he used a glass tube containing the cathode (α). “All of the parts marked β are in good metallic connection

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with each other, and such of them as lie inside the tube form the anode” (Hertz 1896, 249). This included a brass tube surrounding the cathode, such that the only opening through which the cathode rays may pass is a 10mm hole opposite the cathode. They must then pass through a wire mesh, also forming part of the anode. The anode also connected to an external mantel connected to a “delicate electrometer.” Also connected to the electrometer was a metal case “which completely surrounds the greater part of the tube and screens that part of the gas-space which lies beyond the wire-gauze from any electrostatic forces which might be produced by induction from without, e.g., from the cathode” (250). On the basis of the previously described experiment, Hertz regarded the rays that pass through the mesh into the space of the tube as “pure” in the sense of not including any of the current that ﬂows from cathode to anode. Thus, should any electrostatic forces be exerted in the vicinity of the rays, or should they be found to respond to any such forces, he could ascribe these effects to the rays themselves. Here again, Hertz took care to secure his conclusions against a threatening scenario: that in which electrostatic effects are manifested, but only because of a commingling of cathode-anode current with the rays which he had established as a distinct phenomenon. But Hertz took a further step, the consideration of which shows how studying the error scenarios deemed relevant by an investigator might shed light on his understanding of the conclusions he draws. To show that his apparatus was adequate to discriminate between the presence and absence of the phenomenon in question, Hertz considered how to determine the magnitude of the effect to be expected if the rays were to exert electrostatic forces. This he did by simulating the effect in question: he replaced the glass tube inside the mantle with a metal rod “which had about the same size and position as the cathode rays” and was in contact with the cathode. This arrangement produced deﬂections of the electrometer “too great to be measured” but estimated at “two to three thousand scale divisions” which ceased when the current stopped. Note his next comment: “Now if the cathode rays consisted of a stream of particles charged to the potential of the cathode, they would produce effects quantitatively similar to the above, or qualitatively similar if they produced any electrostatic forces whatever in their neighbourhood” (Hertz 1896, 250). When the experiment was performed, Hertz reported that the electrometer exhibited vibrations through “ten or twenty scale divisions from its position of rest.” He infers: “As far as the accuracy of the experiment allows, we can conclude with certainty that no electrostatic effect due to the cathode rays can be perceived; and that if they consist of streams

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A

b ∝ b

b

b

b

b g

g

B

Fig. 17.3. Cathode tube used to “purify” rays from current. From Hertz (1896).

of electriﬁed particles, the potential on their outer surface is at most one-hundredth that of the cathode” (Hertz 1896, 251). The last point about the “potential on their outer surface” deserves attention. The metal rod served as a satisfactory simulation of the effect being investigated because Hertz assumed that cathode rays bearing electrostatic properties would be “particles charged to the potential of the cathode.” Buchwald comments that “Hertz was . . . thinking of small bits of metal literally torn away from the cathode” and retaining the property of conductivity such that they can be “charged to a potential.” To secure his conclusion that cathode rays did not exert electrostatic forces, Hertz needed to rule out the scenario in which, although they did exert such forces, his apparatus was unable to detect them. But his treatment of this scenario indicates that he was in fact thinking of the “charged ray” hypothesis according to a particular model quite distinct from that later supported by Thomson’s experiments, for example.

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Of course, to judge Hertz’s accomplishments in his cathode ray research in light of ideas that were not available to him would reek of anachronism. Nonetheless, by following Buchwald’s lead in paying close attention to the error scenarios that did concern Hertz, we can engage in a non-vicious form of anachronism. In particular, we can use a weakening strategy on Hertz’s behalf to clarify in what sense Hertz’s conclusion from this experiment was justiﬁed, but in a way that is informed by our knowledge of later developments. The fact that the developments that make our reconstruction possible resulted from later work can form the basis of understanding why Hertz himself did not employ this strategy. The following weakening strategy seems applicable: replace h: “the electrostatic and electromagnetic properties of the cathode rays are either nil or very feeble” with the weaker claim that “either h or else the cathode rays bear those properties in some manner distinct from that in which bodies with the property of conductivity bear them.” The latter possibility did not occur to Hertz, and in that sense he justiﬁably drew his conclusion. Yet his justiﬁcation did not meet the ideal set forth in JE. Ideally, experimenters anticipate all of the error scenarios relevant to their inferences and acquire the resources to rule them out. In truth, the ideal is rarely met, and Hertz did not meet it. Employing the framework of security in understanding the ideal, along with additional empirical knowledge about the phenomena Hertz was investigating, allows us both to acknowledge the justiﬁcations available to him, and to note those that eluded him.

(3) Cathode rays are not affected by electrostatic forces Finally, Hertz addresses the question of whether electrostatic forces affect cathode rays. Hertz used a “ray purifying” tube similar to that in Figure 17.3, but this time placed between “two strongly and oppositely electriﬁed plates” (Hertz 1896, 252). In the path of the rays Hertz placed a “ﬁne wire” that cast a shadow on the phosphorescent patch at the end of the tube. Hertz proposed that a movement of the shadow would indicate any deﬂection of the rays. This effect he did not observe. In another instance of anticipating an error scenario, Hertz notes, “But here there was a doubt whether the large electrostatic force to which the tube was subjected might not be compensated by an electrical distribution produced inside it” (Hertz 1896, 252). As Buchwald notes, the concern here was directed at the idea that the gas inside the tube may have been rendered conductive in the manner of “an attenuated metal,” not in the sense of the gas becoming ionized—the effect later identiﬁed by Thomson (Buchwald 1994, 166).

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To rule out this possibility, Hertz moved the plates to the inside of the tube. Under these conditions, Buchwald notes, conductivity in the gas as Hertz conceived it would result in discharge between the plates, an effect that was not observed. The shadow showed no displacement. To investigate the effect of electromotive rather than electrostatic forces on the cathode rays, Hertz then connected the plates to a battery sufﬁcient to induce arc-discharges between them. Hertz observed that under these conditions the phosphorescence appeared “distorted through deﬂection in the neighbourhood of the negative strip; but the part of the shadow in the middle between the two strips was not visibly displaced” (Hertz 1896, 252). This ﬁnal series of observations acquired particular importance later insofar as Thomson’s series of experiments included a similar arrangement but with a superior evacuation of the tube to rule out precisely the kind of ionization of the gas (and resultant shielding of the rays from the electric ﬁeld) that was not the target of Hertz’s concern about the gas being rendered conductive. Buchwald notes that, although many believe that Hertz’s tube suffered from an ionization effect, such a scenario “would not even have occurred to Hertz in 1883, because he understood conductivity as an extensive property of matter in bulk . . . from Hertz’s point of view the gas in the tube was either conducting, in which case it behaved like an attenuated metallic mass, or else it was not, in which case it behaved like an insulator. He had to examine whether the rays were or were not deﬂected under both circumstances, which he did” (Buchwald 1994, 168). Here again we see how meticulously Hertz ruled out error scenarios that he deemed relevant against the background of the theoretical possibilities within his ken. Nonetheless, possibilities did emerge later that would have been relevant had they occurred to him.

4. CONCLUSION Under Achinstein’s interpretation, the claim that Hertz’s results are evidence that “cathode rays are not electrically charged” is correct insofar as we take the relevant evidence concept to be ES-evidence, but Thomson’s later experiments show that it is incorrect in terms of potential or veridical evidence. Here I take no issue with these claims. The purpose of the above discussion has been to show how we can regard much of what Hertz did in the course of his experimental activities as serving two purposes simultaneously. First, he sought to arrive at results that stand as a matter of

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objective fact in a relationship of evidential support for a hypothesis of interest. Second, he sought to acquire the epistemic resources to justify the claim that those results are such evidence for that hypothesis, particularly by being able to rule out scenarios that, if actual, would invalidate such a claim. Furthermore, although Achinstein’s evidence concepts— particularly the notion of veridical evidence—might serve us well in understanding how Hertz’s efforts were directed at the ﬁrst aim, he has no account of justiﬁcation that will shed substantive light on the second aim. I propose that the securing of evidence, as here discussed, can illuminate this justiﬁcatory aspect of science.

REFERENCES Achinstein, P. 2001. The Book of Evidence. New York: Oxford University Press. Buchwald, J. Z. 1994. The Creation of Scientiﬁc Effects. Chicago: University of Chicago Press. Chalmers, D. 2011. The Nature of Epistemic Space. In Epistemic Modality, ed. A. Egan and B. Weatherson. Oxford: Oxford University Press. DeRose, K. 1991. Epistemic Possibilities. Philosophical Review 100 (4): 581–605. Hertz, H. 1896. Miscellaneous Papers, trans. D. E. Jones and G. A. Schott. London: MacMillan and Co. Hintikka, J. 1962. Knowledge and Belief: An Introduction to the Logic of the Two Notions. Ithaca, N.Y.: Cornell University Press. Mayo, D. 1996. Error and the Growth of Experimental Knowledge. Chicago: University of Chicago Press. Mayo, D. and A. Spanos. 2009. Error and Inference: Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science. New York: Cambridge University Press. Staley, K. and A. Cobb. Forthcoming. Internalist and Externalist Aspects of Justiﬁcation in Scientiﬁc Inquiry. Synthese. DOI: 10.1007/s11229-010-9754-y

NOTES 1. Here Achinstein refers speciﬁcally to epistemic justiﬁcation, and one should construe all references to justiﬁcation in this essay likewise. 2. The discussion in this section parallels that of Staley and Cobb (forthcoming), in which we articulate a similar suggestion in the context of Deborah Mayo’s error-statistical account of evidence (Mayo 1996; Mayo and Spanos 2009). 3. Just how to formulate the semantics of such statements is, however, contested (see, e.g., DeRose 1991 and Chalmers 2011). The central claims of the present proposal are independent of disputed issues regarding the semantics of epistemic possibility. 4. One might entertain as well an alternative formulation that replaces potential with veridical evidence. Such a formulation entails that the ideal is met only

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if one already knows h to be true (lest it be the case that for all one knows h might be false, in which scenario e is not veridical evidence for h). Because I do not wish to claim that JE is the only justiﬁcatory ideal that might be relevant to science, I offer (1) and (2) as sufﬁcient but not necessary conditions. Someone who wishes to embrace a single ideal of justiﬁcation might reformulate these conditions as both sufﬁcient and necessary. 5. For details regarding Hertz’s research, see Jed Buchwald’s fascinating and careful discussion (Buchwald 1994, 131–74), on which I draw heavily in what follows.

18 What Was Perrin’s Real Achievement? Bas C. van Fraassen

1. PHILOSOPHY LORE ABOUT THE PERRIN EPISODE There is a bit of conventional wisdom often recounted by Peter Achinstein and other Scientiﬁc Realists concerning the history of science: LORE: until the early twentieth century, there was insufﬁcient evidence to establish the reality of atoms and molecules; but then Perrin’s experimental results on Brownian motion convinced the scientiﬁc community to believe that they are real.

There are two views regarding the rationale for the nineteenth century disputes over, and in opposition to, the atomic theory. Steven Brush and John Nyhof, for example, argued that the opponents held positivist philosophical presumptions against admitting the unobservable1. Penelope Maddy holds, on the contrary, that the dispute was purely scientiﬁc. Either way, once the philosophers’ lore is accepted, the question becomes only how we can understand Perrin’s work as epistemically legitimating the conclusion drawn from it, that is, the reality of atoms and molecules. This question of legitimation (with its presupposition intact) is addressed by Wesley Salmon, Clark Glymour, and Peter Achinstein, with different answers (Salmon 1984, 221; Glymour 1975, 409, n. 12; Achinstein 2001, 243–65). Achinstein criticizes earlier accounts of Perrin’s reasoning, and offers his own “legitimation”—surprisingly, the premises he lists include a prior probability of at least ½ for the atomic hypothesis, and the conclusion is only that it is “greater” (Achinstein 2001). Maddy takes for granted that Perrin’s reasoning and results do legitimate the conclusion, and does not offer a competing account to these (Maddy 2001). Of course, this question of legitimation arises on the assumption that the story presents both historical events that happened and what was scientiﬁcally at stake, and therefore it presents the real signiﬁcance of this scientiﬁc advance. One presumption involved is that success of a theory means that

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it comes to be believed to be true, and that the work done to that end was signiﬁcant precisely in the way and to the extent that it produced evidence and arguments to justify that belief. This presumption is supported by a plethora of quotes from eminent scientists of the time, including erstwhile opponents of the atomic theory who changed their minds, that show that the advance consisted in demonstrating, beyond all reasonable doubt, that the atomic hypothesis was true. But do scientists, in practice, make the distinction so familiar to philosophers, between what is true and what is good for the future of their enterprise? Do they make the distinction between, on the one hand, counsel to doubt that there are atoms and, on the other, counsel to doubt that the atomic hypothesis points in a good direction for the advance of physics? When scientists describe the acceptance of a scientiﬁc theory, do they think in terms of such distinctions as those between truth, empirical adequacy, and pragmatic value? Even if particular scientists do so, should we take their judgments as free of interpretation? Or should we take them as unconditioned by social, cultural, or educational factors? Whether on the lips of scientists or of philosophers, it remains that LORE is an interpretation, though unacknowledged as interpretation. It can be challenged—or perhaps I should say, exposed as such—by presenting an alternative interpretation, and scrutinizing the credentials these rival interpretations may have. Only if alternative interpretations are considered can we see whether there are ambiguities in the story, and whether there are interpretative leaps.

2. DIFFICULTIES BESETTING THIS PHILOSOPHICAL LORE When the story is told in terms current in philosophy of science, we must be especially critical. Thus Maddy says simply: . . . in a case like the post-Einstein/Perrin atomic theorist, it seems incorrect to interpret the claim “there are atoms” to mean that the assertion of the existence of atoms is empirically adequate: it was considered empirically adequate before Einstein and Perrin; afterwards it graduated to another status. (Maddy 2001, 59)

But “empirically adequate” is a philosophical term of art; the scientists did not have that term. If they had had it, they certainly could not have thought that the evidence established that the atomic theory was empirically adequate, for that claim would extend far beyond the evidence. The history is anyway badly portrayed! If the reference is instead to empirical success conceived in a broader sense (taking “empirically adequate”

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in a less philosophically technical sense), then Maddy does follow Perrin’s presentation, but that portrayal looks Pollyannic given the severe problems of the atomic theory in the two decades preceding Perrin’s work.2 As always, the bottom line in the empirical sciences is to meet the criteria of success that relate directly to test and experiment. So let us leave this philosophical lore and the realism/empiricism debate behind and look into some actual empirical constraints on theories and models.

3. THE EMPIRICAL GROUNDING CRITERION The understanding in practice of what is required for a good empirical theory was in evidence throughout the development of modern science, but was not explicitly formulated until recently. I will begin with an early example to guide us, and then present a contemporary formulation, before entering on its application to the development of the atomic theory.

(1) Newtonians and the Cartesian critique The Cartesians’ critique of Newton was that, with his introduction of non-kinematic parameters such as mass and force, he had brought back “occult qualities.” The Newtonian response was, in effect, that admittedly what is measured directly are lengths and durations, but that they could show nevertheless how to measure mass and force. The rationale of this response was thoroughly reinvestigated in the nineteenth and early twentieth century, by Mach, Duhem, and Poincaré.3 As they showed, the measurement of those dynamic parameters on a body is an operation that counts as such a measurement relative to Newtonian theory. To say that the operation measures mass, for example, is to presuppose the applicability of Newton’s second and/or third law. So, for example, measurements of mass ratios with the Atwood machine,4 or by contracting springs, presuppose that the setup as a whole is a Newtonian system. The values of the masses are indeed calculated from the observations of kinematic quantities, but via Newton’s laws. The Newtonian response was precisely to the point, and it reveals quite clearly the norms concerning empirical constraint accepted in modern scientiﬁc practice. All the parameters in the theoretical models must admit of such empirical grounding.5 If not, they are empirically superﬂuous, and provide an obstacle to the acceptability of the theory. The baseline criteria for science are empirical. That explains why hidden variable theories do not get any attention among the scientists

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T

M T

Mg m

mg

Fig. 18.1. The machine of Rev. George Atwood (1746–1807). The accelerations are equal but opposite in direction, and proportional to (M−m)/(M+m), which determines M/m.

SPRING-CONNECTED MASSES

M m

CM

Fig. 18.2. The system’s center of mass (CM) is unchanged as the two carts approach one another.

themselves, as opposed to philosophers, until and unless there is some suggestion of a possibility of empirical testing. It is not relevant to object that all the evidence is as much in accord with the hidden variable variant as with the original. Parameters introduced into modeling must not be empirically superﬂuous—there must be, in some way, even if at some distance, coordination with empirically differentiating phenomena. Sometimes the parameters that appear to be empirically superﬂuous can be simply removed without imperiling either the coherence of the theory or its empirical strength and credentials. The “grounding” requirement turns into a salient problem only when elimination is not possible, that is, when

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there are no theoretically speciﬁable conditions in which their values can be determined, relative to the theory, on the basis of measurement results. The appropriate, and typical, response in that case is to start enriching the theory so that it becomes more informative, informative enough to allow the design of experiments in which this empirical determination of the values does become possible.6 But meanwhile, can we imagine the Cartesians’ feelings? Those measurements of mass or force make sense only in the context of the assumption that the setup or target is itself a Newtonian system—something that the Newtonian postulates. So how, in what sense, is this evidence that bears out Newton’s theory? How can the evidence, taken in a way that is neutral between the Cartesians and the Newtonians, legitimate the conclusion to the truth of the Newtonian theory? We can imagine the Cartesian asking these questions, and the dissatisfaction with this on the Cartesian side, especially since Cartesian general epistemology is paradigmatically foundational. But in this (uncharitable? anachronistic?) imagined response, the Cartesian is barking up the wrong tree—as are philosophers today if they remain ﬁxated on the question of evidence for the truth of a theory or for the reality of the entities a theory postulates.

Weyl and Glymour: The empirical constraints on science. The relevant methodological insight was, as I said, formulated much later; some of the current philosophical “conventional wisdom” seems never to have assimilated it. As initial formulation, here is Hermann Weyl in his Philosophy of Mathematics and Natural Science:7 1. Concordance. The definite value which a quantity occurring in the theory assumes in a certain individual case will be determined from the empirical data on the basis of the theoretically posited connections. Every such determination has to yield the same result. . . . Not infrequently a (relatively) direct observation of the quantity in question . . . is compared with a computation on the basis of other observations . . . 2. It must in principle always be possible to determine on the basis of observational data the definite value which a quantity occurring in the theory will have in a given individual case. (Weyl 1963, 121–2)

It is easier to read these points in reverse order. Given that one is called Concordance let us call the other Determinability. This deserves detailed discussion, but for now I just want to put the following empirical grounding requirement on center stage: • Determinability: any theoretically signiﬁcant parameter must be such that there are conditions under which its value can be determined on the basis of measurement.

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• Concordance has two aspects: ° Theory-Relativity: this determination can, may, and generally must be made on the basis of the theoretically posited connections Uniqueness: the quantities must be “uniquely coordinated”; there ° needs to be concordance in the values thus determined by different means.8 There is, at ﬁrst blush, a glaring possible objection to the completeness of this formula, if viewed as putatively sufﬁcient. If the theory’s being thus borne out by experimental and measurement results is on the basis of the theoretically posited connections, why does that fact not trivialize the putative evidence? This concern was addressed explicitly by Clark Glymour in his account of relevant evidence and testing. Glymour was explicitly following Weyl here, but saw the need for the additional constraint to prevent self-fulﬁlling prophecy in science. I will adapt the following to our present purpose, from Glymour’s Theory and Evidence—adapt and amend, since his presentation of the “bootstrapping method” was confusingly conﬂated with what was then called “conﬁrmation theory.”9 For simplicity let’s take theory T to be presented as a set of equations, involving certain parameters, some directly measurable and some theoretical, and take relevant evidence to consist similarly in a set of equations that simply assign values to some of the measurable parameters. Then Glymour imposes the constraint that there must be an alternative possible outcome for the same measurements that would have refuted the hypothesis on the basis of the same theoretically posited connections. His conception may be presented initially as follows: E provides relevant evidence for H relative to theory T exactly if E has some alternative E’ and T some subtheory T’ such that: (1) (2) (3) (4)

T ∪ E ∪ {H} has a solution. T’ ∪ E’ has a solution. All solutions of T’ ∪ E are solutions of H. No solutions of T’ ∪ E’ are solutions of H.

For example, if T consists simply of the equation P(t)V(t) = RT(t), with R a theoretical constant, then we can take H to be just T itself, and E could be E = {P(1) = 2, V(1) = 3, T(1) = 30; P(2) = 3, V(2) = 1, T(2) = 15}

which satisﬁes T while determining the value of R to be 5. It has the requisite possible alternative that could have been found instead; for example: E¢ = {P(1) = 2, V(1) = 3, T(1) = 30; P(2) = 3, V(2) = 1, T(2) = 11}

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which does not satisfy T for any possible value of R. (Here the subtheory T’ is trivial, empty, or tautologous, which is what makes the example very simple.) The threat of trivializing circularity or vacuity may not be entirely eliminated, in logical principle, by Glymour’s additional requirement. It would be surprising if we could ﬁnd complete sufﬁcient conditions for having an empirically solid theory so quickly. But satisfaction of the above requirements characterizes well and clearly what can be offered on behalf of the signiﬁcance of a particular empirical grounding of the theoretical parameters in any speciﬁc case.

4. THE PROBLEM OF EMPIRICAL GROUNDING IN THE NINETEENTH CENTURY Now we have come to the besetting problem of the atomic theory that Dalton introduced early in the nineteenth century, and that was extended into the kinetic theory of heat, and ﬁnally into the statistical mechanics that rivaled phenomenological thermodynamics. I’ll use the term “kinetic theory” to refer to all of that, for short. This methodological demand for empirical grounding, that we see so clearly operative throughout the modern history of science, applies to the kinetic theory as well. The attitude toward the atomic and molecular structure postulated in the nineteenth century was precisely that the models provided by the atomic theory must be thoroughly coordinated with measurement procedures. Let’s make the demand explicit in general terms: (I). If two such models of a given phenomenon differ only in the values of certain parameters, there must be in-principle measurement results that will differentiate between them. (II). Similarly, for any distinct states in the theory’s state-space, in which the model locates the systems’ trajectories, there must be in-principle measurable quantities that differentiate them. The term “in-principle” refers here not just to the idealization that measurements have unlimited precision, but also to Weyl’s observation that the differentiation is not crudely theory-neutral, but on the contrary, relative to the theory itself (and perhaps to additions from background theory). If these demands are satisﬁed, let us call those parameters, or the theory, empirically well-grounded. In a kinetic model of a gas, there are many parameters that pertain to the individual molecules. The empirical success of such models is related to the measurement of “gross” quantities such as mean kinetic energy. If two such

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models of a gas agreed on those quantities that were meaningfully measurable in phenomenological thermodynamics, but differed in the values of such parameters as individual masses, sizes, momenta, or number of molecules, could there be measurements to differentiate those, in principle? Philosophers’ history of the scientiﬁc research directed to this question has largely seen it displaying philosophical rather than scientiﬁc motivations. But if we look at the texts with new eyes we see that the objections and challenges concerned precisely the question of whether the parameters in the atomic theory could have their values determined by measurement relative to the theory—the question of empirical grounding.

5. PERRIN BEGINS To report on Perrin’s work here I will rely on the general presentation he gave of his work in 1909, just a year after the publication of his epochmaking experimental results.10

(1) How and where empirical grounding is needed Early on in his account, Perrin lists the parameters that have resisted satisfactory or sufﬁcient empirical grounding to date. Throughout the nineteenth century, hypotheses had been added to enrich the basic kinetic theory, and this meant that more and more procedures could be designed that would count as measurements, to determine values or at least to relate values of various quantities to each other. The prime example, very early on, was the addition of Avogadro’s hypothesis that allowed deduction of molecular mass ratios. In Perrin’s formulation, that hypothesis is that any two gram-molecules of a substance contains the same number of molecules, Avogadro’s number N.11 There is a similar theoretical relation between N and the mean kinetic energy of the molecules, via the ideal gas law; and this can in the same way be used to yield an equation connecting N and the mean square molecular speed. The perfect gas law is the well known equation PV = RT, where R is the perfect gas constant and the temperature T was proved to be proportional by the factor 3R/2N to the mean kinetic energy (Perrin 2005, 11–2). So we have as resultant the equation pV = (1/3)Nm<s2>, where • N = the number of molecules • m = the mass of each molecule • <s2> = the mean square speed of the molecules

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Pressure p and volume V can be measured directly; but on the right we see three theoretical parameters. The number of unknowns can be reduced still more if we bring in more such equations. For example, Perrin points out, when the theory of electricity is also brought into the fold, a relation can be deduced between the minimal electric charge e and this number N. On the kinetic theory, electrolysis is explained by postulating that in electrolysis the molecules are dissociated into ions carrying a ﬁxed electric charge. A Faraday is the quantity F of electricity that passes in the decomposition of 1 gram-molecule of hydrochloric acid; it is at the same time equated to the charge carried by one gram-molecule of hydrogen ions. It is known empirically that the decomposition by current of a gram-molecule of an electrolyte displays always the passing of the same quantity of electricity, and it is always a whole number of Faradays. This number must be the product of the number of ions taken with the number of minimal electric charges e that they carry. Putting these equations together and noting that by hypothesis one gram-molecule of hydrogen consists of N hydrogen atoms, we have Ne = F

where F is an empirically known quantity, and we have two theoretical parameters. Of course the two above equations can be combined, so as to place an equivalent constraint on just three of the theoretical parameters, with the fourth deﬁned in terms of the other three. It is easily seen that these theoretical developments consist only partly in calculations, and partly in the introduction of further hypotheses to elaborate on the basic kinetic model. At this point, measuring an electric charge, a mass, and a volume places on the numerical relations between parameters pertaining to the molecules and their motion some quite deﬁnite constraints relative to the theory as developed so far. In his exposition prior to the statement of his results, Perrin continues these points by adding in a similar hypothesis due to Maxwell, on the statistical independence of the spatial components of molecular speeds. To be speciﬁc, Maxwell derived a law of the distribution of molecular velocities in a gas, but on the special assumption that the distribution along spatial direction x is statistically independent of the distribution along the orthogonal y and z axes. Adding then a special hypothesis relating the internal friction between two parallel layers of a gas that are moving at different speeds to exchange of molecules between these layers, Maxwell found a further linkage to measurement, namely that:

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the coefﬁcient z of internal friction, or viscosity, which is experimentally measurable, should be very nearly equal to one-third of the product of the following three quantities: the absolute density δ of the gas . . . the mean molecular speed Ω . . . and the mean free path L which a molecule traverses in a straight line between the two successive impacts. (Perrin 2005, 14)

This gives information about the mean molecular speed, here designated as Ω. Adding to this a further hypothesis that provides a kinetic model for the internal friction between two parallel layers of gas, moving at different speeds, Maxwell arrived at the equation z = 0.31dWL

where: • z is the coefﬁcient of internal friction (viscosity)—an experimentally measurable parameter • δ is the absolute density of the gas (also measurable) • W is the mean molecular speed (mentioned above) • L is the mean free path of the molecules Given the hypotheses and measurement results so far then, the mean free path is calculable. Then with the still further addition that the molecules are spheres— one of very few shapes the kinetic models had admitted—Clausius and Maxwell derived an equation that ﬁxes the molecular diameter approximately as a function of the mean free path and the number n of molecules per cubic centimeter. The latter will bring us to Avogadro’s number N, but what is still needed to solve the equation in question is a second constraint on the relation between the molecular diameter and that number n. So now we have seen what the ﬁrst part of the 1910 monograph was devoted to spelling out: that empirical research and theoretical development in tandem had progressed to the point where you could see that relative to the theory (taken sufﬁciently broadly) only one more parameter needed empirical grounding to ﬁnish the job. At this stage in history Perrin can point out that relative to the theory, the measurement of any of these so far undetermined, or only partially determined, parameters would ﬁx the others as well (Perrin 2005, 12). Thus we see in principle a number of approaches to the empirical grounding of the so far remaining indispensable parameters in the models provided by the kinetic theory. By this we must mean of course: operations that will count as measurement, relative to the theory, that is, utilizing the above theoretically derived equations.

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Perrin’s research on Brownian motion is directed precisely to this end; and to begin it was quite independent of the new theoretical results due to Einstein. After his initial successes in determining values for those parameters, he continued by guiding further experiments in ways linked to Einstein’s work, and found good agreement with the previous results.12 To be realistic, we should note that the theoretical derivations that Perrin assumes are also largely dependent on assumptions added to the kinetic theory, in the construction of speciﬁc models. Most of the work proceeds with models in which the molecules are perfect spheres, for example, though Perrin notes that other hypotheses are needed in other contexts (Perrin 2005, 14). As long as the simple models work, to allow a transition from the empirically obtained results to values for the theoretical parameters, and as long as these values obtained in a number of different ways agree with each other and with what is theoretically allowed—to within appropriate margins of error—this counts as success. The addition Perrin made to this already almost century-old story follows the same pattern. As Achinstein emphasizes, Perrin also introduces an addition to the theory, a “crucial assumption, viz. that visible particles comprising a dilute emulsion will behave like molecules in a gas with respect to their vertical distribution.” (Achinstein 2001, 246) Not that this is a blithe addition: Perrin argues for its plausibility, but in terms that clearly appreciate the postulational status of this step in his reasoning. After a discussion of the range of sizes of molecules (according to results derived from measurements via such extensions of the theory as we have just been inspecting) he writes, Let us now consider a particle a little larger still, itself formed of several molecules, in a word a dust. Will it proceed to react towards the impact of the molecules encompassing it according to a new law? Will it not comport itself simply as a very large molecule, in the sense that its mean energy has still the same value as that of an isolated molecule? This cannot be averred without hesitation, but the hypothesis at least is sufﬁciently plausible to make it worthwhile to discuss its consequences. (Perrin 2005, 20)

On this basis, the results of measurements made on collections of particles in Brownian motion give direct information about the molecular motions in the ﬂuid, always of course within the kinetic theory model of this situation. But that is just what was needed for empirical grounding of those remaining theoretical parameters. This was not the end of the story for Perrin. What Weyl calls the requirement of concordance and unique coordination was apparently very much on his mind. Perrin begins Part III of this 1910 work with the remark

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that his experiments have allowed “the various molecular magnitudes to be determined” but then adds, But another experimental advance was possible, and has been suggested by Einstein at the conclusion of the very beautiful theoretical investigation of which I must now speak. (Perrin 2005, 51)

Perrin notes that Einstein obtained his results in part “by the aid of hypotheses which are not necessarily implied by the irregularity of the Brownian movement” and details two of them. These include his own main hypothesis, namely that “the mean energy of a granule is equal to the molecular energy” (2005, 53). After discussing a rather large amount of experimental work bearing on Einstein’s results, and its nevertheless inconclusive outcome, Perrin himself set about (to use his own words) an experimental conﬁrmation of Einstein’s theory. In this he was very successful as well. Not only that: in his experimental work related to Einstein’s theory, he arrived at the same values for the theoretical quantities as he had found in his own previous research. Logically speaking, the outcomes could have been at odds with each other, since no matter how tightly the theory is constructed, the actual results of measurement are after all “up to nature”. So we can read this part of the story as not simply a further inquiry but a demonstration that Weyl’s concordance requirement is taken into account and the credentials of the theory with respect to this empirical constraint are demonstrably provided.

(2) How Perrin ends his 1910 monograph Finally, although Perrin’s text is such a boon to scientiﬁc realist writing, I think we should attend to his own emphasis on how thoroughly empirical his work was. His explanation is precisely in line with what I have here displayed as the project of empirical grounding. This comes in his ﬁnal section, headed “43. Molecular reality,” and begins with the telling sentence Lastly, although with the existence of molecules or atoms the various realities of number, mass, or charge, of which we have been able to ﬁx the magnitude, obtrude themselves forcibly, it is manifest that we ought always to be in a position to express all the visible realities without making any appeal to elements still invisible. But it is very easy to show how this may be done for all the phenomena referred to in the course of this Memoir. (Perrin 2005 [1910], 91)

He then explains how to isolate the empirical content (still, although he does not say so, relative to the theory!) of the theoretical results. For example, he suggests comparing two laws in which Avogadro’s constant enters:

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The one expresses this constant in terms of certain variables, a, a¢, a², …, N = f[a,a¢,a²....];

the other expresses it in terms of other variables, b, b¢, b²,…, N = g[b,b¢,b²….].

Equating these two expressions we have a relation f[a,a¢, a²….] = g[b,b¢,b²….]

where only evident realities enter, and which expresses a profound connection between two phenomena at ﬁrst sight completely independent, such as the transmutation of radium and the Brownian movement (Perrin 2005, 91–2). Once again, it seems to me mistaken to read this in a philosophical vein. I do not offer this as a case of an apparent scientiﬁc realist contributing grist for the empiricist’s mill. Rather, this passage is important because of how it illustrates how the factors of Determinability and Concordance function in empirical grounding.

6. CONCLUSION In sum then, I propose we see the century-long story of research to establish the credentials of the kinetic theory as a truly empirical enterprise— not as a century-long search for independent evidence for the truth of a well-deﬁned hypothesis about what nature is like, but in a quite different light! Perrin aimed to develop the theory itself, and to enrich it so as to allow construction of models for special cases in its domain—all so as to make empirical grounding possible for its theoretical quantities. That enterprise essentially involves the concurrent development of measurement procedures to implement the grounding thus made possible. It is neither purely theoretical nor purely empirical, the theoretical and empirical are indissolubly entangled, but what is achieved is an empirical success. One greatly gratifying aspect of Perrin’s work was that when he followed up his own research on Brownian motion with an experimental inquiry into Einstein’s new theoretical development, he found a satisfactory concordance in the results obtained. It is still possible, of course, to also read these results as providing evidence for the reality of molecules. But it is in retrospect rather a strange reading—however much encouraged by Perrin’s own later prose and by the commentaries on his work in the scientiﬁc and philosophical

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community. For Perrin’s research was entirely in the framework of the classical kinetic theory in which atoms and molecules were mainly represented as hard but elastic spheres of deﬁnite diameter, position, and velocity, at a time when Rutherford was earning the Nobel prize for subatomic research. Moreover, the monograph begins with the conviction on Perrin’s part that there is no need at this late date to give evidence for the general belief in the particulate character of gases and ﬂuids. On the contrary (as Achinstein saw), Perrin begins his theoretical work in a context where the postulate of atomic structure is taken for granted. What can we make of all those triumphant remarks that suggest otherwise? I submit that we can interpret them as follows: that Perrin’s work laid to rest the idea that it might be good for physics to opt for a different way of modeling nature, one that rivaled atomic theories of matter. Precisely that is what was, in retrospect, well vindicated—an outcome as welcome to empiricists as to scientiﬁc realists, I would say. But for the methodology and epistemology of science the most salient conclusion to draw is, it seems to me, that evidence can be had only relative to the theories themselves (the “bootstrapping” moral) and that this is so because a theory needs to be informative enough to make testing possible at all. Thus the extent to which we can have evidence that bears out a theory is a function of two factors: ﬁrst, of how logically strong and informative a theory is, sufﬁciently informative to design experiments that can test the different parts of the theory relative to assumptions that the theory applies to the experimental set-up; and second, of how well the measurement results in situations of this sort are in concord with each other. But third, the testing involved cannot be adequately or properly portrayed as just checking on implied consequences (along such lines as suggested by the “hypothetico-deductive method” or Hempel’s “conﬁrmation theory”). To properly credential the theory, the procedures that count as tests and measurements in the eyes of the theory must provide an empirical grounding for all its signiﬁcant parameters. The completion of this task, which made the kinetic theory into, at least in principle, a truly empirical theory, was Perrin’s real achievement.

ACKNOWLEDGMENTS This is a somewhat modiﬁed version of my 2009 paper (van Fraassen 2009), offered here gratefully to Peter Achinstein for all that I learned from his work over the years. My thanks to the commentary by Helen Longino and the discussion at the 2008 Oberlin symposium, and for Greg Morgan’s help with revision. Research for this essay was supported by NSF Senior Scholar Award SES-0549002 and Award 1026183.

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REFERENCES Achinstein, P. 2001. The Book of Evidence. Oxford: Oxford University Press. Brush, S. G. 1976. The Kind of Motion We Call Heat. Amsterdam: North-Holland Publishing Company. Clark, P. 1976. Atomism Versus Thermodynamics. In Howson ed. Method and appraisal in the physical sciences. Cambridge: Cambridge University Press. De Regt, H. W. 1996. Philosophy and the Kinetic Theory of Gases. British Journal for the Philosophy of Science 47 (1): 31–62. Duhem, P. 1996. Essays in the History and Philosophy of Science, trans. R. Ariew and P. Barker. Indianapolis: Hackett. Earman, John, ed. 1983. Testing Scientiﬁc Theories. Minnesota Studies in the Philosophy of Science, vol. X. Minneapolis: University of Minnesota Press. Glymour, C. 1980. Theory and Evidence. Princeton: Princeton University Press. ——— . 1975. Relevant Evidence. Journal of Philosophy 72 (14): 403–26. Hanson, N. R. 1958. Patterns of Discovery. Cambridge: Cambridge University Press. Kuhn, T. S. 1961. The Function of Measurement in Modern Physical Science. Isis 52 (2): 161–93. Mach, E. 1960. The Science of Mechanics: A Critical and Historical Account of Its Development, 6th English edition. LaSalle, Ill.: Open Court. Maddy, P. 2007. Second Philosophy: A Naturalistic Method. Oxford: Oxford University Press. ——— . 2001. Naturalism: Friends and Foes. Philosophical Perspectives 15: 37–67. ——— . 2000. Naturalism in Mathematics. Oxford: Oxford University Press. Nyhof, J. 1988. Philosophical Objections to the Kinetic Theory. British Journal for the Philosophy of Science 39 (1): 81–109. Perrin, J. 2005. Brownian Movement and Molecular Reality, trans. F. Soddy. New York: Dover. Poincaré. 1905. Science and Hypothesis. London: Walter Scott Publishing. Salmon, W. 1984. Scientiﬁc Explanation and the Causal Structure of the World. Princeton: Princeton University Press. Van Fraassen, B. C. 2009. The Perils of Perrin, in the Hands of Philosophers. Philosophical Studies 143 (1): 5–24. ——— . 2008. Scientiﬁc Representation: Paradoxes of Perspective. Oxford: Oxford University Press. ——— . 1983a. Glymour on Evidence and Explanation. In Testing Scientiﬁc Theories, ed. J. Earman. Minneapolis: University of Minnesota Press. ——— . 1983b. Theory Comparison and Relevant Evidence. In Testing Scientiﬁc Theories, ed. J. Earman. Minneapolis: University of Minnesota Press. Weyl, H. 1963. Philosophy of Mathematics and Natural Science. New York: Atheneum.

NOTES 1. “In retrospect it seems clear that the criticisms of the kinetic theory in this period were motivated not primarily by technical problems, such as speciﬁc heats of polyatomic molecules but, rather by a general philosophical reaction against mechanistic or “materialistic” science and a preference for empirical or phenomenological theories. as opposed to atomic models” (Brush 1976, 245). See further Nyhof 1988.

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2. Perrin took a deﬁnite side in a live controversy, though one that was already being overtaken by the radical conceptual departures from classical mechanics at that time (in which Perrin took no part). The difﬁculties of the kinetic theory between 1880 and 1905 are graphically described by Clark (1976, 82–8), and while his philosophical take on this period is challenged by Nyhoff (1988), and their dispute evaluated critically by De Regt (1996), the role and impact of those difﬁculties on scientiﬁc research in that period are not challenged. 3. See Mach 1960, 264–6 and discussions in Duhem 1996, 121–2 and Poincaré 1905, 89–110. 4. I will make this more precise below. It is appropriate, I think, to relate this to the older term “coordination” of Mach, Schlick, and Reichenbach; see van Fraassen 2008, 115–40. 5. It is not the case that a logically weaker theory is automatically better conﬁrmed or better supported by the evidence. The weaker theory may not be informative enough to allow for the design of a test. So, for example, the mere hypothesis of atomic structure, taken by itself, is not a well-tested theory (or tested at all!), though it is part of well-tested theories. 6. This is quoted in Glymour 1980, 50 and discussed there, though it is not clear just how Glymour connects what Weyl writes with Glymour’s own central concern, which was conﬁrmation of hypotheses relative to theories. 7. This third point emphasizes here what Schlick and Reichenbach insisted on in the phrase “unique coordination,” though this was obscured by the lack of clarity, at the time, on the distinctions and relations between truth and veriﬁcation. 8. In fact Glymour’s conception, to replace the then (and still!) current notions of conﬁrmation, was a measure that was a function of both conﬁrmation and information. For an analysis see van Fraassen 1983a and 1983b. 9. This was translated into English within the year as the book Brownian Movement and Molecular Reality. Although less historically and technically informative on one hand, and on the other hand less explicit with respect to Perrin’s own interpretation of his results, it is much closer to the actual work than his later book Atoms. 10. A gram-molecule of a substance is the mass of this substance which in the gaseous state occupies the same volume as two grams of hydrogen measured at the same temperature and pressure. 11. Here the philosophical literature is not always in accord with Perrin’s own account. As I shall discuss below, Perrin (2005, originally published in 1910) presents his own research entirely before beginning part III with, “But another experimental advance was possible, and has been suggested by Einstein at the conclusion of the very beautiful theoretical investigations of which I must now speak” (2005, 51). Compare to this the order of presentation in Maddy 2000, 139–40 or Maddy 2007, 72, noting also the omitted background of initial experimental setbacks for Einstein’s work (Clark 1976, 97). 12. For the machine’s uses in measurement procedures cf. Hanson 1958, 100–2; Kuhn 1961, 169–72.

19 Causes, Conditions, and the Pragmatics of Causal Explanation Jim Woodward

1. INTRODUCTION Many standard accounts of causation, whether framed in terms of regularities involving necessary and sufﬁcient conditions, statistical relevance, or counterfactual dependence, fail to distinguish factors that (at least in ordinary language) are described as “causes” from those regarded as mere “enabling conditions.” Suppose, to adapt an example from Judith Thomson (2003), a bridge is constructed (B), providing, for the ﬁrst time, access from the mainland to an island. X crosses the bridge to the island and commits a robbery R there. Suppose B is an INUS condition for R, that it raises the probability of R, and that without B, R would not have occurred. Despite the satisfaction of these standard “objective” conditions for causal relevance, most people are reluctant to judge that B “caused” R. Instead we regard B as merely an “enabling condition” for R. What is the basis for this distinction? Although Peter Achinstein has not, to my knowledge, directly addressed this question, many attempts to answer it appeal to an idea to which (in related contexts) he has been sympathetic: that explanation, including causal explanation, has an important pragmatic dimension, where this means, roughly, that the goodness of an explanation (and perhaps other distinctions we may wish to make among explanations) depends in part on facts about the interests, attitudes, or background knowledge of the explainer or her audience. In particular, many philosophers have claimed there is no “objective” basis for the distinction between causes and conditions, and that the distinction instead has to do with what speakers or their audiences ﬁnd most more salient, interesting, important, or satisfying. Going further, the very fact that we distinguish between causes and condition is often thought to support the view that important aspects of

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causal explanation are pragmatic in character, since (the argument goes) it hard to see what other basis this distinction might have. This essay is organized as follows. Section 2 focuses on the cause/ condition distinction, arguing that in some substantial range of cases there are objective, structural, “out there in the world” differences between the way that causes and conditions are related to effects, and that these features inﬂuence judgments about the cause/condition distinction. Section 3 explores some consequences for pragmatic approaches to causal explanation like Achinstein’s.

2. CAUSAL SELECTION To set the stage for more detailed discussion, it will be useful to begin with the general notion of one factor, event etc. being causally relevant to another. One natural way of characterizing this is in terms of counterfactuals. Think of C and E as variables taking more speciﬁc values, corresponding, for example, to the presence or absence of some causal factor. In the simplest case (and the only one that will matter to us) C is causally relevant to E if, were the value of C to be different in some appropriate way, then the value of E would be different. This counterfactual should be understood as non-backtracking or “interventionist” counterfactual, in the sense of Woodward 2003. According to this notion of relevance, often many factors will be causally relevant to outcomes, including many that we would not readily describe as causes in ordinary language: the short circuit is causally relevant to the ﬁre, but so is the presence of oxygen and (arguably) the absence of a sprinkler system; X’s desire for Y’s money is causally relevant to the robbery X commits, but so is the existence of the bridge. In both cases, the ﬁrst factor cited is typically described as a cause of the outcome in question, while the other factors may be described as mere conditions. To avoid confusion I will write “causen” for this narrow notion of cause that contrasts with “condition.” The problem of “causal selection” is that of understanding the basis on which the causen/condition distinction is made. A widespread philosophical view is that causal selection is capricious and arbitrary, reﬂecting idiosyncratic facts about explainer and audience, but having no other more objective basis. John Stuart Mill writes, “Nothing can better show the absence of any scientiﬁc ground for the distinction between the cause of a phenomenon and its conditions, than the capricious manner in which we select from among the conditions that which we choose to denominate the cause” (Mill 1846, 198). David Lewis expresses a similar sentiment.

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We sometimes single out one among all the cause of some event and call it “the” cause, as if there were no others. Or we single out a few as the “causes,” calling the rest mere “causal factors” or “causal conditions” . . . We may select the abnormal or extraordinary causes, or those under human control, or those we deem good or bad, or just those we want to talk about. I have nothing to say about these principles of invidious discrimination. (Lewis 1986, 162)

Many philosophers (and psychologists) frame this claim about the arbitrariness of causal selection primarily as a claim about how we use (or ought to use) the word “cause,” but there are larger issues at stake. In many areas of scientiﬁc inquiry, researchers seem to distinguish among factors that are causally relevant in the broad sense to some explanandum of interest, focusing primarily on just a few of these, and relegating many others to the status of background. For example, many biologists focus on “genes” or “DNA” in contrast to other factors that are also causally relevant to phenotypic outcomes. This in turn prompts critics (e.g., Oyama 2000) to respond that this selective focus is arbitrary and without any principled basis. According to the critics, if two factors C1 (e.g., DNA, genes) and C2 (other cellular machinery, environmental factors) are both causally relevant to some outcome E, considerations of “causal parity” or “causal democracy” favor giving each equal attention. In effect, the critics agree with Mill and Lewis that any distinction among these factors must be without “any scientiﬁc ground” or “invidious” and take this to argue for a more egalitarian approach. One obvious response to Mill and Lewis is this: even if the conceptions of causation they favor (causation as the instantiation of a regularity of some kind in Mill’s case, causation as the ancestral of counterfactual dependence in Lewis’s case) provide no resources for distinguishing among the factors that are causally relevant to E (all such factors seem symmetrically related to E) perhaps there are other considerations that, even if inﬂuenced by pragmatic considerations, also draw on more objective facts about causal structure that contribute to the basis for the causen/condition distinction. This is the position I favor, but before turning to details, some further explanation is in order. The considerations I will discuss, having to do with (what I call) stability and speciﬁcity, should be understood as considerations that often or typically bear on causal selection; I do not claim these give us either strictly necessary or sufﬁcient conditions for some factor to be regarded as a causen (or as causally important, interesting, etc.) Moreover, these are certainly not the only considerations bearing on causal selection. In saying that these considerations bear on selection, I intend to make a broadly empirical claim: both ordinary people’s and scientist’s

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judgments about the cause/condition distinction and related matters are inﬂuenced by these considerations. I also think that it makes normative sense that people’s judgments are so inﬂuenced, but defending this claim is beyond the scope of this essay1. Turning to details, I begin with stability. Suppose that we have a relationship of causal relevance (understood as counterfactual dependence) between C and E. The stability of this relationship has to with the extent to which it will continue to hold as various background factors/circumstances Bi change, where a background factor is simply any factor distinct from C and E. The “larger” the range of background factors over which the C ® E relationship continues to hold, or the more “important” these factors, the more stable is the C ® E relationship. Other things being equal, we tend to treat factors C1 that are causally relevant to E and that bear more stable relations to E as “causesn” of E (or more important causes) and those factors C2 that are causally relevant to E but bear less stable relationships to E as “conditions.” Here are two examples, both from Lewis 1986, illustrating the intuition behind stability. In the ﬁrst, Lewis writes (R) a letter of recommendation with the result that X gets a job she would not otherwise have gotten, meets and marries someone she would not otherwise have met and married, and has children who would not otherwise exist, who then engage E in certain activities. R is causally relevant to the birth B of these children and to E. Nonetheless, we do not ﬁnd it natural to describe R as a cause of either B or E; instead R is at best an enabling condition. My suggestion is that this judgment is inﬂuenced by the fact that the relationship between R and B (and E), although one of causal relevance, is highly unstable or “sensitive” in Lewis’ language. Change any one of a large number of background factors, and the relationship of causal relevance (counterfactual dependence) between R and B/E would no longer hold— this would happen if, for example, a stronger candidate had applied for the job X got, if X had lingered a little less long in the bar where she met her spouse and so on. Contrast this with an example in which Y is shot (S) through the heart by a large caliber bullet at point blank range and dies (D). S is certainly causally relevant to D, but in addition, in comparison with the previous example, the relation of counterfactual dependence between S and D is relatively stable. No doubt there are some possible background circumstances in which, were Y shot in this way, she would not die, but (we may assume) these are unlikely or far-fetched. In most realistic non-science ﬁctitious scenarios in which Y is shot in this way, she dies. This is connected, I suggest, to our willingness to regard S as a cause, and not a mere condition for D.

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I said above that the “larger” or “more important” the range of background factors over which the C ® E relation holds, the more stable this relationship. I lack both the space and the ability to satisfactorily unpack the quoted phrases, but the following considerations are relevant. First, sometimes a natural measure, supplied by subject-matter-speciﬁc considerations, over relevant ranges of background conditions will be available and this will allow us to sensibly talk about larger or smaller ranges of such conditions. A gas released into a larger container will expand for all but a set of measure zero initial conditions—this counts as a “large” set and makes the claim about expansion a stable one. Second, background conditions that are common or frequent or typical (around here, right now) count more for purposes of assessing stability than background conditions that are not common—this is part of what led us to regard the S ® D relationship as relatively stable. The limiting case is a situation in which there is a condition Bk, the presence of which is sufﬁcient for E to be counterfactually dependent on C, and Bk is virtually always present—as, for example, oxygen is near the surface of the earth. Third, subject-matterspeciﬁc considerations can also tell us that, for certain causal relationships, stability under some background conditions is more important than stability under others. For example, if a gene G is causally relevant to phenotypic trait P in highly speciﬁc environmental conditions E, but the G ® P relationship would not continue to hold under environmental conditions different from E, then, ceteris paribus, biologists are likely to regard the G ® P relationship as unstable and to this extent a condition rather than a cause for P. As an illustration, suppose the expression of gene G is required for learning mathematics and let P be the acquisition M of some particular bit of mathematical knowledge. G is causally relevant to M but most biologists would be unlikely to describe G as a cause of M, again at least in part because the G ® M relationship is highly unstable under changes in environmental conditions—place the learner in a different pedagogical environment and she would not learn M. Expression of G is instead an enabling condition for acquiring M, with a better candidate for the causen of M being, for example, the learning regime involved in acquiring M. I believe a similar analysis applies to many other examples discussed above. The construction B of the bridge is causally relevant to R in Thomson’s example, but the B ® R relationship is naturally regarded as highly unstable. Change any one of a large number of background conditions, including X’s desire to commit robbery, the availability of a victim and so on, and the B ® R relationship would be disrupted. This inﬂuences us in the direction of thinking of B as a “condition for” rather a “causen” of R. A second set of considerations that is relevant to the cause/condition distinction has to do with speciﬁcity. Speciﬁcity has several different

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dimensions but for reasons of space I focus on just one, which is related to Lewis’s (2001) notion of inﬂuence. Suppose that C is causally relevant to E. The relation of C to E will be causally speciﬁc (or C will be a speciﬁc cause of E) to the extent that C and E are variables that can be in any one of a number of different possible states or can take a number of different possible values (c1 . . . cn), (e1 . . . em) and there is a pattern of systematic dependence between these two sets of values. More speciﬁcally, there should be a mapping F from C to E such that for many different states of C each such state has a unique image under F in E (that is, F is a function or close to it); not too many different states of C are mapped onto the same state of E (the ideal being that F is 1–1); and most states of E are the image under F of some state of C (ideally F should be onto). F should describe patterns of counterfactual dependence between states of C and states of E, where the dependence in question is of the sort associated with non-backtracking or interventionist counterfactuals. To the extent that this condition is satisﬁed, then which particular state of C is realized provides for the possibility of a kind of ﬁne-grained control over (or modulation of) which particular state of E is realized. The contrasting notion of a non-speciﬁc cause is that of a causally relevant factor, the operation of which is more nearly switch-like: in the limiting case, there are just two possible states of C, c1 and c2, and two possible states of E, e1 and e2. Changing from, for example, c1 to c2 changes which state of E is realized but no further; more ﬁne-grained modulation of E by altering the state of C is possible. As an illustration, consider an ordinary copying machine. Any one of an indeﬁnitely large number of different texts T = t1 … tk may be introduced into the machine and, as long as the machine is on, in each case a correspondingly different copy R is produced. The text inputted is a highly speciﬁc cause of the text that is outputted—by varying T, one may achieve a very ﬁne-grained, modulated level of control or inﬂuence over R. The copying machine also has an on-off button B, capable of assuming just two states, also causally relevant to the output of the machine. For the machine to produce copies at all, B must be in the “on” rather than the “off” position, but it is not possible, by introducing more ﬁne- grained variations in the value of B, to further modulate what the output of the machine is. B is a relatively non-speciﬁc cause of whatever output the machine produces. My suggestion is that, other things being equal, we are more likely to regard causally relevant factors that are relatively speciﬁc as “causes” in the narrow sense (causen) that contrasts with “condition” and more likely to regard causally relevant but non-speciﬁc causes as conditions. In the copying machine, both the text being copied and B are causally relevant

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to the output, but, if we are engaged in causal selection, we are more likely to regard whether the machine is on as mere condition for the output and the text being copied as “the” causen of the output. Now consider a more scientiﬁcally interesting example. Molecular biologists sometimes argue that the state of the cellular DNA plays a different kind of role in determining which proteins are synthesized than other factors that are also causally relevant to protein synthesis, such as the presence of RNA polymerase (an enzyme involved in RNA synthesis) and other elements of the “cellular machinery” involved in protein synthesis, even though all are causally relevant to protein synthesis. Davidson (2001), for example, tells us that it makes sense to focus on DNA sequence in explaining protein synthesis and the generation of morphological diversity, because DNA sequence is a “more speciﬁc” cause of these outcomes than the other machinery involved in producing it. This ﬁts with the idea that considerations of speciﬁcity play a role in causal selection. Variations in DNA sequence are causally speciﬁc in the sense described above while the presence of RNA polymerase is non-speciﬁc; if the latter is absent or diminished, protein synthesis will slow down or stop, but variations in the level of RNA polymerase do not modulate which proteins are synthesized in a ﬁne-grained way. Let us take stock. I have drawn attention to two kinds of considerations— stability and speciﬁcity—that I claim are relevant to causal selection and to the cause/condition distinction. These considerations have an objective structure or core that I have tried to characterize. However, I do not claim that these considerations can be speciﬁed in a completely abstract, noncontextual way that is entirely independent of the interests and background knowledge of inquirers. Instead, contextual and interest-relative considerations inﬂuence the ways in which stability and speciﬁcity are understood or ﬂeshed out or applied in particular situations, but they do so in a way that is mediated or structured by the content of these ideas. The stability of a relationship has to do with whether it holds under some range of background circumstances, but which such circumstances are regarded as most important for the purposes of assessing stability may depend on subject-matter-speciﬁc considerations, or the interests of inquirers. Similarly, judgments of speciﬁcity will be inﬂuenced in part by how ﬁne- or coarse-grained the predicates are that we use to describe nature, and this will in part reﬂect our cognitive and practical interests. The presence of a short circuit is likely to strike us as a more speciﬁc cause of a ﬁre than the presence of oxygen, in part because we ﬁnd it natural to think of possible variations in the place or time at which the short circuit occurs, and hence to think in terms of the time and place of the ﬁre as subject to modulation by means of these variations. By contrast, special circumstances

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aside, the presence of oxygen is likely to be conceptualized in such a way that the only two possibilities are that it is either present everywhere in the situation of interest or not, which encourages us to think of it as non-speciﬁc. But while context and interests inﬂuence the ways in which stability and speciﬁcity are interpreted, and hence inﬂuence processes of causal selection, this inﬂuence does not, so to speak, operate in a completely indiscriminate and unstructured way, but rather through more structured considerations of a sort that I have attempted to describe. And while context and interests inﬂuence judgments of stability and speciﬁcity, so too do “objective” facts about the structure and behavior of the systems we are trying to describe—it is in part facts about what the world is like that make it the case that, for example, the relationship between Lewis’s letter of recommendation and the births of X’s children is relatively unstable. So far I have said nothing about the relationship between causal selection and another feature of causal claims—that they exhibit contrastive focus—that has been a topic of a considerable philosophical discussion. By contrastive focus, I mean that causal claims often (perhaps always) can be understood as exhibiting a “rather than” structure in both the effect and cause position: C caused E is perspicuously rendered as something like “C’s being in state c1 rather than state c2 caused E’s being in state e1 rather than state e2.” Often selection of a causally relevant factor as a causen rather than a condition can be naturally expressed in terms of contrastive focus—indeed thinking of a causally relevant factor as a causen rather than a condition is often tantamount to thinking of an effect in terms of one contrastive focus rather than another. If we think of the occurrence of a short circuit as a causen, and the presence of oxygen as a condition, then it will be natural to think of the effect as something like the occurrence of a ﬁre at time t and place p, rather than the occurrence of a ﬁre at some other time and place. The cause is then understood as the occurrence of a short circuit at some particular time and place, appropriately related to the ﬁre, rather than the occurrence of a short circuit (or perhaps some other ﬁre-causing agent) at some other time and place. Since oxygen is assumed to be ubiquitous, its presence does not cause (cannot be used to causally explain) the ﬁre at one place or time rather than another. Or to put the matter the other way around, to think of the effect as the occurrence of a ﬁre at t and p, rather than some other time and place is to think of the occurrence of the short circuit as a cause and the presence of the oxygen as a mere condition. Similarly in Thomson’s example, if, as would be natural, one thinks of the effect as X’s committing robbery rather than engaging in some other activity Z, such as sight-seeing on the island, then the presence of the bridge is not a causen of this effect since it is a precondition for both X and Z.

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Does this mean that there is nothing more to the problem of causal selection than the choice of one contrastive focus rather another in causal inquiry? No. For one thing, problems of causal selection can remain even if the contrastive focus of the effect is ﬁxed, as happens when one must select among causes that are more or less proximal to the effect or at different “levels” of analysis. But in addition, if one thinks of selection and contrastive focus as connected in the way described, then one can equally think of factors affecting selection like stability and speciﬁcity as also affecting choices about contrastive focus—stability and speciﬁcity lead us to conceive of the explanatory problem we face in terms of one contrastive focus rather than another. To the extent that we value identifying causes that are speciﬁc, this leads us to think of the effect we are trying to explain as, for example, the synthesis of one particular protein rather than another, and not as the synthesis of some protein or other (rather than none at all.) Similarly, to the extent that we value stability, it will be natural to think of the effect of interest as X’s robbing rather than X’s engaging in some other island-involving activity. In other words, although contrastive focus gives us a (partial) framework for representing problems of causal selection, considerations like stability and speciﬁcity remain in the picture, as factors inﬂuencing the choice of contrastive focus.

3. PRAGMATICS I now turn to some connections with Achinstein’s views on the pragmatics of explanation. According to Achinstein (1984), an explanation-sentence is “strongly pragmatic” if (i) it contains terms that refer to an explainer or audience and (ii) the truth-value of the explanation-sentence can vary with the person giving or receiving the explanation. Peter discusses the following notion of a “good explanation” that is strongly pragmatic: “E will be a good explanation for an explainer to give in explaining q to an audience if E is capable of rendering q understandable in an appropriate way to that audience by producing the knowledge of the answer to Q that it supplies that it is correct . . .” (Achinstein 1984, 284). In a striking discussion, Achinstein goes on to suggest there will be counterexamples to both the necessity and sufﬁciency of any purported universal condition for explanatory goodness (including those advanced in familiar philosophical theories of explanation) that is speciﬁed in a non-contextual, non-audience-relative way. For any such condition, there will be audiences for whom some explanations satisfying the condition do not produce the appropriate sort of understanding and explanations not satisfying the condition that do produce understanding.

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I don’t want to directly challenge this claim, but rather to suggest that, even if it is correct, traditional non-pragmatic theories of explanation may remain valuable and illuminating. (I don’t think that Peter would disagree.) First, let us note that the notion of a “strongly pragmatic explanation” is consistent with a range of possibilities. One possibility is that (as an empirical matter) some common set of features of many explanations is judged as contributing to their explanatory goodness by many different audiences, even if not by all possible audiences. In other words, the assessment of these features as good may be relatively (even if not universally) robust across variations in audience. And the good-making features in question may admit of some interestingly general characterization in terms of shared structural features (as illustrated, perhaps, by stability and speciﬁcity.) Another contrasting possibility is that the assessment of some class of explanations is highly non-robust across variations in audience, changing in capricious and idiosyncratic ways depending on audience characteristics. Relatedly, there are no general features or patterns in these explanations that account in a non-trivial way for this variation—all that can be said is that some audiences ﬁnd the explanations satisfying or appropriate and others do not. This second possibility might be characterized as a kind of “radical” (as opposed to merely “strong”) pragmatism about explanation. Something like this may be what Mill and Lewis have in mind in connection with causal selection. Their claim is not just that for any principle that might be proposed as governing causal selection, there will be some cases in which some audience does not ﬁnd the selection of the cause recommended by the principle appropriate or satisfying, and some cases and audiences with the opposite proﬁle. They endorse the much more radical view that there is lots and lots of audience-relative variation; causal selection varies widely and arbitrarily across different audiences, depending on the vagaries of their interests. Relatedly, they also hold there are no objective features out there in the causal structure of the world that play a role in guiding causal selection. My discussion above is intended to illustrate the possibility that causal selection (and causal explanation more generally) can have a “strongly pragmatic” aspect to it, in Peter’s sense, without being idiosyncratic to particular audiences in the way suggested by radical pragmatism. A second, related theme is that, supposing that we agree that context, interests, and background knowledge affect assessments of explanations, this can happen in different ways. One possibility—again perhaps illustrated by the Lewis/Mill view of causal selection—is that their inﬂuence is unstructured and conforms to no general patterns. Another possibility is that their inﬂuence is more structured, patterned and mediated: people’s interests do guide their causal selections but there are general patterns of a

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non-idiosyncratic sort that in turn inﬂuence what they ﬁnd interesting: for example, other things being equal, people are more interested in stable causal relationships, ﬁnd them more explanatorily satisfying, are more likely to cite them in causal judgments, and so on. It is this possibility that is consistent with traditional accounts of explanation remaining valuable and interesting. It would be worthwhile to try to distinguish between these possibilities empirically. One could see whether for different groups of subjects, their causal selections, explanatory judgments, and so on are correlated with or independent of the presence of features like stability and speciﬁcity in presented causal scenarios.2 If the account sketched above is correct, there will be such correlations even if they fall well short of 1.0 (as will be the case if there are no strictly necessary or sufﬁcient conditions for selection as cause rather than a condition). The Mill/Lewis view predicts no such correlations, at least when subject’s interests are manipulated independently of these structural features. REFERENCES Achinstein, P. 1984. The Pragmatic Character of Explanation. In Proceedings of the Biennial Meeting of the Philosophy of Science Association, ed. P. D. Asquith and P. Kitcher. Chicago: University of Chicago Press. Davidson, E. H. 2001. Genomic Regulatory Systems: Development and Evolution. San Diego: Academic Press. Lewis, D. 2000. Causation as Inﬂuence. Journal of Philosophy 97 (4): 182–97. ——— . 1986. Philosophical Papers. Oxford: Oxford University Press. Mill, J. S. 1846. A System of Logic. New York: Harper & Brothers. Oyama, S. 2000. Causal Contributions and Causal Democracy in Developmental Systems Theory. Philosophy of Science 67 (Proceedings): S332-S347. Thomson, J. J. 2003. Causation: Omissions. Philosophy and Phenomenological Research 66 (1): 81–103. Woodward, J. 2010. Causation in Biology: Stability, Speciﬁcity, and the Choice of Levels of Explanation. Biology and Philosophy 25 (3): 287–318. ——— . 2003. Making Things Happen: A Theory of Causal Explanation. New York: Oxford University Press.

NOTES 1. See Woodward 2010 for such a defense and for more details on stability and speciﬁcity. 2. Forthcoming experimental work by Tania Lambrozo explores these questions.

20 Achinstein’s Replies

I feel most honored by the contributors for their essays on my views in the philosophy of science. Below I respond to them individually. I want to express deep appreciation to Greg Morgan not just for getting the idea for such a volume, but for his wisdom and patience in organizing and editing it. He informed me that according to the agreement with Oxford University Press (and its classy editor Peter Ohlin), the volume was not to be the usual sort of festschrift in which contributors submit a paper on some topic or other that I might enjoy reading, but a paper about my views that I might not enjoy reading, to which I was to reply. Greg has accomplished his mission: the papers confront my work directly; and in fact I did enjoy reading them even when my philosophical foibles were exposed. What they did, which I fully appreciate, is force me to think in new ways about my views, to see implications that I have not previously appreciated, and in the space I have been allotted, to offer compact formulations that will enable readers to more easily identify and understand the main differences between the positions I take and those of others, including my critics. It is my good fortune to have had outstanding graduate students during my career, ten of whom are contributors to this volume. They are Victor Di Fate, Gerald Doppelt, Steve Gimbel, Adam Goldstein, Fred Kronz, Helen Longino, Jeff Maynes, Greg Morgan, Richard Richards, and Kent Staley. Some of them explain my views, some criticize them, some extend them, some do all three—for which I am very grateful. I am also very pleased to have such formidable philosophers as Nancy Cartwright, Jordi Cat, Philip Kitcher, Larry Laudan, Deborah Mayo, John Norton, Stathis Psillos, Michael Ruse, Bas van Fraassen, and Jim Woodward critically discuss my positions. In my responses below I hope that I have interpreted the account of each of the contributors correctly and that what I say will help clarify my positions and even successfully answer some of their challenges. Finally, I offer special thanks to Linda S. Brown for very perceptive comments and suggestions that helped improve my replies.

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GIMBEL AND MAYNES ON MY PROVENANCE Many thanks to Steve Gimbel and Jeff Maynes for their very perceptive account of early major inﬂuences on my thinking: logical positivism, particularly the views of Rudolf Carnap and Carl G. Hempel; ordinary language philosophy, especially as practiced by John Austin and Peter Strawson; and the views about logic and pragmatism of W. V. Quine. To Carnap and Hempel I am indebted for raising the question of what it means, or should mean, to talk about evidence and explanation in science, and for providing answers that I have found very stimulating, even though I suggest quite different ones of my own. Austin’s work on speech acts, particularly illocutionary ones, has been inﬂuential in the development of my own theory of scientiﬁc explanation. Strawson got me to think in new ways about induction and its justiﬁcation. Finally, in developing my own views about evidence, I found that I needed to respond to Quine’s challenging doctrine of holism. I have been fortunate in having had personal contact with, and learning from, these major philosophers. Quine, Hempel, Austin, and Strawson were teachers of mine. Carnap was not, though we exchanged ideas in letters and in print.

CARTWRIGHT ON MY “MANTRA” It is most pleasing for me to know that I have an ally, especially such an important one, in the person of Nancy Cartwright. She is concerned with “effectiveness predictions” stating that a certain policy treatment T will result in an outcome O, where randomized controlled trials (RCTs) are standardly taken to be evidence for such predictions. Using the mantra “evidential relevance = explanatory relevance” that she ascribes to me, she questions whether RCTs really do provide evidence, and she explains what is generally missing in such studies in terms of that mantra. Cartwright and I use somewhat different terminologies, but she is right in claiming that evidence (which she also calls “evidential relevance”) requires correct explanation. Even if p(h/e) or p(e/h) are high, or even if p(h/e) > p(h), this is not sufﬁcient. On my own view, e is (veridical) evidence that h (the kind that scientists in general seek), given background information b, if and only if (1) p(there is an explanatory connection between h and e/e&b) > ½; (2) e, b, and h are all true; (3) e does not entail h; and (4) (in the strongest and most interesting type of veridical evidence) there is an explanatory connection between h and e. By an explanatory connection between h and e I mean that the fact that e is true correctly explains why h is true; or the fact that h is true correctly explains why

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e is true; or some hypothesis correctly explains why both e and h are true. Cartwright has a more nuanced way of expressing this idea, but I think we are in general agreement here. We are also in agreement that what I call an explanatory connection, and what she calls explanatory relevance, is an objective concept, not to be relativized to anyone’s epistemic situation. She is not at all worried if the concept of correct explanation is not further deﬁnable (though, unlike her, I do attempt to provide a general deﬁnition that I claim will work). On her view, as well as mine, one can have evidence for an evidential claim, since the latter is most usually an empirical claim. And she asserts that in randomized controlled trials, if we do want to claim that the policy treatment will result in a certain outcome, then we must have evidence that this explanatory connection holds. The latter is frequently not the case with RCTs—which is why she believes that such evidential claims are given insufﬁcient justiﬁcation by their proponents. For Cartwright, the most interesting cases are ones in which what she calls a “study conclusion” is taken to be evidence for a “target conclusion.” Here a policy treatment T is given to one group (the study group) and the results are then taken to be evidence that the treatment will have similar effects in the target group. Such a claim presupposes that there is a common explanation for effects in both groups (or, at least, this is the simple way I would put her point). Yet such a presupposition may well be false, as many examples show. That is why in such cases the evidential claims are faulty. I am sure Nancy and I can ﬁnd aspects of evidence in which our views don’t coincide. But I accept the mantra she has given me with pleasure, and I welcome her claims about interesting cases in the social sciences in which “explanatory relevance” is necessary for evidence.

CAT ON MAXWELL Before turning to Cat’s discussion of my claims about James Clerk Maxwell’s “method of physical speculation,” it is important to note that throughout much of his career Maxwell was concerned with an important methodological question: is it scientiﬁcally legitimate to introduce physical hypotheses dealing with “unobservable” entities and causes, and if so, how can this be done? He provided different answers at different times. In 1855, in his paper “On Faraday’s Lines of Force,” when dealing with “electrical science,” Maxwell chose to avoid such hypotheses altogether in favor of what he called “physical analogies.” He introduced an analogy between the electromagnetic ﬁeld and a purely imaginary

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incompressible ﬂuid ﬂowing through tubes of varying section. He believed that such an analogy would provide a “simpliﬁcation and reduction of the results of previous investigation to a form in which the mind can grasp them” without postulating or inferring the real existence of the analog introduced or of any “unobservable” entities or causes. In 1860, in his ﬁrst paper on kinetic-molecular theory, although Maxwell introduces “unobservable” molecules, he speaks of the theory as providing a “physical analogy,” as he did in the previous case. Nevertheless, this case is very different from the electrical one. In the latter, the properties of the imaginary incompressible ﬂuid are analogs of, but not identical with, those of the electromagnetic ﬁeld (e.g., the velocity of the ﬂuid at a point in the ﬂuid is the analog of the electrical force at a point in the ﬁeld). But in the kinetic theory case, the properties attributed to the system of molecules postulated are the same as those attributed to a gas (e.g., pressure, temperature, volume, satisfying Boyle’s law). Rather the idea here seems to be to engage in pure speculation about the internal structure of gases, by supposing that a gas is identical with (not an analog of) a system of molecules; by supposing that such a system satisﬁes a set of simplifying assumptions Maxwell introduces; and by showing how to derive interesting theoretical and observational consequences from these assumptions. All of this is done without making inferences that the hypotheses introduced are true, or probable, or believable. At one point, Maxwell refers to this as an “exercise in mechanics.” (For a discussion of this paper, and a contrast with the previous one, see my Particles and Waves.) In 1875, Maxwell took yet a third approach to “unobservables” in his paper “On the Dynamical Evidence of the Molecular Constitution of Bodies” when he introduces what he calls a “method of physical speculation.” (It is this method that I discuss in my paper “What to Do If You Want to Defend a Theory You Cannot Prove,” Journal of Philosophy, Jan. 2010, reprinted in my Evidence, Explanation, and Realism.) In his 1875 paper, Maxwell claims that in dealing with unobservable molecules, he will employ a method that will yield less than decisive proof but more than mere “conﬁrming instances” supplied by the hypothetico-deductive method. Such a method, if properly employed, can furnish justiﬁed belief, at least in the central and distinctive assumptions of a theory. The method, as I reconstruct it, has four components. The ﬁrst component, independent warrant, contains experimental results arrived at independently of the theory in question from other domains that provide a causal-inductive basis for supposing that the postulated unobservables exist and have the properties attributed to them. It may include other sorts of reasons as well; for example, in defense of the dynamical principles introduced that

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are supposed to govern molecules, Maxwell cites their generality and fundamental nature. But whatever reasons are given in favor of the basic assumptions, they are not of the hypothetico-deductive form “if we make these assumptions, then we can explain and predict such and such.” The second component consists of derivations and explanations of known phenomena. The third is a “theoretical development” of the theory, which involves raising and answering a range of questions about what properties and principles in addition to those introduced in components 1 and 2 the unobservables satisfy. This task usually requires introducing new theoretical assumptions for which there may not be independent warrant, and derivations of new results that may not be testable at the time (e.g., Maxwell’s distribution law for molecular velocities). Depending on how extensive the “theoretical development” is, it can provide an important basis for defending the theory non-epistemically on grounds of completeness and precision—criteria that Maxwell valued particularly highly. The ﬁnal component consists of a listing of unsolved problems. In my paper I show how, especially with respect to components 1 and 3, this method is different from hypothetico-deductivism. With this brief summary of Maxwell’s “method of physical speculation,” let me respond to three of Cat’s claims about my understanding of this method. First, he claims that I examine Maxwell’s method “in pursuit of a theory-oriented argument for realism.” Although I am indeed a scientiﬁc realist, in the paper in question I explicitly reject the idea that Maxwell’s method must be understood in the context of, or as presupposing, realism (see fn. 2 in that paper). Anti-realists can raise the same question as Maxwell is by asking how to defend a theory when you cannot prove that it “saves the phenomena.” Maxwell’s method of physical speculation can be understood as a method for answering this question as well. My paper was not written with the aim of defending realism. Second, Cat claims that whereas I understand Maxwell’s method in a “disuniﬁed” way, he understands it rather simply as (A) “an inductive method linked to empirical warrant. The method of physical speculation, I propose, is the method of generalized hypothesis.” Whether my account is “disuniﬁed” because it doesn’t cover all of Maxwell’s various pronouncements about methodological strategies, or whether it is because my reconstruction of the method involves four distinct components, Cat does not say. If it is the latter, then I invite him to say why a method with four components is disuniﬁed. (This is not like postulating four distinct forces in nature.) If it is the former (which I suspect), then I would simply repeat what I say in the ﬁrst part of my reply above: throughout his career Maxwell struggled with the question of how to deal with hypotheses involving “unobservables,” and he did in fact

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employ quite different methodological strategies for doing so in the three papers I mentioned. Cat’s characterization of the method of physical speculation in (A) is sufﬁciently broad and vague to apply to my reconstruction of that method, since the latter involves “generalized hypotheses” as well as induction. But it also applies to the method of hypothesis, which Maxwell rejects in his 1875 paper. Third, Cat objects to some of the examples I invoke in the “independent warrant” component of the method, although his grounds for doing so are not completely clear to me. In my paper I refer to experiments of Rumford and Davy at the end of the eighteenth century, showing the impossibility of treating heat as a ﬂuid (caloric), and those of Joule in the 1840s on heat produced by friction of bodies establishing a relationship between mechanical work and heat. I claim that Maxwell may well have had these experiments in mind in his 1875 paper when he speaks of having “experimental proof that bodies may be divided into parts so small that we cannot perceive them.” I also cite Maxwell’s explicit claim regarding the success of dynamical principles in astronomy and electrical science as his basis for applying those principles to molecules. Cat’s objection seems to be that these experiments, as well as the appeal to dynamical principles, can be understood hypothetico-deductively. No doubt a hypothetico-deductivist can respond to Maxwell by showing how he can interpret the appeal to experiments and the success of dynamical theories in accordance with his viewpoint. But in the 1875 paper Maxwell rejects hypothetico-deductivism. And his appeal to the success of dynamical theories is pretty clearly an inductive argument to their success in the molecular realm. In his brief comment, Cat makes a reference to a different work of Maxwell’s, namely, an encyclopedia article entitled “Atom,” published just one year after his paper introducing the “method of physical speculation.” Here Maxwell cites various experiments, and Cat may be claiming that Maxwell is simply arguing hypothetico-deductively that because molecular theory can explain the experimental results, it is made probable by such results. In this article there is no mention of the method of physical speculation and no explicit rejection of hypothetico-deductivism. Nevertheless, Maxwell does begin his section on “Modern Molecular Science” by offering independent warrant for some of the basic assumptions of the theory, and as in the earlier paper he proceeds by introducing the Clausius virial equation, which is derived from classical mechanics. I believe the strategy employed by Maxwell in this encyclopedia article can be shown to conform reasonably well to his method of physical speculation, as I have interpreted it, although I will not pursue that here. Whatever the case, my interest is in the latter method, and what that commits one to, whether or not Maxwell

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earlier or later failed to employ it. I regard this method as an important one for philosophers to examine, since scientists are, I think, frequently in the position outlined by Maxwell at the beginning of his 1875 paper. They are frequently able to defend a theory both epistemically and nonepistemically without having experimental proof, but having a sufﬁcient basis to claim that the theory is a good one and a sufﬁcient basis to be justiﬁed in the belief that the central ideas of the theory are correct.

DI FATE AND “JUSTIFICATORY FORCE” In a relatively short space, Victor Di Fate has characterized my views about induction and evidence better than I could have. For this, and for his help intellectually and practically in many matters, I am very grateful. His more critical comments and questions are reserved for his ﬁnal section 4, and I will try to respond to them in the course of what follows. My claim is that whether an inductive argument of the sort championed by Newton and Mill is valid, and whether some fact is evidence for a given hypothesis, are usually, and in the most interesting cases, empirical and objective matters. The question then arises as to how my view is different from that of John Norton, who makes a similar claim, in arguing against the possibility and usefulness of universal formal rules governing induction and evidence such as those supplied by Newton and Mill. (Norton says all inductions are “local” and make no use of, and receive no justiﬁcation from, universal formal rules.) Yet, in opposition to Norton, and I think, in the spirit of Newton and Mill, I claim that such universal rules are useful and do have a “justiﬁcatory force.” Di Fate asks, reasonably: how can this be? To begin with, Mill (unlike Newton) provides a “formal” deﬁnition of induction as “the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times.” He makes it clear in his discussion that some inductions are justiﬁed, some are not, and that whether they are justiﬁed is empirically decidable by examining how the instances were selected as well as by invoking other empirical background information. The mere fact that something is an induction from all observed A’s are B’s to all A’s are B’s does not mean that its conclusion is justiﬁed on the basis of its premise. I think Newton would have agreed. Of what value, then, is Mill’s deﬁnition, and for that matter, Newton’s inductive rules 3 and 4, or his causal rules 1 and 2? For one thing Newton’s rules help guide us through a long and rather complex argument of the sort that he gives for his law of universal gravitation. “Here is my empirical argument for universal gravity,” Newton

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in effect is saying, “and notice how this step involves an inductive generalization, and that one an inference to the same cause from similar effects.” (See my Evidence, Explanation, and Realism, Ch. 4, for speciﬁc examples.) Citing his universal rules, as he does, serves as a useful guide through rather difﬁcult terrain. This is by no means all. Newton is also claiming that the only legitimate way to proceed in science is by “deductions from the phenomena,” that is, by producing arguments that are valid inductive or causal inferences, or by deriving propositions (as we would now say) deductively from others so established. And for Mill, in cases typical in science involving inferences to propositions invoking multiple causes, we are to use what he calls the “deductive method,” the ﬁrst step of which requires inductions to the various causes involved. So the rules of Newton and Mill have a normative aspect to them. Proceeding to scientiﬁc conclusions by deriving such conclusions from a priori ﬁrst principles, such as Descartes did in the case of his laws of motion, or by using the hypothetico-deductive method or “inference to the best explanation” (as suggested by Whewell), are forbidden strategies for both Newton and Mill. The rules tell us, in a general and abstract way, what sorts of arguments are to be used to support scientiﬁc conclusions. Finally, then, what about my claim—one that Di Fate focuses on critically—that these rules have a “justiﬁcatory” force or role? What could that mean? My answer is not that the mere fact that the inference has a form corresponding to Mill’s deﬁnition of “induction” (or to what Newton took an induction to be) justiﬁes the particular inference in the sense of making the conclusion believable on the basis of the premise. There are good and bad inductions with such forms. My claim is only that, for Newton and Mill, having such a form is a necessary but not a sufﬁcient condition for being the sort of inference (or one of them) that scientists should be making. (Unlike Di Fate and Norton, I don’t regard such a necessary condition as “trivial”; indeed, it is a pretty strong claim.) Having established that a particular inference has, or can be given, a formal structure of the sort Mill and Newton demand, determining whether that inference is a good scientiﬁc one does indeed require that empirical facts be invoked.

DOPPELT’S “RELEVANCE” Gerald Doppelt seeks “relevance” in any concept of evidence, and he thinks I do too. However, he claims that my concepts of potential and veridical evidence, in contrast to his own version of “inference to the best explanation,” fail to satisfy this criterion.

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“Relevance” is not a term I use, but perhaps Doppelt is referring to my claim (in the opening pages of The Book of Evidence) that standard theories of evidence proposed by philosophers are, and ought to be, ignored by scientists, because such theories are based on assumptions incompatible with ones scientists make when they speak of, and offer, evidence for their hypotheses. One assumption many philosophers make is that evidence is a weak notion; you don’t need very much to have evidence for a hypothesis (e.g., on the standard Bayesian view, you just need something that increases the probability of the hypothesis). A second assumption (made, e.g., by Carnap’s logical theory, hypothetico-deductivists, Glymour’s bootstrap theory, and Hempel’s satisfaction theory) is that the evidential relation is logical, not empirical: whether e if true is evidence that h, and how strong it is, are logical, or mathematical questions whose answers can be determined by a priori “calculation.” Both assumptions I strongly reject. And my claim is that no concept based on these assumptions will be of interest to (or, to use Doppelt’s term, “relevant for”) scientists. Doppelt wants to make much stronger claims about “relevance.” First, he wants to say that “relevance” requires a concept of evidence that is tied to an epistemic situation. But unlike my concept of ES-evidence, Doppelt’s “evidence” refers to a judgment made by someone in a given epistemic situation—for example, our judgment that Thomson’s experimental results provide veridical evidence for the charge hypothesis, which rests, of course, on our own epistemic situation. (My ES-evidence is relativized to an epistemic situation, but requires no judgments to be made by anyone, or indeed that anyone be in that epistemic situation.) Second, he seems to be saying that unless a theory of evidence tells us how to make such a judgment by telling us how to determine whether, in any particular case, it is true that e is veridical evidence that h, it fails the “relevance” test. It may fail his test, but not mine. I distinguish between (a) the meaning of a statement of the form “e is veridical evidence that h” from (b) how to determine the truth of such a statement in a given case. For (a) I provide a general deﬁnition of veridical evidence. For (b) I provide no general account, since veridical evidence statements are empirical; and, as with empirical statements generally, how one determines their truth varies from case to case. (One can deﬁne “bachelor” as “an adult unmarried male,” but determining that a particular person satisﬁes this deﬁnition requires empirical investigation, the nature of which can vary from one case to another.) My “relevance” claim pertains to (a), not (b). My aim is to deﬁne a concept of evidence that is “relevant” to scientists in the sense that it reﬂects what scientists actually seek when they seek evidence. (See also my replies to Kitcher and Longino.)

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Perhaps Doppelt’s thought that I have a notion of “relevance” requiring that a judgment be made about whether e is veridical evidence that h arises because of the way he characterizes my concept of veridical evidence. On his characterization, e is veridical evidence that h only if both e and h are true, and “the reasoning from e to h is correct.” The quoted phrase is his, not mine, and I think it is misleading, since it suggests that someone is in fact doing some reasoning. My claim is that veridical, as well as potential, evidence are like “sign” and “symptom.” X’s rash may be a sign of a poison ivy contact, whatever (good or bad) reasoning someone in a given epistemic situation might use in inferring one from the other, indeed, even if no one at all is reasoning. Analogously, the rash is a good reason to believe that there was a poison ivy contact whatever reasoning (good or bad) someone in a given epistemic situation might use in inferring one from the other, and even if no one makes such an inference. Veridical evidence requires that e provide a good reason to believe h, not that someone in a given epistemic situation be reasoning in some particular way. Finally, I will respond brieﬂy to Doppelt’s complaint that I provide no general account of correct explanation, or at least not one that plays any role in my account of veridical evidence. In The Nature of Explanation as well as in The Book of Evidence, I give general conditions for an explanation to be correct. It is an objective notion that is not tied to any particular context or explainer, in contrast to what, following Austin, I call “illocutionary” ways to evaluate explanations, which are contextual and perfectly legitimate as well. (See my reply to Goldstein.) But for the concept of veridical evidence, what is needed is a non-contextual concept of “correct explanation.” Contrary to what Doppelt seems to be suggesting in his essay, this concept, I claim, is sufﬁcient for understanding “correct explanation” underlying the idea of veridical evidence.

GOLDSTEIN ON A PRAGMATIC ACCOUNT OF EXPLANATION In various writings I have defended what is called a pragmatic account of explanation. Where q is an indirect question, and Q the direct form of the question, I take sentences of the form “E is an explanation of q” to be true if and only if Q is what I call a content-question, and E is an ordered pair whose ﬁrst member is what I call a complete content-giving proposition with respect to Q and whose second member is the act-type explaining q. We need not consider the details here. The main point is that on this view an explanation is something that provides an answer to certain types of questions—an answer that can be given in an act of explaining. (In my book The Nature of Explanation all of these technical ideas are deﬁned.)

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Several things make this view pragmatic. One is the introduction of the idea of a type of explaining act in which a speaker explains q by uttering something u with the intention that his utterance of u render q understandable by producing the knowledge that u expresses a correct answer to Q. The other is the idea that one important way to evaluate an explanation is by considering the needs, interests, and backgrounds of the potential explainer and audience. What may be a good explanation for one explainer and audience may not be so for another. Scientiﬁc textbooks illustrate this all the time. An elementary text may explain a given phenomenon in one way, a more advanced one in a very different way. Both may be perfectly good explanations for the respective audiences, and not good for others. In his paper Adam Goldstein is concerned with the importance of pragmatic evaluations, which he illustrates nicely in the case of population genetics. There is, however, another way to evaluate an explanation, namely, non-pragmatically, which is important for my theory of evidence. Since Goldstein focuses solely on pragmatic evaluations and does not mention non-pragmatic ones, and since some critics ask how my non-pragmatic theory of (veridical, as well as potential) evidence, which invokes a concept of explanation, squares with my pragmatic views on explanation, let me say just a few words. The explanation that the soldier died because he received a severe chest wound in Iraq may be perfectly correct, even if, “pragmatically” speaking, this might not be a good (enough) explanation for his commanding ofﬁcer or the medical examiner to give in his report. This evaluation as “correct” is non-pragmatic since it is independent of the intentions and interests of any particular or type of explainer or audience. It can readily be explicated using the ordered pair theory sketched above. Where Q and E satisfy the ordered pair conditions given in the previous paragraph, and u is the complete content-giving proposition with respect to Q that is the ﬁrst member of the ordered pair, E is a correct explanation of q if and only if u is true. In the soldier case, Q = why did the soldier die?; u = the soldier died because he received a severe chest wound in Iraq. The idea of a non-pragmatic “correct” explanation is built into my concept of veridical evidence. Finally, let me note that most standard theories of explanation, such as ones proposed by Hempel, Salmon, and Railton, are non-pragmatic. They too are meant to provide conditions for being a “correct” explanation. However, there are numerous problems I ﬁnd with these theories. I’ll mention two. First, as I have shown elsewhere, there are counterexamples to each of them, that is, explanations satisfying the conditions they impose that, nevertheless, provide incorrect answers to the explanatory question raised. Second, these models propose conditions that are much too stringent.

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For example, all of them require explicit use of scientiﬁc laws, whether universal or probabilistic. But as the “soldier’s death” example above shows, we may give a perfectly “correct” explanation without invoking any laws whatever, and without even knowing what laws, if any, could be invoked. If the response is “Yes, but the explanation you gave above, while correct in some sense, is not very good,” I would reply by saying that now you are introducing pragmatic considerations. For certain contexts (e.g., one involving a medical autopsy) such an explanation may be inadequate. For another context (e.g., an explanation given to the soldier’s parents) this may be perfectly adequate. In The Nature of Explanation I argue that the same holds for “scientiﬁc” explanations, even ones involving laws of nature. Unlike what the usual non-pragmatic theories assume, there is no set of “universal instructions” by reference to which all explanations in science must be evaluated.

KITCHER’S CHALLENGE The ﬁrst chapter of The Book of Evidence is entitled “The Dean’s Challenge.” I claim that the usual philosophical accounts of evidence are, and should be, of little scientiﬁc interest because they yield concepts that are much too weak, and because in general they assume (incorrectly, I claim) that the relationship between evidence and hypothesis is always a priori. The Dean’s Challenge is to provide one or more concepts of evidence that reﬂect what scientists mean when they speak of, and offer, evidence for their hypotheses, and that are not incompatible with assumptions scientists make when they do so. Philip Kitcher raises the meaty question: am I really giving scientists anything of use to them? He is skeptical that I am, and, indeed, he is skeptical that he himself, or perhaps any philosopher, could. What does Kitcher want in order to meet the Dean’s Challenge? His answer: the philosopher should be able to say when a scientist is “scientifically responsible” in making a judgment about the evidence (i.e., a judgment about whether to accept or reject a hypothesis on the basis of that evidence) that “accords with the evidence.” That, he claims, is what a scientist really needs to know about evidence, and that is what I don’t supply and he is not able to either. But is that really my aim, and should it be? To begin with, I don’t deal with the question of when and whether a scientist is “responsible” in his judgments about evidence. If, as Kitcher claims, this is really what the Dean (either Kitcher’s practical dean or his more theoretical one) wants, then I have not met the challenge. Kitcher claims that the closest I come to this is with my concept “e’s being ES-evidence that h,” which requires that e be true and that anyone in the

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epistemic situation ES be justiﬁed in believing that e is veridical evidence that h. I am not convinced that this is close to what Kitcher wants, since e can be ES-evidence that h even if there are no persons in that epistemic situation; even if there are, such persons may not be making any judgments about evidence. ES-evidence has nothing to do with such judgments, if that means judgments about the truth of claims of the form “e is evidence that h.” (See my reply to Longino.) Kitcher is right in saying that I don’t provide any general account of “justiﬁcation” needed for the concept of ES-evidence. My main concerns are (i) with “veridical evidence,” since (as Kitcher agrees) this is in fact the sort of evidence scientists seek, and (ii) with “potential evidence” needed for the deﬁnition of this concept. For these concepts, deﬁnitions are provided that do not appeal to, or presuppose, any judgments of the scientist or any notion of “responsibility.” My claim is that whether e is veridical (or potential) evidence that h is an objective, empirical fact (like that of something’s being a sign or symptom of some state of affairs) that is independent of judgments of particular scientists about the evidence, about their “responsibility,” or anything else. The results of J.J. Thomson’s experiments constituted (veridical) evidence that cathode rays are electrically charged; the results of Hertz’s experiments did not constitute (veridical) evidence that cathode rays are electrically neutral. The deﬁnitions I offer of veridical (and potential) evidence are meant to clarify what such claims mean. One of Kitcher’s complaints is that my deﬁnitions appeal to probabilities, and in real scientiﬁc life, where the situation gets messy (since different parts of the evidence may point in different directions), I offer no way of assigning probabilities. But my deﬁnitions don’t require that I do. Even in messy situations of the sort Kitcher likes to cite (the sort I deal with in a section of my book on different meta-analyses), all that is necessary is that the hypothesis be more probable than not. (More strictly, what is necessary is that the probability that there is an explanatory connection between h and e, given e, be greater than the probability of there being no such connection.) Although in the book I try to characterize an objective concept of probability of the sort required, and I do provide deﬁnitions of “explanation” and “explanatory connection,” these will not enable the scientist to churn out a priori an answer to the question of whether e is evidence that h. My claim is that whether the requisite probability and explanatory conditions hold is not an a priori matter for which armchair philosophers can crank out formulas (à la Carnap), but an empirical one, for which scientists themselves do, or ought to, provide reasons. Thomson himself gave strong empirical reasons for his conclusion that his experimental results are evidence that cathode rays are charged. These empirical reasons constitute the basis for saying that there is a high probability of an explanatory

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connection between his experimental results and the presence of negatively charged particles. With the highly evacuated cathode tubes Thomson was able to obtain, the fact that the cathode rays were deﬂected toward the positively charged electric plate makes it probable that the reason for this deﬂection is that the cathode rays are negatively charged. Of course, the latter claim can itself be defended by appeal to further empirical facts, for example, that oppositely charged bodies attract. On my view, when we provide such empirical reasons in defense of an evidential claim we are doing physics, not philosophy. What the philosopher of science ought to do is ﬁgure out what the original evidential statement means. This is what I am supposing (or at least hoping) that my dean had in mind. In addition, following in the footsteps of Newton and Mill, the philosopher of science can and should identify certain basic forms of inductive and causal reasoning that scientists do and ought to follow in defending an empirical claim, including an evidential one. (See my “The War on Induction,” reprinted in my Evidence, Explanation, and Realism; also my reply to Di Fate in this volume.) But, as is the case with evidential claims, whether any particular causal or inductive inference satisfying one of these forms is justiﬁed is an empirical issue. Perhaps Kitcher and his deans want more. If what they seek are empirical ways to defend or criticize particular evidential or other scientiﬁc claims, then neither Philip nor I, as philosophers of science, will be able to supply what is wanted.

KRONZ’S HYPOTHETICAL METHOD Frederick Kronz notes that on my view, as well as on the views I attribute to Newton and Mill, “induction and hypothetico-deduction are mutually exclusive.” He argues, on the contrary, that these methodologies are compatible and complementary, and indeed that “neither Mill nor Newton . . . is really averse to the use of hypotheses in science.” I have two responses. The ﬁrst is to distinguish the “use of hypotheses” from “hypothetico-deduction” (or what is also called the hypothetical or hypothetico-deductive method). The latter constitutes a form of reasoning in which the hypothesis is inferred to be true, or probable, given the empirical data, on the grounds that the hypothesis entails, explains, or predicts the data. In more sophisticated versions, certain conditions may be imposed, such as Whewellian “consilience”—requiring that the hypothesis explain and predict data not only of the kind that generated the hypothesis in the ﬁrst place, but of other different kinds as well. Whatever these additional conditions are, however, they do not include the requirement that there be inductive support of a sort demanded by Newton and

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Mill. So, Newton and Mill would say, the fact that Newton’s law of gravity explains and predicts a wide range of observed phenomena is not sufﬁcient to infer its truth. What is necessary is the sort of causal-inductive reasoning to the law from observed phenomena involving the planets and their satellites that Newton gives in Book 3 of the Principia. Now, contrast this with “the use of hypotheses” in science. Newton deﬁnes a hypothesis as a proposition that is not “deduced from the phenomena” using causal-inductive reasoning of the kind he requires. Although Newton famously wrote that “hypotheses . . . have no place in experimental philosophy,” he does introduce them from time to time. (For example, in the Principia the proposition that “the center of the system of the world is at rest” is labeled “hypothesis 1.”) So, despite his famous claim to the contrary, Newton is not averse to introducing and using hypotheses. What I take his position to be is this: you can introduce a hypothesis, but from the fact that it helps to explain and predict phenomena you cannot infer that it is true or probable, since a conﬂicting hypothesis may explain and predict the same phenomena. In other words, Newton is distinguishing between the use of the hypothetico-deductive method and the use of hypotheses. The same goes for Mill, who allows hypotheses to be introduced to suggest possible explanations of phenomena. But from the fact that a given hypothesis yields such an explanation one cannot infer its truth or probability. In the ﬁrst part of his paper, Kronz does not sufﬁciently emphasize this distinction between the use of hypotheses and the use of the hypothetico-deductive method. My second response is to Kronz’s “enhanced hypothetical method,” which is designed to show, among other things, how the inductivism of Newton and Mill is not incompatible with, but complementary to, hypothetico-deductivism. In addition to stipulating that the empirical consequences of the hypothesis obtain, the enhanced hypothetical method requires “an inductive inference to the hypothesis” and the satisfaction of an incompletely formulated disjunctive set of conditions (including “consilience,” novel prediction, etc.) Now besides the incompleteness of Kronz’s set, there is a problem that I see with this proposal. What exactly does Kronz mean by an “inductive inference” here? Is it (1) any inference from the truth of the observed consequences of a hypothesis to the truth or probability of the hypothesis? Or is it (2) any inference that “what is true of certain individuals of a class is true of the whole class”? If it is (1), then Newton and Mill will object, and deny complementarity. For example, as mentioned, one of Kronz’s disjuncts is Whewellian consilience. But Mill explicitly rejects the idea that you can infer that a hypothesis is

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true or probable on the grounds that it explains or predicts a range of observable phenomena, even if they are of different kinds. As Kronz notes, Mill defends what he calls the “deductive method,” which he sharply distinguishes from the hypothetico-deductive method. The former has three components: ﬁrst inductions (in Mill’s sense, viz. (2)) to a set of causal laws; second, “ratiocination,” which involves deductions from the set of inductively inferred causal laws; third, empirical veriﬁcation of phenomena newly predicted from this set. For Mill, the hypothetico-deductive method omits the ﬁrst step and contains only the second and third. It is clear from his discussion that adding any of the disjunctive requirements in step 4 of Kronz’s “enhanced hypothetical method” to his inductive requirement, understood in the sense of (1), will not sufﬁce to generate a justiﬁed conclusion. So if (1) is how “inductive inference” is to be understood, then Mill’s inductivism and hypothetico-deductivism are mutually exclusive. On the other hand, if by an “inductive inference” Kronz means what Mill does, that is, (2), then we end up with Mill’s “deductive method,” perhaps enhanced with a disjunction of further conditions, the satisfaction of any of which is supposed to strengthen the inference to the hypothesis. I will not here discuss whether the additional conditions Kronz lists are indeed “inference enhancing.” I will note that some are vague, for example, “a new organization of facts that facilitates solving a problem,” and a “suitable condition (other than those already mentioned).” If this is the way “inductive inference” is to be understood then I would conclude that Kronz’s “hypothetico-deductivism” is pretty close to Mill’s inductivism (as expressed in his “deductive method”). Indeed, it includes it; it is not really a complementary methodology.

LAUDAN’S NINETEENTH-CENTURY WAVE-THEORIST I have long admired Larry Laudan’s historical-philosophical work, despite our different takes on the nineteenth century wave-particle debate. He understands that debate to be largely inﬂuenced by a difference in methodological viewpoints. On his view, the wave theorists, being proponents of the method of hypothesis, or hypothetico-deductivism, were free to introduce unobservable waves and an ether to support such waves, so long as the theory gave correct predictions for a variety of observable optical phenomena. The particle theorists, being proponents of an inductive methodology, required that any entities or causes introduced be observable or at least have properties like those found in observable cases. (The latter, Laudan claims, is how eighteenth- and nineteenth-century followers of Newton understood his “vera causa” rule 1 in the Principia.)

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On my reconstruction of the debate, Laudan’s methodological schism is exaggerated. As he notes, I claim that a strategy wave theorists use is typically this: (i) start with the assumption that light is either a wave phenomenon (a wave motion or pulse transmitted through some medium), or a stream of particles (subject to forces obeying Newton’s laws of motion); (ii) show how each theory explains various observed optical phenomena (e.g., rectilinear propagation, reﬂection, refraction, diffraction); (iii) show that the particle theory, in explaining one or more of these phenomena, introduces improbable hypotheses, while the wave theory does not; (iv) conclude that the wave theory is very probably true, while the particle theory is not. This eliminative strategy is one adopted by wave theorists such as Young, Fresnel, Herschel, and Lloyd. So far it is an open question whether this should be given an inductive or a hypothetico-deductive, or some other, methodological interpretation. Laudan denies even this much. Wave theorists, he claims, did not, and could not, employ an eliminative strategy, since the number of different speciﬁc wave theories was too great to be exhaustively considered and rejected. Perhaps Laudan has difﬁculties here, but wave theorists such as Young, Lloyd, and Herschel did not. Here is Young. It is allowed on all sides, that light either consists in the emission of very minute particles from luminous substances, which are actually projected and continue to move with the velocity commonly attributed to light, or in the excitation of an undulatory motion . . . in a highly light and elastic medium pervading the universe; but the judgments of philosophers of all ages have been much divided with respect to the preference of one or the other of these opinions.

Here is Herschel. Among the theories which philosophers have imagined to account for the phenomena of light, two principally have commanded attention: the one conceived by Newton . . . in which light is conceived to consist of excessively minute molecules of matter projected from luminous bodies. . . . The other hypothesis is that of Huygens . . . which supposes light to consist, like sound, of undulations or pulses, propagated through an elastic medium.

Unlike Laudan, these authors had no difﬁculty reducing the (most plausible) competing theories to two, and then arguing that one is superior to the other. Now for my inductive take on this. I claim that step (i), noted above, can be, and was in fact, inductively supported by wave theorists. (Such theorists did not say simply: let’s just make this assumption and see what follows.) For example, Lloyd supported it by saying that it was empirically established that light travels from one point to another with ﬁnite velocity,

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and that in nature one observes motion from one point to another occurring either by the motion of a body or by the motion of vibrations through a set of bodies or medium. (“Nature,” says Lloyd, “affords numerous examples of each of these modes of propagated movement.” If there were others that had been observed presumably Lloyd would have mentioned them.) I take Lloyd to be offering inductive support for his claim. A second part of inductive support appears in the defense of (iii). The reason for the claim of improbability in the type of force particle theorists introduce to explain diffraction, for example, is that the force postulated is unlike any observed forces. It requires that “bodies of different forms and of various refractive powers should possess an equal force of inﬂection” (Young), which is not observed to be the case with other known forces acting at a distance. (In Particles and Waves I show that if the probability that such a force exists is much, much greater on the assumption of the particle theory than it is without that assumption, then the probability of the particle theory is close to zero.) By contrast, the wave theory introduces no such forces or other improbable causes to explain diffraction It is step (ii), the explanatory one, that Laudan pushes (perhaps to the exclusion of the others). His 19th century wave theorist (a model hypothetico-deductivist) argues for his theory (whether some generalized wave theory or a particular version) simply by showing that it can explain and predict a variety of known phenomena. And, Laudan claims, my characterization of step (ii) downplays its importance. If the wave theorist establishes the high probability of his theory W on the basis of inductive background information b, and inductively supported claims about diffraction d, then I argue that p(W/b & d) is high. However, the wave theorist wants this probability to be high not just on this basis but on the basis of all known and successfully predicted optical phenomena. If his theory can explain and predict these other optical phenomena by deriving them from the theory, then he gets what he wants. Where O1, . . . ,On are these additional phenomena, he obtains the result that p(W/O1, . . . ,On & d &b) is at least as high as p(W/b&d), which follows probabilistically. It is not my claim, of course, that the wave theorist uses the probability calculus, only that this is a way of understanding the wave theorist’s strategy in steps (i)–(iv) so that it gives that theorist what he is seeking. In Particles and Waves I argue that Laudan’s explanatory-predictive account by itself cannot give the wave theorist high probability. Finally, there are several claims that Laudan makes about my view that are too strong. One is that I am a Bayesian. I am not. Another is that, on my view, an eliminative strategy is the only one that can be used to show high probability for any theory. I make no such claim. Indeed in other writings, for example on Newton’s argument for his law of gravity, I analyze

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the inductive strategy in a non-eliminative way. These claims, and other differences between us, I look forward to discussing with Larry on another occasion.

LONGINO’S CONTEXTUALISM Helen Longino sees the need for what she calls a “contextualist” account of evidence. In The Book of Evidence there is a chapter entitled “Old-Age and New-Age Holism” to which she refers. One version of new-age holism that she mentions is this: where h is some “isolated” hypothesis and e is some “isolated” fact, it is never true that e is evidence that h. Rather e is evidence that h, relative to some set of assumptions b. She calls this a form of contextualism, since on this view, “the relevance of some state of affairs to an hypothesis requires background assumptions.” How and why is this a “contextualist” position? Her answer is not always clear to me. At one point she writes that (1) The truth of an evidential claim of the form “e is evidence that h” depends on “a context of background assumptions that are themselves empirical in nature, not known to be true, and that might be false.” More often her view seems to be that (2) When we assess or determine the truth of an evidential claim of this form, we make background assumptions of the sort described in (1). How is (1) a “contextualist” position? Is Longino saying that an evidential claim of the form “e is evidence that h” is incomplete as it stands, that to have a truth-value it must be relativized to some set of background assumptions b, and that which set this is depends on the context of utterance? But then the “completed” relativized claim “e is evidence that h, given b,” which is the sort of claim I am concerned with, is not “contextual.” It is either true or false independent of any context, indeed, independent of whether anyone knows the truth of b or of the evidential claim itself. Where, then, is the “contextualism” in (1)? To be sure, whether someone is in a position to utter an evidential claim (whether relativized or not) depends on contextual conditions satisﬁed by the utterer. But that is so for any claim whatever, whether evidential or otherwise. Accordingly, if this all that evidential contextualism amounts to, then the doctrine is, I think, minimal, and not one I would dispute. What about position (2)? There are usually different ways we can assess or determine the truth of a claim that e is evidence that h (different pieces

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of background information we can appeal to). Which we choose depends not only on the evidential claim itself but also on our own knowledge and interests as well as on those of a potential audience, which, of course, can vary from one context to another. But this is true of any claim we make, whether evidential or not. So if (2) is an expression of, or leads to, evidential contextualism, then, again, the doctrine is, I think, minimal, and not one I would dispute. One of Longino’s main concerns (suggested in the latter part of the quote in (1)) may be this. Evidential claims are useful to us only if we can determine whether they are true or false, which involves determining whether some background assumption is true or false. But, given our epistemic situation, we are often not in a position to do the latter. My response is this. Surely sometimes we are in a position to know that some particular background assumption being made is true (I am not a skeptic). But even if we are not in a position with respect to a particular b, we may be in a position to determine whether there is evidence that b is true. Longino is right in worrying about how, given the epistemic situation we happen to be in, we are to determine the truth of an evidential claim. (My concern in the book was not with this question, but with the question of what it means to make evidential claims of the sorts I have in mind.) But I am not as pessimistic as she is about the question of assessing the truth of evidential claims of the form “e is veridical evidence that h, given b.” Contrary to what Longino seems to suggest, such assessments are not restricted to cases involving lotteries where probabilities are usually easy to determine. One does not have to be able to assign a probability to an hypothesis h to determine whether, given e and b, it is more probable than not that there is an explanatory connection between h and e (a crucial necessary condition for veridical evidence, on my view). Nobel Prize committees depend on evidential assessments all the time. Perrin was given the Nobel Prize for his experiments on Brownian motion. The Nobel Committee, or its referees, were able to assess the claim that the results of these experiments provided (veridical) evidence that chemical substances are composed of molecules the number N of which in a gram molecular weight of any substance is approximately 6 x 1023. My theory of evidence explains what such an evidential claim means. It does not say how to go about assessing its truth. The evidential claim itself is empirical, and so, needs to be defended, if it does, empirically – presumably by scientists themselves. In The Book of Evidence I offer no general account of how empirical claims, whether evidential or otherwise, are to be defended. My own view is indeed contextual in a sense indicated earlier: what, if anything, needs

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to be defended and how depends on the knowledge and questions of the defender and the audience, which vary from one context to another. For this reason I do not think any general philosophical account of how evidence claims are to be defended can be provided. If this is Helen’s position on contextualism, or part thereof, we are in agreement.

MAYO ON SEVERE TESTING As Deborah Mayo notes, she and I are in agreement about various important issues regarding evidence. For example, we both hold that evidence (at least in the most central sense) is an objective, not a subjective, concept, and that a claim that e is evidence that h (in typical cases) is empirical, not a priori. We both agree that, contrary to the standard Bayesian idea, increase in probability is neither necessary nor sufﬁcient for evidence, and that high probability is not sufﬁcient. There is, however, one signiﬁcant difference between us. Mayo believes that e is evidence that h only if e results from “highly probing” hypothesis h (in a sense that she deﬁnes). I believe that e is (potential or veridical) evidence that h only if e provides a good reason for believing that hypothesis h is true. On my view, this occurs if e is true, e does not entail h, and (most importantly) given e, the probability is high that there is an explanatory connection between h and e. (The latter entails that h is highly probable, given e, which I take to be a necessary condition for evidence.) For her, “passing a severe test” is both necessary and sufﬁcient for evidence; for me, it is neither. Mayo and I have been debating this for some time now, as the references in her paper indicate. Here I will simply focus on one example that will bring out this difference between our views, and show why I cannot accept her “severe testing” as a basis for evidence. (I have used this example in “Mill’s Sins or Mayo’s Errors,” in Deborah Mayo and Aris Spanos, eds., Error and Inference. For my purposes in this reply, it is an easier one to construct, and, I hope, a better one in terms of which to appreciate our contrasting views than her “college ready” and my “Stand and Deliver” examples cited in her present reply.) Suppose there is a very rare disease S, which is such that only one person in ten million in the general population has S. In such a case, I will assume, we can assign a prior probability for having S, (1) P(S) = .0000001. (In what follows probability denoted by a capital P represents a relative frequency). Now suppose there is only one test T for this disease, which

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can yield one of two results: the test result turns either red or blue. Of those with S, 80% who take test T test red, so that (2) P(red result with test T/disease S) = .8, and of those who don’t have S, 2 out of 100,000 test red, so that (3) P(red result with test T/-S) = .00002. Now we consider a particular individual, Irving, for whom we can write the following probabilities, based on those above. (4) P(Irving’s getting a red result with test T/Irving has disease S) = .8 (5) P(Irving’s getting a red result with test T/Irving does not have disease S) = .00002. Because the probability in (4) is much greater than that in (5), Irving’s test result of red “ﬁts” the hypothesis that Irving has S in a sense of “ﬁts” that seems to conform to Mayo’s idea. Furthermore, because the probability in (5) is so low, Irving’s getting the red result with test T should count for Mayo as passing a severe test for the hypothesis that he has disease S. On her view (as expressed, e.g., in her “Evidence as Passing Severe Tests,” in Achinstein, ed. Scientiﬁc Evidence, 99), if we have a hypothesis h, a test T for that hypothesis, and some data D produced as a result of employing the test, then for h to pass a severe test T yielding D, it is required that the data “ﬁt” the hypothesis—in a fairly weak sense of “ﬁt” such as the one suggested above; and it is required that the probability be very low that T would yield results that ﬁt h as well as data D if h were false. In her contribution for the present volume, Mayo avoids talk of probabilities in characterizing a severe test. Such probabilities presuppose priors, which, being a frequentist about probability, she doesn’t much like, since frequency priors are often not “ascertainable.” However, in the present example, we have such a prior, since I am stipulating a base rate for disease S. To continue the example, using Bayes’ theorem, from the probabilities (1)–(3) above we compute that P(S/red result with test T) = .004; that is, four out of 1000 people who get the red result from test T (less than half of 1%) have disease S. My own take on this is that T is a very poor test for disease S, despite the fact that it seems to satisfy Mayo’s criteria for being a good test. (If it doesn’t, I invite her to say why.) To see why I regard this as a poor test, let us use these frequency probabilities as a basis for what I call objective epistemic ones (represented with a small p). Doing so, we obtain (6) p(Irving has disease S) = .0000001 (7) p(Irving has disease S/Irving got a red result with test T) = .004.

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That is, (6), the prior epistemic probability (the degree of reasonableness of believing) that Irving has the disease, is miniscule; and (7), the posterior epistemic probability that he has the disease, given that he got the red result with the test, is still very small. Despite the fact that Irving has passed a “severe test” for disease S in what I take to be Mayo’s sense, Irving’s test result gives very little reason to believe that he has disease S. As (7) indicates, the degree of reasonableness of believing that he has S, even given that he tested red, is very low. On my view, passing a severe test for a hypothesis h, and hence having evidence for h, should mean that there is a good reason to believe that h is true. On her view, as characterized above, passing a severe test T for hypothesis h with data D, and hence having evidence for the hypothesis, entails this: given that test T continues to be repeated, the relative frequency of outcomes ﬁtting hypothesis h as well as data D will at some point in the testing sequence be and remain very low, under the assumption that h is false (see, e.g., her major work Error and the Growth of Experimental Knowledge, 121–4). Sometimes she puts this by saying that passing a severe test means that the hypothesis is “reliable,” in the sense that “what h says about certain experimental results will often be close to the results actually produced” (10). But, as my example is intended to show, this does not entail that passing a severe test (in Mayo’s sense) provides a good reason to believe that the hypothesis is true. That, as I see it, is a signiﬁcant difference between her concept of evidence and mine. I will now comment on three issues Mayo raises in her paper. First, she asks whether I am claiming that in the sort of case above when I assert that Irving’s testing red is not evidence that he has disease S, I am committed to saying that the fact that he tested red is evidence that he does not have disease S. After all, the probability that he does not have S, given that he tested red is very high (.996). To her that would be paradoxical, since testing red is passing a “severe test” for having disease S. The answer is that I am not committed to saying this, because in this case my explanation condition for evidence is violated. Given that Irving tested red, the probability is not high that there is an explanatory connection between his not having the disease S and his testing red. (It is not probable that the reason he does not have the disease is that he tested red, or conversely, or that some hypothesis explains both why he does not have the disease and why he tested red.) Second, my example avoids what Mayo calls the “fallacy of probabilistic instantiation,” in which a relative frequency probability for a single case is inferred from a relative frequency for a type of property or situation. It avoids this because the probability “instantiated” is not a relative frequency, but an objective epistemic probability, which is applicable to

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hypotheses about single cases (e.g., the probability that Irving has disease S). My claim is that, in the case I am imagining, the objective epistemic probability statement (7) above can be defended empirically by appeal to the relative frequency probability statement (5) above. I see no fallacy in such a defense. Third, Mayo raises a general “ascertainability” question for anyone appealing to numerical probabilities in a deﬁnition of evidence: how are such probabilities to be determined (whether these are conditional probability statements of the form p(h/e) = r, or priors of the form p(h) = r)? This is a large and controversial topic, but let me respond brieﬂy by saying that I distinguish the question of “ascertainability” from that of the meaning of probability, and evidence, claims. Moreover, if we do consider the question of how to ascertain the truth of evidence claims, my account of evidence does not require ascertaining numerical probability values, whether or not these are conditional probabilities or priors. To ascertain the truth of “e is (potential or veridical) evidence that h,” what is required is to determine whether given e, it is more probable than not that there is an explanatory connection between h and e, which does not require determining how probable it is. To give a simple example, let e = I own more than 90% of the tickets in a fair lottery, one ticket to be drawn at random. Let h = I will win. To determine whether it is true that e is (potential or veridical) evidence that h, we don’t need to compute p(h/e), p(h), or p(there is an explanatory connection between h and e/e). Finally, in this connection, evidential claims of the form “e is evidence that h,” being empirical (in the kinds of cases Mayo and I are concerned with), there are usually many different empirical ways to “ascertain” their truth, or to provide evidence for such claims. I do not subscribe to the idea that the philosopher of science can provide a general account of such ways. (See my replies to Doppelt, Kitcher, and Longino.) Although there are other issues raised in Deborah’s present contribution to which I would like to respond, induction tells me that we will have an opportunity to continue our debate on another occasion, even if that hypothesis has not been severely tested.

MORGAN ON COHERENCE William Whewell claimed that the coherence of a theory is a sign of its truth (indeed a pretty darn good sign). But he never argued for such a claim, much less proved it. Whewell’s concept of coherence is rather vague. In Particles and Waves, in attempting to assess his claim, I offer a precise probabilistic deﬁnition of coherence that Gregory Morgan cites in

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his thought-provoking paper. I argue that at least with this notion of coherence, Whewell cannot establish his claim that coherence is a sign of truth—either in the sense that it makes a theory highly probable or in the sense that it increases its probability. Morgan and I are in general agreement about this conclusion, although unlike me, he does not deﬁne coherence. (He regards my deﬁnition as a “sanitized” version of Whewellian coherence, since it does not capture certain “subjective” features of that concept.) Morgan considers a version of Whewell’s claim that coherence is a sign of truth to be committed to saying that for any theory T (1) If T is coherent, then there is a reason to believe T. One way Morgan expresses this idea probabilistically is this: (2) p(T/T is coherent) > .5 He calls such coherence a sign1 of truth. Another way he expresses the idea in (1) probabilistically is this: (3) p(T/T is coherent) > p(T), in which case he calls coherence a sign2 of truth. Morgan is assuming that in (1) “a reason to believe T” either makes T more probable than not, or increases its probability. But as I see it, (1) itself is a conditional statement, with the idea of probability, if any, expressed or presupposed in the consequent of the conditional; it does not seem to be expressing or presupposing a conditional probability. Accordingly, if we are to construe it probabilistically, I would understand (1) to be saying not (2) or (3) but (4) If T is coherent, then p(T) > .5, or in the case of the weaker probabilistic version, something like (5) If T is coherent and T’ is not, or if T is more coherent than T’, then, other things being equal, p(T) > p(T’). Even though Morgan does not do so, I propose to assess the weaker claim (5), which I will do in a way that does not make use of my deﬁnition of coherence. Such an assessment requires saying something about coherence, even if we do not supply a full-scale deﬁnition. Among other things, Whewellian coherence pertains to how well a given theory explains something, which in turn depends on how it is formulated (a point Morgan recognizes in his paper). Indeed, two logically equivalent formulations may not be equally explanatory. For example, let T be a conjunction of Newton’s laws of motion and his law of gravity. Let T’ be a conjunction of T together with

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the tautology “either Socrates was bald or he wasn’t.” Now one thing we demand of a good explanation (even Hempel demands it in his D-N model) is that all parts of the explanation be relevant, that is, be used to generate the explanation. (Whewell himself writes that in a system in which coherence is lacking “the new suppositions are something altogether additional;—not suggested by the original scheme. . . .”) The tautology in T’ is irrelevant for an explanation of why the planetary orbits are elliptical, as well as for explanations of numerous other phenomena explained by Newton. T, let us say, is coherent, T’ is not, or at least T is more coherent than T’ with respect to these phenomena. Since T and T’ are otherwise the same, on the basis of (5) we can assume that p(T) > p(T’) or at least that these probabilities are not the same. But this violates the rules of probability, since T and T’ are logically equivalent. The argument above does not impugn (4). My own preference would be to try to give a complete formal deﬁnition of coherence to see if Whewell can or cannot justify the probabilistic claims (4) and (5). But on this occasion I will settle for the brief informal remarks above to show a difﬁculty Whewell faces in making coherence a sign of truth via probability, even in the weaker sense of “sign.” (A more formal approach with more elaborate arguments appears in my Particles and Waves, which includes a deﬁnition of coherence, and in Morgan’s paper, which does not.) Having said this my claim would be that coherence (as well as other virtues, such as simplicity, generality, and precision) are important considerations in defending a theory non-epistemically. However they are deﬁned, and even if they are not but are recognizable without deﬁnition, they can be appealed to in defending a given theory without affecting its probability or believability. In my paper, “What to Do If You Want to Defend a Theory You Cannot Prove” (reprinted in my Evidence, Explanation, and Realism), I show how James Clerk Maxwell appeals to the precision and the completeness of his development of the kinetic-molecular theory in its defense, in addition to less than decisive experimental evidence. Maxwell does not claim or assume that the non-epistemic virtues are signs of truth, but only that they are legitimate criteria of goodness in a theory. Criteria of both epistemic and non-epistemic sorts can be invoked in evaluating a theory. However, the non-epistemic ones may carry at least as much weight as (or even more weight than) the epistemic ones in such an evaluation at a given moment of time if the evidence for the truth of the theory at that time is less than decisive. Trial lawyers say: if the facts are not as strong as you would like in favor of your client, pound the law; if the law is not as strong as you would like, pound the facts; if neither is, pound the table. Maxwell emphasized both epistemic and non-epistemic virtues in his presentation of kinetic theory, without pounding anything, let alone the table.

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NORTON’S “INTRACTABLE PROBLEM OF INDUCTION” In a series of very striking papers, John Norton has defended the thesis that inductive inferences are justiﬁed, when they are, not by any universal formal principles of induction (such as those Mill and Newton seem to be supplying), but only by material facts that vary from one induction to another. Universal principles of induction are worthless, and even dangerous for Norton, since they suggest the possibility of justifying particular inductions by reference to formal schemas that cannot possibly do any justiﬁcatory work. In the present essay, Norton presents a new sort of case, that, on his view, is inductively “intractable.” It involves observationally indistinguishable spacetimes in which, for example, it is natural to infer inductively to a fully extended Minkowski spacetime rather than to an extendable halfMinkowski spacetime. But, unlike indeterministic cases in quantum mechanics, no material fact seems to ground this inference, nor do empirical laws, or any appeals to universal principles of induction, metaphysical principles of simplicity, or anything else. I am tempted to say that whereas Hume found that although we make inductive inferences none is justiﬁed, Norton restricts his “inductive skepticism” to a particular case (or perhaps a few) in theoretical physics. I ﬁnd relief in that. Let us suppose that Norton is right about his case, and that we ﬁnd the induction to a fully extended Minkowski spacetime natural and compelling. Let us also suppose that no material warrant exists (or we can’t ﬁnd any) for such an induction, and that no general principles of induction can justify such an induction. What follows? Norton’s answer: we have an intractable problem, “the ground crumbles around our feet.” But there is another possibility. In such a case, even though we ﬁnd it natural and compelling to make the inductive inference in question, since there is, or we can ﬁnd, no inductive warrant, what this shows is that we should not make the induction despite the temptation to do so. Why exactly is this an “intractable problem” for an inductivist, even of the “material” sort that Norton identiﬁes himself as being? After all, Norton, unlike Hume, is not saying that no induction is rationally justiﬁed. Why should it be a problem if there is a case in which although we ﬁnd the induction natural, we also ﬁnd that it has no justiﬁcation in fact. That is just an interesting case! It becomes “intractable” only if we further assume that for any induction we ﬁnd natural and compelling there will always be a justiﬁcation. If that is what Norton is assuming, he needs more argument. For more general remarks about the differences between Norton’s view of induction and my own, and for a defense of Newton’s methodological rules and Mill’s methods against Norton’s sort of criticism, see my essay

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“The War on Induction,” in my Evidence, Explanation, and Realism, and my reply to Di Fate in the present volume. I ﬁnd a place for such rules in the justiﬁcatory process; Norton does not.

PSILLOS ON PERRIN I welcome Psillos’s stimulating essay, both for its historical background on Perrin and for its attempt to provide a probabilistic account of Perrin’s reasoning that is better than mine. Let me start with Psillos’s claim about my account. As he notes, I formulate Perrin’s major experimental result concerning Brownian motion as follows: C = the calculation of N (Avogadro’s number) by means of Perrin’s experiments using equation (9) is 6x1023 and this number remains constant when values for various empirically determined parameters in equation (9) are varied. Equation (9) relates Avogadro’s number (the number of molecules in a substance whose weight in grams equals its molecular weight) to various other quantities measurable in the experiments Perrin performed. (Strictly speaking, equation (9) represents a number for visible Brownian particles, where Perrin is assuming that any quantity of these particles equal to their molecular weight will contain the same number N of particles—a number that will be the same as Avogadro’s number for molecules.) On my reconstruction, experimental result C is supposed to provide evidence for the following theoretical claim. T = Chemical substances are composed of molecules, the number N of which in a gram molecular weight of any substance is (approximately) 6x1023. Now, according to my deﬁnition of potential evidence, C is (potential) evidence that T, given the background information b Perrin cites, if and only if (i) C and b are true; (ii) C does not entail T; (iii) p(E(T,C)/C&b) > 1/2. (The latter is equivalent to the requirement that the product p(T/ C&b)xp(E(T,C)/T&C&b) > ½. (E(T,C) means there is an explanatory connection between T and C—see my reply to Cartwright for a deﬁnition of this.) What I argue in my writings is that C is indeed potential evidence that T, given the background information employed by Perrin. Psillos says that on my view all that Perrin achieved is to show that the atomic hypothesis is more likely than not (which would follow from the satisfaction of condition (iii) above). I don’t accept that characterization. On my view, although satisfaction of (iii) is necessary for evidence, it doesn’t follow that Perrin simply established that the probability cited in (iii) is greater

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than ½. As I argue, what probability Perrin in fact established for an explanatory connection between C and T is an empirical matter. One needs to look at the speciﬁc empirical arguments he employed to determine whether this probability is simply greater than ½ or much greater (which Perrin himself claimed). Accordingly, I believe that my position on evidence can readily deal with Psillos’s concern. Let me comment on one important feature in Psillos’s own probabilistic reconstruction of Perrin’s argument. Psillos claims that Perrin argued that the probability of getting the experimental results he did (my C above), given the atomic hypothesis (I will consider simply T above), is very high, while the probability of getting these results, given the falsity of T, is low, that is, (i) p(C/T) is high; (ii) p(C/–T) is low. Using Bayes’s theorem, together with some other plausible assumptions, we may conclude that the probability of T, given Perrin’s experimental results, that is, p(T/C), is high. A crucial passage Psillos cites from Perrin states that before his experimental results no one would have expected that the Brownian particles would not have fallen to the bottom of the vessel (in which case N would be inﬁnite), or that they would not have fallen at all (in which case N would be zero). Perrin concludes: “It cannot be supposed that out of the enormous number of values [of N] a priori possible, values so near to the predicted number have been obtained by chance for every emulsion and under the most varied experimental conditions.” (Atoms, 105). Psillos interprets this as saying that the probability of obtaining result C, given the atomic hypothesis, is high, and the probability of obtaining C, given that the atomic hypothesis is false, is low. This passage, I believe, does not say, or support, the second half of that conclusion. Perrin does not here argue that if the atomic theory were false then it would be very unlikely he would have obtained the value he did for N over his range of experiments, but only that the atomic theory, or in my more speciﬁc formulation, T, will make it likely that one will get consistent values for N, that is, p(C/T&b) is high. (I relativize the latter probability to background information b that includes results of other experiments in the nineteenth century that make it probable that Brownian motion is not caused by various external factors.) If, as Perrin argues, p(T/b) is (very) high, then it can be demonstrated that p(T/C&b) is too, which in my writings is how I suggest reconstructing Perrin’s argument to the high probability of T. (For the proof, see “Jean Perrin and Molecular Reality,” reprinted in my Evidence, Explanation, and Realism.) Finally, although I do not have the space to give a decisive argument here, I am skeptical of what Psillos calls second-order evidence from the track record of scientiﬁc theories generally and the reliability of scientiﬁc methodology. (He claims that philosophers need to balance ﬁrst- and second-order

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evidence, something that is contextual.) As an example of second-order evidence Psillos mentions the “pessimistic induction” from the failure of past theories to the probable failure of a particular one. I don’t regard the failure of past theories as potential or veridical evidence of the failure of any particular theory we are considering. Let e be the fact that most theories have turned out false, and let h be some particular theory we are now considering, say T above. For e to be (potential or veridical) evidence that –T, it must be the case that p(there is an explanatory connection between –T and e/e) > ½. But I regard this probability as very low if not zero. Even given e (that most theories have turned out false), it is not probable that a correct explanation for (–T), that chemical substances are not composed of molecules and so on, is that most theories have turned out false; or that a correct explanation of why most theories have turned out false is that chemical substances are not composed of molecules, or that some hypothesis correctly explains why –T and e are both true. (Just to take the ﬁrst part of this disjunction, it is probable that a correct explanation of why chemical substances are not composed of molecules, assuming they are not, would be some particular chemical one, not the fact that most theories have turned out false.) Is “second-order evidence” evidence in some different sense? I invite Stathis to relieve me of my skepticism concerning such evidence.

RICHARDS’S DARWINIAN PUZZLE I am grateful to Richard Richards not only for his present contribution, but for his friendship over the years as well as for his encouragement, advice, and philosophical insights. In his essay Richards concentrates on a very interesting but puzzling claim made by Darwin, namely, that although he (Darwin) at one point came to believe in branching evolution on the basis of the taxonomic facts, and he believed that he was justiﬁed in doing so, he also believed that these same taxonomic facts were not sufﬁcient for other scientists to believe in branching evolution. By the latter, according to Richards, Darwin means not that these taxonomic facts would fail to persuade others to believe, but that others would not be justiﬁed in so believing. Richards rightfully ﬁnds this puzzling and asks how it can be explained. It cannot be explained, he says, using standard a priori theories of evidence. For example, on Carnap’s logical theory of evidence, or on a hypothetico-deductive view, if e is evidence that h, then this is so “for everyone,” no matter who believes what. Richards’s solution to the problem is rather simple. Using my concept of ES (epistemic situation) evidence, he claims that what Darwin was saying is that relative to the sort of epistemic

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situation he (Darwin) was in, the taxonomic facts did provide ES-evidence; but others were in a different sort of epistemic situation, relative to which the taxonomic facts did not provide such evidence. Richards draws an interesting conclusion from this regarding the history of science. Historians of science should be interested not only in the (epistemic) reasons scientists had for their beliefs—which he associates with my concept of subjective evidence; they should also be concerned with the question of whether, given their epistemic situations, the scientists were justiﬁed in those beliefs—which he associates with my concept of ES-evidence. For example, in describing how Hertz came to believe that cathode rays are electrically neutral, the historian of science Jed Buchwald not only gives Hertz’s own epistemic reasons for that belief, but he also evaluates those reasons as good ones, given Hertz’s particular situation. My only comment here is that not very many historians of science do this sort of thing. More frequently they are concerned with simply identifying the reasons scientists in fact had for believing what they did, whether these reasons are epistemic or non-epistemic (the latter including causal factors inﬂuencing those beliefs). But evaluating those beliefs, particularly in the way Richards suggests, is a much more difﬁcult task. It involves not only (1) discovering what reason e the scientist had for believing h, but also (2) identifying what particular epistemic situation the scientist was in (which, among other things, involves identifying what beliefs other than e and h he had or was in a position to have), and (3) determining whether anyone in that epistemic situation would have been justiﬁed in believing h for the reason e. It is one thing for e to be ES-evidence for some particular ES. It is quite another to satisfy conditions (1)–(3). Is that what historians of science should be doing to do good history of science? Speaking as a philosopher of science, I am quite satisﬁed if the historians tell me what reasons scientists in fact had for their beliefs (i.e., (1) above). I would also like to learn from them whether other scientists at the time or later regarded e as a good reason for believing h, and why they did so. And, of course, as I have emphasized elsewhere, what scientists want to know is whether e really is a good reason for believing h (or, in terms of evidence, whether e is veridical evidence that h), which is a scientiﬁc issue that historians of science do not usually investigate. But none of these tasks requires what Richards

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seems to have in mind (i.e., satisfying all the conditions in (1)–(3)). He sets a very high goal indeed for the historian.

RUSE’S GOOD BREEDING As an eminent philosopher of biology, Michael Ruse’s inﬂuence in his own ﬁeld has been considerable. But he is also one of the very few philosophers who has had a signiﬁcant impact on applications of philosophy of science to important practical and political issues such as those taken up in the courts regarding the teaching of evolution. I admire him for being able to wear both hats, and I am glad to learn that my ﬁrst book, Concepts of Science, played at least some role in his formative years, especially in weaning him from logical positivism. In his essay, Ruse discusses the vexing question of the role of artiﬁcial selection by breeders in Darwin’s development of the theory of natural selection. According to Ruse, “the world of the breeders provides a crucial piece of Darwin’s thinking. It offers a model or analogy leading to the central evolutionary force of natural (and its sister sexual) selection.” Ruse sees three roles for artiﬁcial selection as a model or analogy. One he calls “heuristic”: Darwin claimed that he got the idea of natural selection by considering artiﬁcial selection. A second he calls “pedagogical”: the model or analogy of artiﬁcial selection is used to introduce us to, and teach us about, the more general idea of natural selection. The third role is that of evidential support for his theory: “Darwin always looked upon the world of the breeders as part of the justiﬁcation for his theory.” It is this third role that I want to focus on. Philosophically speaking, this I take to be the most interesting and controversial. I begin with a few remarks about models and analogies generally, using some simple examples from physics. One of the most famous models discussed by philosophers of science is what came to be known as the “billiard ball model of a gas,” developed by James Clerk Maxwell in his ﬁrst paper on kinetic-molecular theory in 1860. Another often cited example is Rutherford’s “solar system” model of the atom developed in the early years of the twentieth century. In considering these we need to make an important distinction between the model itself and an analogy that it may employ. The expression “billiard ball model,” for example, is used to refer to a set of simplifying assumptions that Maxwell (among others) made about the molecules that, he postulated, comprise a gas. These assumptions included that molecules are spherical, that they exert no forces on one another except at impact, that they travel in straight lines except at impact, that they are subject to standard laws of dynamics,

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and so forth. The term “analogy” here I take to refer to the analogy between molecules so described and billiard balls exerting no forces on one another except at impact, traveling in straight lines otherwise, and being subject to standard laws of dynamics. A similar distinction can be made in the case of Rutherford’s planetary model of the atom. Now consider the notion of “support for the theory.” Maxwell was explicitly agnostic regarding whether the ideas of his 1860 simpliﬁed billiard ball model of a gas could be applied to real gases. Writing to Stokes in 1859 just before the publication of his paper he says: “I do not know how far such speculations may be found to agree with facts. . . . I have done so as an exercise in mechanics. Now do you think there is any so complete a refutation of this theory of gases as would make it absurd to investigate it further so as to found arguments upon measurements of strictly “molecular” quantities before we know whether there be any molecules?” By the 1870s, Maxwell had more indirect evidence for the existence of molecules, and so he was able to make claims about them that he thought were justiﬁed. But he did so without use of the original model. More generally, whether a model can be extended to the “real world” depends crucially on the assumptions made in the model, and on whether there is any justiﬁcation for them. Sometimes there is, sometimes not. What about the “analogy” here? (Keep in mind this is our analogy, not Maxwell’s.) The analogy consists in the (partial) similarity we draw between molecules and their motions in a gas and billiard balls and their motions on a billiard table. Here it is questionable what, if anything, we can infer about real world molecules from billiard balls and their motions. Obviously we cannot infer that molecules have numbers imprinted on them, that they all move in the same plane, that some of them fall into pockets, or, most importantly, that there are forces exerted by humans, in addition to intermolecular ones, responsible for their motions—as in the case of billiard balls. Analogies, which are by their very nature partial and frequently loose, are not, in general, particularly reliable support for the theory about the entities for which they are providing an analogy. (“It’s only an analogy,” we say, “don’t expect too much.”) They may help one to think about the entities in the theory— they may be of “heuristic” and “pedagogical” value—but that doesn’t mean they provide evidential support for the theory. If the analogy drawn between two systems is perfect or close to it, and, if we have reason to suppose that both systems are governed by some common or similar mechanism, then we can use our knowledge of one system to make inferences about the other. But the closer to perfection the analogy, the less inclined are we to speak of it as an analogy, but simply as two systems subject to the same principles.

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My own theory of veridical evidence provides a justiﬁcation for claims in the last paragraph. For e to be veridical evidence that h, the high probability of an explanatory connection is required between e and h. Let h be the claim that the hypothesized entities (e.g., the molecules) have certain properties P, and let e be fact that the “analog” entities (e.g., the billiard balls) have certain analogous properties P’. It is not that the putative fact (h) that the molecules have the properties P probably correctly explains why (e) billiard balls have the analogous properties P’; nor is the reverse true. For the required explanatory connection, the best we can hope for is that some hypothesis h’ correctly explains both h and e. The closer to perfection the analogy is—the more similar the properties in P and P’, the larger the sets in question, and the less dissimilar are other properties (the “negative analogy”)—the more probable it is that we are dealing with two systems subject to the same principles or “mechanism,” which can explain properties of both systems. In such a case the behavior of one system can supply evidence for claims about the behavior of the other. But then, as noted above, we are not likely to speak of this as an analogy. The more dissimilar the two systems, the less likely it is that there is some common explanation for analogous properties of each, and hence the less justiﬁed we would be in the claim that the behavior of the analog system provides evidence for corresponding claims about the hypothesized system. Turning ﬁnally to artiﬁcial selection, when Ruse claims that this “model” or “analogy” provides support for Darwin’s general theory of natural selection—or at least that Darwin thought it did—to what is he (Ruse) referring by “model” and “analogy”? Let us suppose ﬁrst that it is intended by Darwin simply as an analogy, in roughly the same way as we use the idea of billiard balls as an analog of molecules, or solar systems as an analog of atoms. There is a partial similarity between what happens in breeding and, according to the theory, what happens in nature. Both involve certain changes in the characteristics of animals and plants, and both involve selection broadly speaking. But as with analogies generally, there are dissimilarities as well. For example, there is a human agent selecting in the case of breeding, none postulated in nature; there is no evolution to a new species Darwin observed in breeding, although this is what he postulated for the case of natural selection in the long run; breeders breed for one or a few characteristics, none of which may involve selective advantages for survival and reproduction, and indeed may be harmful for these purposes; nature, according to Darwin, works very differently; and so forth. Such disanalogies, of course, were noted by Darwin’s opponents. So if Ruse is claiming that for Darwin artiﬁcial selection served as an analogy that provided evidential support for the general theory of natural selection as the mechanism for evolution, then I want to know a good deal more

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about how such support is supposed to work. Why aren’t the disanalogies sufﬁcient to make it unlikely that there is a common explanation for the effects of artiﬁcial and natural selection? What happens if we treat artiﬁcial selection as a model? How would that work? Here we need to be careful if we have in mind something like the billiard ball model of a gas or the planetary model of an atom. A model in this sense is a set of simplifying assumptions about the real world. So in the Darwin case the model would assume that in nature, members of the same species differ at least slightly with respect to many different characteristics; that some of these differences have selective advantages for survival and reproduction; that over long periods of time changes favoring these characteristics will transpire forming new species; and so forth. Perhaps these were regarded by Darwin as simplifying assumptions, and perhaps he was led to think about them by thinking about artiﬁcial selection. But the problem here is that “the model” (even if considered simpliﬁed and suggested in part by considering artiﬁcial selection) is simply Darwin’s theory of natural selection. I don’t see how conceived as a model it provides support for the theory of natural selection—any more than treating Maxwell’s (simplifying) assumptions about gas molecules as a model provides support for the claim that real-world molecules behave (approximately) in these ways. I leave Michael with a challenge, which I feel sure he can meet: tell me more about your notion of “support” and about how the “model/analogy” of artiﬁcial selection is supposed to provide support for natural selection—whether in Darwin’s mind or any other.

STALEY ON “SECURING EVIDENCE” Kent Staley is right to point out (as Kitcher does as well) that my account of ES-evidence appeals (among other things) to being “justiﬁed in believing” something, which I don’t further explicate. Staley makes a very interesting attempt to bolster my account of evidence by providing such an explication. He arrives at this result, which he calls JE (justiﬁed evidence): an assertion of h as a conclusion inferred from observed fact(s) e is fully justiﬁed relative to epistemic situation K if (1) e is potential evidence for h (using my concept of potential evidence); and (2) the proposition “e is potential evidence for h” is secure throughout all scenarios that are epistemically possible relative to K. Prior to arriving at this result, he offers both a formal and an informal deﬁnition of a proposition being “secure throughout a scenario relative to an epistemic situation K.” The informal deﬁnition is this: a proposition is secure for an epistemic agent

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“just in so far as, whatever might be the case for all that the agent knows, that proposition remains true.” He then illustrates what he has in mind with a more detailed account of Hertz’s cathode ray experiments than I offered in my book. I will discuss Staley’s proposal using an example from Galileo’s Dialogues on the Two Chief World Systems. In that work Simplicio, following Aristotle, asserts that the earth is stationary and does not turn on its axis (h). He infers this from the observed fact that a stone dropped from the top of a tower falls at the base of the tower, not a distance away (e). Is Simplicio’s assertion h “fully justiﬁed” by e relative to his own epistemic situation (in Staley’s sense)? Not if we understand Staley to be providing necessary as well as sufﬁcient conditions. (He uses “if,” but I want to consider “if and only if”). The reason is that on my view, e is not potential (or veridical) evidence that h in this case, so Staley’s ﬁrst condition in JE is not satisﬁed. Therefore, no matter how well Simplicio argues for his conclusion h given his epistemic situation, his assertion of h will not be justiﬁed even relative to his own epistemic situation K. Similarly, and perhaps even more strikingly in the Hertz case, on the present conception of justiﬁcation, Hertz’s claim that cathode rays are not charged is not justiﬁed, even relative to his own epistemic situation, since his experimental results were not potential evidence for this conclusion. This is too rich a sense of “justiﬁcation” for my blood, even if Staley calls it “ideal justiﬁcation.” It is not what I had in mind for ES-evidence. (On my view, Hertz’s results were ES-evidence for his hypothesis, relative to his ES; hence, he was justiﬁed in believing that hypothesis, even though the results were not potential evidence for the hypothesis.) On the other hand, if Staley’s conditions for being “fully justiﬁed” are not necessary conditions, but only sufﬁcient ones, what conditions are necessary? Staley needs to tell us. Suppose that we drop Staley’s ﬁrst condition for justiﬁcation and keep the second as both necessary and sufﬁcient. Could my concept of ES-evidence be understood using this idea? We could say that e is ES-evidence that h, relative to a given ES, if and only if e is true and the proposition “e is potential evidence that h” is secure throughout all scenarios that are epistemically possible relative to that ES (or just secure relative to that ES). Presumably, the fact that the stone drops to the base of the tower would then be ES-evidence for the stationary earth hypothesis for someone in Simplicio’s epistemic situation. That would be okay with me. Now my worry pertains to the importance Staley wants to place on “justiﬁed evidence” (or someone might want to place on my notion of ES-evidence) in this sense. Let me put the point perhaps more boldly than I should. Besides a few historians and philosophers of science (and Simplicio himself), who cares (and who should care) whether, relative to

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his own epistemic situation, Simplicio was justiﬁed in concluding that the earth is stationary? Who cares if this e is ES-evidence relative to his ES? Even if this is a sense of “evidence,” as I think it is, the major concern (it was certainly Galileo’s) was whether the fact that the stone lands at the base of the tower is veridical (and hence potential) evidence that the earth is stationary. Galileo famously argued that it is not. In short, Staley’s concept of “justiﬁed evidence,” if understood as requiring the satisfaction of both of his conditions, yields much too strong a sense of justiﬁcation, at least for my purposes. The weaker concept in the last paragraph leaves me with the question: If this were to be Staley’s idea of “justiﬁed evidence,” why should one value such a concept as much as he seems to?

VAN FRAASSEN’S PERRIN I am a scientiﬁc realist. With respect to Perrin, van Fraassen places me in the good company of Wesley Salmon, Clark Glymour, and Penelope Maddy in subscribing to the “philosophy lore” that understands Perrin’s work as “epistemically legitimating the conclusion” that atoms and molecules are real. In his challenging response to this “lore,” van Fraassen proposes a very different, and quite interesting, interpretation of Perrin and other scientists as well. Tracing his ideas to a 1927 work of Herman Weyl, van Fraassen claims that when scientists “describe the acceptance of a scientiﬁc theory,” even if, as with Perrin, they make explicitly realist assertions, another, and I take it better, way to understand what they are claiming is only (what van Fraassen calls) “empirical grounding” for the theory. Basically (if I understand this correctly) the idea is that each signiﬁcant “theoretical” parameter in the theory must be such that its value can be determined on the basis of measurement (of some “observational” quantities or other), where this determination is theory-relative, that is, is made with the aid of theoretical assumptions. So, for example, Perrin derives the formula: (1) n¢/n = 1—Nmg(1-d/D)h/RT in which n´ represents the number of Brownian particles per unit volume at the upper level of his experimental tube and n the same at the lower level; D is the density of the material comprising the Brownian particles; d is the density of the liquid in the tube; and N is Avogadro’s number (the number of molecules in a gram molecular weight of a substance—the theoretical parameter of interest). All of the other parameters are measur-

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able experimentally. In different experiments using different ﬂuids, and Brownian particles with different sizes and masses, Perrin calculated N to be approximately the same in the various experiments. In doing so, van Fraassen emphasizes, Perrin made various “theoretical” assumptions, including that molecules exist, that they cause the Brownian motion, and that the visible Brownian particles comprising the liquid will behave like molecules in a gas with respect to their vertical distribution. For van Fraassen, this is what is necessary for “empirical grounding” for N. The satisfaction of this condition for other theoretical parameters as well is all that Perrin needed or should have wanted for the acceptance of molecular theory. Before responding, let me mention another example cited by van Fraassen. It involves Maxwell’s determination of molecular speeds. From a virial equation of Clausius, Maxwell derives a formula (2) Vp = 1/3Mc2 where V = volume of the gas, p = pressure of the gas, M = mass of the whole quantity of the gas, and c2 = mean square velocity of a gas molecule. Using this, and assuming a very rareﬁed gas and that the velocity of every molecule is the same, from the measurable quantities V, p, and M, Maxwell calculates that the velocity of a molecule of oxygen is 461 meters per second, that of nitrogen is 492, and hydrogen is 1844, at 0 degrees centigrade. (See The Scientific Papers of James Clerk Maxwell, vol. 2, W. D. Niven, ed. (Dover, 1965), 426.) So here again we have “empirical grounding” for the theoretical parameter “molecular velocity.” And, in this case, like that of Perrin, we have such grounding using theoretical assumptions. There is, I would claim, an important difference between these cases. Intuitively, Maxwell had no empirical method for determining whether the molecular velocities he computed were correct or approximately so, even for the idealized case he considers. By contrast, Perrin, I would claim, had, or at least thought he had, a good empirical method for determining a value for Avogadro’s number. What’s the difference? One difference is mentioned by van Fraassen: “concordance.” Perrin got the same number with different experiments, whereas Maxwell had no experiments whatever to determine the correctness of his claims about molecular velocities. But there is another difference as well. The theoretical assumptions Perrin uses to derive his formula are ones for which he offers arguments: for example, arguments from experiments of Gouy and others that Brownian motion is caused internally by bombardment with molecules, and at least some argument for the claim that Brownian particles can be treated like large molecules for purposes of the equation (1) above. Maxwell does

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offer some general arguments for the existence of molecules, and for the assumption that they satisfy Newtonian dynamical laws, that are independent of the kinetic-molecular theory. (See my “What to Do if You Want to Defend a Theory You Cannot Prove: A Method of Physical Speculation,” The Journal of Philosophy 107 (2010), 35–55, reprinted in my Evidence, Explanation, and Realism.) But these are not of the strength of those supplied by Perrin (or at least that is what Perrin would have claimed). Even if we grant Maxwell some justiﬁcation for assuming that the Clausius virial equation that holds for macro-particles in an enclosed vessel will also hold for molecules, he offers none for the supposition that the molecules in the enclosure will all have the same velocity—a theoretical assumption he needs to get his conclusion regarding molecular velocities. More generally, contrary to what van Fraassen seems to be suggesting, I would claim that whether “empirical grounding” of theoretical parameters yields enough for “acceptance”—at least for acceptance of the values of those parameters—depends importantly on whether a justiﬁcation is given for the theoretical assumptions employed, and on how strong that justiﬁcation is. This can vary signiﬁcantly from one case to another. A larger question, of course, pertains to the realist-anti-realist debate. Here I will simply say that both Maxwell and Perrin clearly believed that they themselves were realists. They sought to establish that molecules are real and that the claims each was trying to make about them were true. As van Fraassen agrees, there are plenty of quotes from the writings of Perrin, as well as from Maxwell, that attest to this. They believed that “empirical grounding” (together even with “concordance”) is not sufﬁcient for acceptance of a theory. And, since “empirical grounding” (even, I would argue, with “concordance”) can vary considerably in its strength, I think they were right. However, I will not pursue the larger question here. (My own defense of realism, as well as a critique of van Fraassen’s anti-realism, can be found in my “Is there a Valid Experimental Argument for Scientiﬁc Realism?” Journal of Philosophy 99 (2002), 470–95, reprinted in my Evidence, Explanation, and Realism.)

WOODWARD’S CAUSES VS. CONDITIONS Among “causally relevant” factors that play roles in producing events, Woodward wants to distinguish causes (in some narrow sense) from enabling conditions. So, for example, in the robbery example he cites from Judith Thomson, the construction of the bridge was an enabling condition of the robbery, but not its cause. Some philosophers claim that this dis-

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tinction is “capricious and arbitrary” with no objective basis whatever. Woodward argues that there are objective factors—what he calls “stability” and “speciﬁcity”—that play an important role in selecting causes from mere conditions. I have not discussed this distinction in my own work, but I have talked about “pragmatic” conditions for giving evaluations of explanations, including causal explanations, as being good or appropriate for certain contexts and not others. Woodward connects this with his discussion of the cause-conditions distinction by admitting that both “stability” and “speciﬁcity” are subject to “pragmatic” conditions: what counts as stable or speciﬁc in one context may not in another. Yet, on the “objective” side, he thinks that it is an empirical fact about ordinary people and scientists alike that for a range of different contexts there will be agreement about what is stable and speciﬁc. I agree with Woodward in recognizing the importance of pragmatic factors in determining causes. What caused the soldier’s death? Was it the terrorists’ roadside bomb, or a lack of proper body armor? Which is selected as the cause, as opposed to a mere condition, although not “arbitrary and capricious,” depends in some measure on the context of inquiry. The military ofﬁcer making the report to his superiors will cite the bomb as the cause; a congressional committee investigating the army might pick out the lack of proper body armor. Whether Woodward’s (pragmatically inﬂuenced) factors of “stability” and “speciﬁcity” yield more of the objectivity that Woodward seeks in this distinction is an interesting question for which I can here offer no general answer. I will raise just one question. Can’t there be “unstable” causes? Woodward’s “stability” condition is concerned with the extent to which the relationship between cause C and effect E will continue to hold as various background factors change, where a background factor is any factor distinct from C and E. Now think of those scary warnings on prescription blurbs for pills, for example, “this pill can cause stomach upset.” Suppose that the pill caused John’s stomach upset yesterday, but not today when he took another one. (We rule out other causes one by one.) C can cause E (the blurb tells us, although this is rare), and yesterday it did in John’s case, but there isn’t much “stability” here, since if background conditions distinct from C and E change, the causal connection will probably not exist. To be sure, Woodward says that “stability” is not a necessary condition for the selection of a cause, only a “relevant” one. Whether this is so, and also what exactly is supposed to count as “stable,” are questions I will leave for Jim for another occasion. But I do welcome his pragmatism in these matters.

Index

Achinstein, Peter, his inﬂuences, 3–6, 259 on analogy, 204–5, 214, 289–92 on evidence, see Evidence on explanation, 15, 72, 74–6, 247, 255, 267–69 on Jean Perrin, 177, 185–87, 231, 241, 241, 285–87, 294–96 on James Clerk Maxwell, 29–34, 40, 260–64 on John Stuart Mill, 96–99, 106, 147–48 on Isaac Newton, 44–55, 96–99, 264–65 on William Whewell, 106, 152–53, 281–83 on the wave-particle debate, 109–20, 273–76 on scientiﬁc realism, 188, 231, 241, 294–96 on rules of induction, 44–55, 110, 164–65, 264–65, 284–85 Analogy, 30, 38, 41, 178, 205–12, 214, 260–61, 289–92 Anti-realism, 294–96 Anscombe, G. E. M., 17 Avogadro’s number, 68, 132, 180–88, 238–42, 285, 294–95 Aristotle, 293, 52–3 Artiﬁcial selection, 205–10, 214, 289–92 Atwood, Rev. George, 233–234 Austin, John L., 5–10, 13, 259 Ayer, A. J., 5–6 Bacon, Francis, 110, 194–195, 209 Bayesian methods, 59, 105, 112–13, 116, 135–37, 143–45, 148, 157, 176n, 183, 195, 266, 275, 278–79 Bentham, George, 211 Bootstrapping, 236, 244, 266 Braithwaite, Richard, 203

Brownian motion, 10, 132, 177, 179–185, 188, 231, 241–43, 246n, 277, 285–86, 294–95 Buchwald, Jed Z., 89, 121n, 222, 226–228, 230n, 288 Brush, Steven, 231, 246n Cantor, Geoffrey, 110 Carnap, Rudolf, 3–10, 13, 45, 56n, 135, 194, 259, 266, 287 Cartwright, Nancy, 258, 259–260, 285 Cat, Jordi, 258, 260–64 Cathode rays, 11–12, 46–47, 61, 70, 87, 93, 197–200, 218, 221–28, 270–71, 288, 293 Causation, 4, 7–8, 16, 18, 21, 35, 51, 97, 99, 101–2, 187, 211, 247–257, 265, 295 Coherence, 66, 113, 151–62, 234, 281–83 Conﬁrmation, See Evidence Consilience, 34, 36, 102–4, 110, 152, 271–72 Darwin, Charles, 75, 87, 89–90, 93, 193–201, 205–14, 287–88, 289–92 Davy, Humphry, 263 De Sitter spacetime, 170–71 Dewey, John, 108n De Morgan, Augustus, 41 Descartes, Rene, 48–49, 52–54, 194–95, 265 Di Fate, Victor, 258, 264–65 DNA, 94, 249, 253 Doppelt, Gerald, 258, 265–67, 281 Dorling, Jean, 33, 40, 43n Duhem, Pierre, 105, 127, 178, 184, 189, 233, 246n Dutch books, 158 Earman, John, 156 Electron, 128, Also see Cathode rays

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Index Eliminative causal reasoning, 66–70, 90, 185, 187 Einstein, Albert, 166–67, 232, 241–43, 246n Euclid, 34 Explanation, D-N explanation, 4, 17, 72–3, 283 Pragmatics of, 79, 255–257, 268 Experimental philosophy, 13 Evidence, and explanation, 15, 63–66 epistemic situation (ES) evidence, 11, 60–2, 64–70, 88–90, 125, 127, 132–33, 192, 216–19, 221, 228, 266, 269–70, 288, 292–94 justiﬁed evidence, 221 potential evidence 57n, 60–69, 90, 125, 197–98, 201, 217–21, 228, 229n, 265–268, 270, 278, 281, 285, 287, 292–94 subjective evidence, 60–1, 67, 69, 192, 197–9, 202, 288 veridical evidence, 8, 10, 12, 57n, 60–70, 88–9, 197–98, 216–19, 221, 228–29, 230n, 259, 265–67, 268, 270, 277, 278, 281, 287–88, 291, 293, 294 Fodor, Jerry, 205, 213–14 Friedman, Michael, 74 Fresnel, Augustin-Jean, 115, 274 Galileo, 192–4 Geroch, Robert, 173 Gimbel, Steven, 258, 259 Glymour, Clark, 165, 231, 235–237, 246n, 266, 294 Goldstein, Adam M., 258, 267–68 Goldstein, Eugen, 222 Gouy, Léon, 179 Grue, 176n, 195 Hamilton, William, 41 Hampshire, Stuart, 26 Hare, Richard, 5 Hempel, Carl G., 3–5, 45, 72, 73–80, 194, 203, 244, 259, 266, 268, 283 Hanson, Norwood Russell, 204, 246n Herschel, John, 118, 121n, 194, 195, 211, 274 Hertz, Heinrich, 11–12, 46–47, 61, 85–93, 197–298, 200, 221–28, 270–71 Heuristics, viii, 41, 203, 209–10, 213, 289–90

299 Holism, 124, 127–33, 259, 276 Hume, David, 5, 110, 195, 284 Huygens, Christian, 48, 111, 274 Hypothetico-deductive (H-D) method, 31–2, 35–41, 50, 59, 96, 99, 106, 110, 127, 140, 179, 187, 194, 203, 244, 261–63, 265–66, 271–75, 287 Indeterminism, 165, 168–69, 171–72, 176n Induction, 5, 45, 47–48, 54, 59, 96–99, 101–106, 110, 116, 121n, 147–48, 164, 171, 194–5, 225, 259, 263, 264–65, 273, 281 Norton’s material theory of, 47, 164–65, 173, 284–85 pessimistic meta-induction, 68–70, 287 Indeterminism, 38, 165, 168–69, 171–72, 176n Inference to the best explanation (IBE), 58n, 59, 63–4, 67, 189, 195, 265 Inference to the best explanation realism (IBER), 63–69 Intelligence quotient (IQ), 95 Janiak, Andrew, 48 Joule, James Prescott, 263 Kant, Immanuel, 10 Kelvin, Lord, 35, 38–9, 42 Kepler, Johannes, 17, 101, 212 Kitcher, Philip, 74, 258, 266, 269–71 Kuhn, Thomas, 86–7, 103, 106, 108n, 204, 205, 210, 213, 246n Kronz, Frederick M., 258, 271–73 Lalande, André, 177 Laudan, Larry, 44, 53, 68, 111, 122n, 258, 273 Lakatos, Imre, 105, 108n Laws of nature, 7, 73, 76–82, 101, 147, 269 Leibniz, Gottfried, 48 Lewis, David, 248–250, 256–57, Logical positivism, 3–4, 259, 289 Logical empiricism, 3, 10, 14, 45, 203–5, 209–14 Longino, Helen, 258, 276–78, 281 Lottery examples, 90, 127–28, 130, 133, 281 Lloyd, Humphrey, 122n, 274–75 Mach, Ernst, 178, 246n, Maddy, Penelope, 231–33, 246n, 294

300 Malament, David, 165 Maxwell, James Clerk, 29–42, 67, 239–40, 260–64, 283, 289–92, 295–96 on method of physical speculation 31, 260–261 1860 kinetic theory, 30, 261, 289–90 Maynes, Jeffrey, 259, 260 Mayo, Deborah G., 127, 229n, 258, 278–81 McMullan, Ernan, 57n Mill, John Stuart, 41, 47, 164–65, 194–95, 248–9, 256–57, 264–65, 271–73, 284 as a sever tester, 147–148 Mill’s methods of experimental inquiry, 97–102 on the hypothetical method, 96–103 Minkowski space-time, 169–73, 175n, 176n, 284 Morgan, Gregory J., 258, 281–83 Newton, Isaac, rules for natural philosophy, 51–53, 98 Neyman-Pearson statistical methods, 105 Nagel, Ernest, 203 Nagel, Thomas, 5 Natural selection, 79–81, 192–93, 212, 289–92 Darwin on, 205–210 as vera causa, 211 Norton, John D., 194–6, 258, 264–65, 284–85 Nyhof, John, 231, 246n Objective epistemic probability, 135–6, 142 Occam’s razor, 171–72 Ostwald, Wihelm, 185 Paradox of the ravens, 84, 195 Peacock, George, 41 Piattelli-Palmarini, Massimo, 205 Perrin, Jean, 10, 68–9, 85, 90, 132, 177–89 and realism, 231–33, 238–44 Pierce, Charles, 103–6, 107n, 142, 150n, 194–95 Poincare, Henri, 182, 233, 146n Popper, Karl, 92, 103, 105, 106, 108n, 194 Psillos, Stathis, 258, 285–87 Putman, Hilary, 68 Quarks, 220 Quine, W.V., 3, 259 Duhem-Quine thesis, 105, 127

Index Random controlled trial (RCT), 15–26 Railton, Peter, 73–4 Reichenbach, Hans, 246n Realism, 29, 30, 39, 42, 58n, 262, 296 Achinstein, Maxwell and, 29–34, 262 No miracles argument, 68, 189 Reductionism, 7, 261 Richards, Richard A., 258, 287–89 Rumford, Count, 263 Ruse, Michael, 258, 289–292 Rutherford, Ernest, 244 planetary model of the atom, 289–90 Staley, Kent, 258, 292–94 Stokes, George Gabriel, 35, 290 Stokes equation, 181 Strawson, Peter, 5–7, 259 Salmon, Wesley, 68, 73–74, 156, 187, 231, 268, 294 Severe tests, 137–148 Sexual selection, 207, 214, 289 Sign of truth, 153–162, 282–83 Simplicity, 283, 284, See also Occam’s razor Sober, Elliott, 195, 202 Tait, Peter Guthrie, 38–9, 42 Thomson, J. J., 85, 93, 266 cathode ray experiments, 11–2, 45–7, 197–98, 218, 221, 226–28, 270–71 Thomson, Judith, 247, 251, 254, 296 Thomson, William, See Kelvin, Lord Toulmin, Stephen, 204 Under-determination, 167 van Fraassen, Bas, 72, 134n, 189, 258, 294–96 Wallace, Alfred Russel, 209, 213–14, Wave and particle theories of light, 66–70, 109–120, 273–76 Weyl, Hermann, 235, 241–42, 246n, 294 Whewell, William, 36–37, 41, 57n, 96–106, 107n, 110, 113, 118–19, 121n, 151–55, 161–62, 194–95, 265, 271–72, 281–83 Wolfram, Stephen, 90 Woodward, James, 258, 296–97 Wright, Sewall, 79, 81 Young, Thomas, 111, 274–75