Laws and Symmetry This page intentionally left blank Laws and Symmetry Bas C. Van Fraassen CLARENDON PRESS · OXFORD Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Bangkok Buenos Aires Cape Town Chennai Dar es Salaam Delhi Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi São Paulo Shanghai Taipei Tokyo Toronto Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © Bas C. van Fraassen 1989 The moral rights of the authors have been asserted Database right Oxford University Press (maker) All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose this same condition on any acquirer ISBN 0–19–824860–1 To Etruscan places This page intentionally left blank Preface The idea that there are laws of nature is by no means the sole property of philosophers. That this idea is the key to what science is, often appears as self-evident in popular thought: in The History of Landscape Painting, John Constable writes ‘Painting is a science’ and he adds, unconscious of any leap in thought, ‘and should be pursued as an inquiry into the laws of nature.’ That these laws constitute also walls of impossibility that border the course of events, is a constant preoccupation of Dostoevsky's narrator in Notes from Underground: ‘all the same’,hesays,‘the laws of nature have mistreated me constantly, more than anything else in my life’. But the idea that there are such laws has also played a major role in philosophy concerned with science. We find this idea perhaps most prominently in the philosopher-scientists of the seventeenth century, but it survived in ours even the logical positivists' radical rejection of history. Reichenbach, Hempel, and Goodman themselves invoked laws to shed light on issues prominently associated with their names. Their invocation was perhaps critical and tentative, but it seeped into other areas of philosophy as certainty. When moral philosophers discuss free will, for example, should they not be allowed to lean on such certainties as philosophy of science has established concerning cause, necessity, counterfactuals, and nomological explanation? And similarly, given those supposed certainties, isn't it quite proper too for philosophy of mind to approach uncritically the question whether there are psycho-physical laws? In the first part of this book I shall argue that no philosophical account of laws of nature does or can succeed. In the second I shall rebut the argument that we must believe in them nevertheless. Now if there are laws of nature we must approach science in one way, but if there are no laws, we are freed to leave behind a whole range of traditional problems. I make a proposal for how to do philosophy of science, and devote the third and fourth part to contributions to the semantic approach (as Frederick Suppe baptized it) which I advocate. The emphasis will be on symmetry, as a key to theory, though not in the sense that laws were. This book was originally twice as long. When a general approach viii PREFACE is announced and advocated, it remains hand-waving except to the extent that it is implemented. Accordingly, the now missing part was devoted to a detailed study of the structure and interpretation of quantum mechanics. It will appear separately, as Quantum Mechanics: An Empiricist View. My colleagues in philosophy of science may be a little surprised by Part I, for the accounts of law taken up belong to the area of metaphysics which they generally ignore. They are of course free to ignore that part and turn to the chapters on inference to the best explanation, theories, symmetry, classical physics, and probability. I too lack sympathy for metaphysics, though not in general: only for pre-Kantian metaphysics— and then only if practised after Kant. I have tried to ensure nevertheless that none of my arguments rests on this rejection; otherwise my critique would not be very effective. Those who don't care to engage the metaphysicians on their own ground, I would like to urge at least this: do not rely on such concept as law without inquiring whether there is anything that could play the required role. For that is similar to other philosophers relying unquestioningly on fifty-year-old philosophy of science. There are many people and institutions I want to thank. The original manuscript was written during a sabbatical leave (1986/7) supported by Princeton University and the National Science Foundation. Specific debts are acknowledged in many sections, but I wish to thank Ernan McMullen, David Lewis, Storrs McCall, Wesley Salmon, Michael Tooley, and Richard Foley for special help with Part I. For Part II I want to acknowledge the help and insights received from Gilbert Harman, Richard Jeffrey, and Brian Skyrms. Elisabeth Lloyd helped me to see new possibilities in the semantic approach to theories, and R. I. G. Hughes in the many uses of symmetry. Discussions with Brian Skyrms, Maria-Carla Galavotti, and Nancy Cartwright helped with causality, while Roger Cooke helped with the intricacies of both classical mechanics and subjective probability. Joint work with R. I. G. Hughes appears in the last chapter. Perhaps needless to say, it was my valued teacher Wilfred Sellars and my eventual colleague Gilbert Harman who started me on the subject of inference to the best explanation, a number of years ago. Margot Livesey suggested a good deal of stylistic improvement in the first three chapters and I hope this had its effect on the later ones as well. PREFACE ix Anne Marie DeMeo typed endless drafts of this material over a period of about three years, and kept my practical life functioning even while I travelled; she deserves special thanks. Finally, I want to acknowledge with some nostalgia the places where I wrote the draft during that initial year: Vancouver, Victoria (BC), Montreal, Notre Dame, Bologna, Assisi, Rome, Jerusalem, Tiberias, Cambridge (Mass.), Cleveland, and London. This page intentionally left blank Summary Table of Contents 1. Introduction 1 PART I. ARE THERE LAWS OF NATURE? 15 2. What Are Laws of Nature? 17 3. Ideal Science: David Lewis's Account of Laws 40 4. Necessity, Worlds, and Chance 65 5. Universals: Laws Grounded in Nature 94 PART II. BELIEF AS RATIONAL BUT LAWLESS 129 6. Inference to the Best Explanation: Salvation by Laws? 131 7. Towards a New Epistemology 151 8. What If There Are No Laws? A Manifesto 183 PART III. SYMMETRY AS GUIDE TO THEORY 215 9. Introduction to the Semantic Approach 217 10. Symmetry Arguments in Science and Metaphysics 233 11. Symmetries Guiding Modern Science 262 PART IV. SYMMETRY AND THE ILLUSION OF LOGICAL PROBABILITY 291 12. Indifference: The Symmetries of Probability 293 13. Symmetries of Probability Kinematics 318 INDEX 387 Contents 1. Introduction 1 1. The need for global constraints 2 2. The secular, global, and axiomatic method 5 3. The end of metaphysics? 7 4. The birth of symmetry 10 PART I. ARE THERE LAWS OF NATURE? 15 2. What Are Laws of Nature? 17 1. The importance of laws 17 2. Peirce on scholastic realism 19 3. A twentieth-century example: Davidson 23 4. Criteria of adequacy for accounts of laws 25 5. Philosophical accounts: the two main problems 38 3. Ideal Science: David Lewis's Account of Laws 40 1. The definition of law 40 2. The definition of necessity 43 3. Laws related to necessity 45 4. Do Lewis's laws explain? 48 5. Lewis's anti-nominalism 51 6. Laws related to the pursuit of science 55 7. A parable 59 8. Conclusion: deceptive success 62 4. Necessity, Worlds, and Chance 65 1. Are there other possible worlds? 65 2. Laws related to worlds 68 3. The identification problem 72 4. Time and the branching universe 74 5. Probability: laws and objective chance 78 6. The fundamental question about chance 81 7. Possible worlds and explanation 86 8. Relation to science: Pandora's box 88 9. The perils of a reified model 90 CONTENTS xiii 5. Universals: Laws Grounded in Nature 94 1. Laws as relations among universals 94 2. The lawgivers' regress 99 3. Does Armstrong avoid the regress? 103 4. Armstrong on probabilistic laws 109 5. A new answer to the fundamental question about chance? 116 6. What the Renaissance said to the Schoolmen 126 PART II. BELIEF AS RATIONAL BUT LAWLESS 129 6. Inference to the Best Explanation: Salvation by Laws? 131 1. On the failures of induction 132 2. Dretske on the remarkable confirmation of laws 134 3. Armstrong's justification of induction 138 4. Why I do not believe in inference to the best explanation 142 5. What good is there in this rule? 149 7. Towards a New Epistemology 151 1. Pascal: the value of a hope 152 2. The probabilistic turn 153 3. Logic of judgement 155 4. Inference to the best explanation is incoherent 160 5.