Hume's Problem: Induction and the Justification of Belief Colin Howson offers a solution to one of the central, unsolved problems of Western philosophy, the problem of induction. In the mid-eighteenth century David Hume argued that successful prediction tells us nothing about the truth of the predicting theory. No matter how many experimental tests a hypothesis passes, nothing can be legitimately inferred about its truth or probable truth. But physical theory routinely predicts the values of observable magnitudes to many places of decimals and within very small ranges of error. The chance of this sort of predictive success without a true theory seems so remote that the possibility should be dismissed. This suggests that Hume's argument must be wrong; but there is still no consensus on where exactly the flaw in the argument lies. Howson argues that there is no flaw, and examines the implications of this disturbing conclusion for the relation between science and its empirical base. end p.i end p.ii Hume's Problem Induction and the Justification of Belief CLARENDON PRESS · OXFORD 2000 end p.iii 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 © Colin Howson 2000 The moral rights of the authors have been asserted Database right Oxford University Press (maker) First published 2000 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 British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Howson, Colin. Induction and the justification of belief: Hume's problem / Colin Howson. p. cm. Includes bibliographical references and index. 1. Induction (Logic). 2. Science—Philosophy. 3. Hume, David, 1711–1776—Contributions in logical induction. I. Title. BC91 .H69 2000 161—dc21 00–056652 ISBN 0–19–825037–1 (alk. paper) end p.iv None but a fool or madman will ever pretend to dispute the authority of experience. (David Hume) The greatest, and perhaps the only, use of philosophy of pure reason is thus purely negative, since it serves not as an organon for the extension of knowledge, but as a discipline for determining knowledge's limits; and, instead of discovering truth, has only the modest merit of preventing error. (Immanuel Kant) The laws of probability are laws of consistency, an extension to partial beliefs of formal logic, the logic of consistency. (F. P. Ramsey) end p.v end p.vi Acknowledgements To Tom Baldwin, Richard Bradley, Craig Callender, David Corfield, Philippe Mongin, Margie Morrison, Demetris Portides, Jon Williamson, all the students taking the Philosophy of Science option in the LSE 1997–8, and two anonymous referees: many thanks for their kind help. I am also very grateful to Charlotte Jenkins for her patience and able assistance in seeing this book through the press. I would also like to acknowledge the patient support of Peter Momtchiloff, a constant source of encouragement and help. My greatest debt of all is to Peter Urbach, whose ideas on these issues over a period of twenty-five years, which included co- authorship of a book on the Bayesian theory, have become so inextricably linked with my own that I can no longer tell which are which, except that his are probably the better ones. end p.vii end p.viii Contents INTRODUCTION 1 1. HUME'S ARGUMENT 6 2. RELIABILISM 22 3. REALISM AND THE NO-MIRACLES ARGUMENT 35 4. PROBABILISM 61 5. DEDUCTIVISM 94 6. THE NATURALISTIC FALLACY 109 7. ‘A NEW SPECIES OF LOGIC’ 121 8. THE LOGIC OF SCIENTIFIC DISCOVERY 168 9. CHANCE AND PROBABILITY 221 FINALE 239 CODA: ‘OF MIRACLES’ 241 References 247 Index 257 end p.ix end p.x Introduction Colin Howson 1 Half-way through the eighteenth century the Scottish 1 Not English, as Glymour states (1992: 108). philosopher David Hume published a philosophical argument that was, metaphorically, dynamite. Its famous conclusion, that there is no justification for regarding what has been observed to happen in the past as any sort of reliable guide to the future, subverted the prevailing methodology of observation and experiment on the back of which rode the new mathematical sciences that seemed at the time Hume wrote to have attained an extraordinary degree of success, and have gone on doing so. Yet no uncontroversially definitive answer has ever been forthcoming to Hume, and most people have followed his own example of behaving as though nothing had happened. I find this extraordinary, and I believe it is time to face up to the unpalatable possibility revealed by Hume that all our hard-won factual knowledge is not secured by any process of demonstrably sound reasoning (and I mean sound reasoning in general, not merely deductive) to an empirical base, and see whether that is true and, if so, what follows from it. In the course of the investigation we shall be obliged to consider the respective claims of all the major ‘isms’ of contemporary philosophy of science: reliabilism, realism, falsificationism, naturalism, and Bayesianism. We shall also encounter the Anthropic Principle, significance tests, and miracles. Evaluating Hume's argument can therefore be made into a stimulating way of acquainting students with a wider class of philosophical issues, at the same time challenging them with a classic open problem which can be simply stated but not simply solved, if it can be solved at all. This book grew out of a course of lectures in philosophy of science employing just such an approach. The first chapter sketches the intellectual background to Hume's argument, presents that argument and then looks at some of the quicker attempts to rebut it. The subsequent chapters examine the more sophisticated replies, touching as they proceed on each of the ‘isms’ listed above. end p.1 My primary purpose in writing this book is not pedagogic, however. It is to support a claim that, despite its seeming absurdity, Hume's argument is actually correct. I shall present the argument, in Chapter 1, in a way that I think best reveals its quite extraordinary power, a power which, I believe, is still too little appreciated. The argument is deservedly one of the great classics of philosophy: Hume, no mean wielder of crushing arguments, produced in this one possibly the most crushing of them all. And not only crushing, but apparently attended by the gravest consequences for our standards of justified belief. But just as the force of Hume's argument is usually underestimated, so the devastation it is supposed to bring in its wake is usually exaggerated, and my supplementary thesis is that there is none the less a positive solution to Hume's problem. Indeed, I will argue the apparently paradoxical claim that there are nevertheless demonstrably sound inductive inferences! The resolution of the paradox is that inductive inference arises as a necessary feature of consistent reasoning, given the sorts of initial plausibility assumptions scientists habitually make. We are already familiar with and accept the idea that deductive soundness is a property of inferences and not their conclusions; I believe that the correct analysis of Hume's problem, and Hume's own view of inductive reasoning, forces us to view inductive soundness in the same way, a property of inferences rather than of what we conclude from them. This may not sound the sort of conclusion to warrant fanfares, but in mitigation two things can be said. First, Hume's argument gives us no reason to suppose that relying on our scientific knowledge is in any way misguided; it does not tell us we are wrong to do so. It merely says that the attempt to show that there is any sound inductive reasoning to that knowledge from observation alone will fail. But it may well be that we are fully justified, in terms of its truth or nearness to the truth, in relying on it. Secondly, I believe that Hume genuinely has solved the problem of induction. He solved it by showing, in general terms, that a sound inductive inference must possess, in addition to whatever observational or experimental data is specified, at least one independent assumption (an inductive assumption) that in effect weights some of the possibilities consistent with that evidence more than others. I take this to be a great logical discovery, comparable to that of deductive inference itself, and with consequences of as much practical as theoretical importance. For the problem of induction, considered as end p.2 the problem of characterizing soundness for inductive inferences, has recently become hot (so to speak). People are now for the first time in their chequered, too-frequently-bloody, history allocating substantial intellectual and material resources to the design of intelligent machinery, and in particular machinery that will learn from data.