THE UNIVERSITY OF WESTERN ONTARIO SERIES IN PHILOSOPHY OF SCIENCE

LIKENESS TO TRUTH

THE UNIVERSITY OF WESTERN ONTARIO SERIES IN PHILOSOPHY OF SCIENCE A SERIES OF BOOKS IN PHILOSOPHY OF SCIENCE, METHODOLOGY, EPISTEMOLOGY, LOGIC, HISTORY OF SCIENCE, AND RELATED FIELDS Managing Editor ROBERT E. BUTTS Dept. of Philosophy, University of Western Ontario, Canada Editorial Board JEFFREY BUB, University of Western Ontario L. JONATHAN COHEN, Queen's College, Oxford WILLIAM DEMOPOULOS, University of Western Ontario WILLIAM HARPER, University of Western Ontario JAAKKO HINTIKKA, Florida State University, Tallahassee CLIFFORD A. HOOKER, University of Newcastle HENRY E. KYBURG, JR., University of Rochester AUSONIO MARRAS, University of Western Ontario JURGEN MITTELSTRASS, Universitiit Konstanz JOHN M. NICHOLAS, University of Western Ontario GLENN A. PEARCE, University of Western Ontario BAS C. VAN FRAASSEN, Princeton University VOLUME 30

GRAHAM ODDIE Philosophy Department, Otago University, New Zealand LIKENESS TO TRUTH D. REIDEL PUBLISHING COMPANY A MEMBER OF THE KLUWER ACADEMIC PUBUSHERS GROUP DORDRECHT/BOSTON/LANCASTER/TOKYO

library of Congress Cataloging in Publication Data Oddie, Graham, 1954- Likeness to truth. (The University of Western Ontario series in philosophy of science; v. 30) Bibliography: p. Includes index. 1. Truth. I. Title. II. Series. BDl71.025 1986 121 86-3883 ISBN-13: 978-94-010-8570-0 DOT: 10.1007/978-94-009-4658-3 e-isbn-13: 978-94-009-4658-3 Published by D. Reidel Publishing Company, P.O. Box 17,3300 AA Dordrecht, Holland. Sold and distributed in the U.S.A. and Canada by Kluwer Academic Publishers, 190 Old Derby Street, Hingham, MA 02043, U.S.A. In all other countries, sold and distributed by Kluwer Academic Publishers Group, P.O. Box 322, 3300 AH Dordrecht, Holland. All Rights Reserved 1986 by D. Reidel Publishing Company, Dordrecht, Holland Softcover reprint of the hardcover 1 st edition 1986 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner

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CONTENTS ACKNOWLEDGEMENTS NOTATION xiv xv CHAPTER ONE: TRUTH AND CLOSENESS TO TRUTH 1.1 1.2 The problem of truthlikeness Explications and intuitions 1 5 1. 3 Some adequacy conditions Notes 10 20 CHAPTER TwO: POPPER ONTRUTHUKENESS 2.1 Truthlikeness in Popper's methodology 21 2.2 2.3 Truthlikeness by truth content and falsity content Measuring truth content and falsity content 24 29 Notes 33 CHAPTER THREE: DISTANCE IN LOGICAL SPACE 3.1 Conceptual frameworks and possible worlds 34 3.2 3.3 Distance between propositions Measuring the symmetric difference 38 42 3.4 Truthlikeness for a propositional framework 44 3.5 Truthlikeness by similarity spheres Notes 51 58 CHAPTER FOUR: TRUTHUKENESS BY DISTRIBUTIVE NORMAL FORMS 4.1 Languages and pictures 60 4.2 Worlds and interpretations 65 4.3 Constituents in a first-order language 68 4.4 The symmetric difference on constituents 75 4.5 The propositional measure extended 91 Notes 1M CHAPTER FIVE: BEYOND FIRST-ORDER TRUTHLIKENESS 5.1 Questions, answers, and propositional distance again 108 5.2 5.3 Infinitely deep theories and ultimate questions Higher-order frameworks 115 122 5.4 Verisimilitude and legisimilitude 131 Notes 1~ CHAPTER SIX: TRUTHUKENESS AND TRANSLATION 6.1 Invariance under translation 136 6.2 Theidentity of states of affairs 141 6.3 Coactualisation and structure 147 6.4 Two criticisms of the structure argument 152 6.5 Numerical accuracy, confirmation and disconfirmation 156 6.6 Privileged properties 159 Notes 165

viii CONTENTS CHAPTER SEVEN: TRUTHUKENESS, CONTENT, AND UTIUTY 7.1 The content condition 7.2 The attractions of brute strength 7.3 Epistemic utilities 7.4 Accuracy and action: a conjecture Notes APPENDIX 8.1 First-order languages and their interpretations 8.2 Higher-order languages 8.3 Examples J and K formalized 8.4 First-order normal forms 8.5 Permutative normal forms 8.6 The distance between constituents Notes REFERENCES INDEX 167 174 178 182 188 189 191 193 197 201 208 211 212 217

PREFACE The concept of likeness to truth, like that of truth itself, is fundamental to a realist conception of inquiry. To demonstrate this we need only make two rather modest realist assumptions: the truth doctrine (that the aim of an inquiry, as an inquiry, is the truth of some matter) and the progress doctrine (that one false theory may realise this aim better than another). Together these yield the conclusion that a false theory may be more truthlike, or closer to the truth, than another. It is the aim of this book to give a rigorous philosophical analysis of the concept of likeness to truth, and to examine the consequences, some of them no doubt surprising to those who have been unduly impressed by the (admittedly important) true/false dichotomy. Truthlikeness is not only a requirement of a particular philosophical outlook, it is as deeply embedded in common sense as the concept of truth. Everyone seems to be capable of grading various propositions, in different (hypothetical) situations, according to their closeness to the truth in those situations. And (if my experience is anything to go by) there is remarkable unanimity on these pretheoretical judgements. This is not proof that there is a single coherent concept underlying these judgements. The whole point of engaging in philosophical analysis is to make this claim plausible. But these low-level, uncontroversial judgements provide us with our grip on the concept (if indeed there is a coherent concept) and any adequate philosophical account of the concept must not violate them. Or rather (recognising that even philosophers do not always traffick in pure truth and that some false philosophical theories are closer to the truth than others) an account of truthlikeness is better (other things being equal) the better it accords with low-level, uncontroversial judgements on simple cases. This is the basic methodological rule which controls theorising throughout the following pages. If one considers the vast bulk of literature devoted to the concept of truth, it is quite remarkable how meagre is the attention paid to the much more interesting concept of truthlikeness. It is only in the last fifteen years or so that a group of philosophers have devoted any serious attention at all to the concept. Karl Popper was the first to see clearly the importance of giving an adequate account of truthlikeness, and it is not difficult to see why. Popper, perhaps more than most philosophers, was deeply impressed by the fact that our favourite theories so often tum out to be mistaken not least in that field of human knowledge with which Popper preoccupied himself: science. But Popper eschewed complete scepticism. He ix

x PREFACE wanted to affirm both the progress of human knowledge, as well as the goal of truth, and, combined with the thesis that the history of human knowledge is the history of a succession of false theories, this immediately generates the problem of truthlikeness. Popper was thus the first philosopher to attempt a rigorous analysis of the concept. However, Popper wanted to show not merely that truthlikeness is as respectable as truth, he wanted the concept to function appropriately within his own account of knowledge. In this account logical strength, or degree of content, plays a leading role-indeed, almost a solo performance. Thus the quest was on for an account according to which logical strength, sheer logical improbability, would be intimately tied to degrees of truthlikeness. Popper made a number of proposals which seemed to achieve just this. In 1973 Popper was a Visiting Professor at Otago University, and I was a second year undergraduate. I could not attend the staff-graduate seminar, but I nevertheless heard the news that in the course of a paper given to the seminar Pavel Tichy had presented a knock-down refutation of Popper's account oftruthlikeness. (Unknown to me at that time David Miller, at Warwick University, independently discovered the same negative result.) The news of Tichy's results intrigued me, and this was the beginning of an interest in truthlikeness which has occupied me, on and off, for the past twelve years. Two years after that eventful seminar (by which time I was eligible to attend) Tichy gave another in which he outlined a positive proposal. This positive proposal explained some of the motivation for Popper's probabilitycontent approach, but it was really the beginnings of an entirely different sort of approach-one which took seriously the likeness in truthlikeness. According to this new approach, propositions present us with a range of different possibilities, and these possibilities are more or less like that possibility which is actualised. The truthlikeness of a proposition depends not on the quantity of its information (that is, on how many possibilities it rules out) but on the quality of its information (that is, on the likeness to the actual state of affairs of the possibilities it does allow). Moreover, Tichy demonstrated a way in which this simple but profound idea could be articulated in a precise and rigorous form-by utilising the structural features of the normal forms discovered by Jaakko Hintikka. While much of what I have thought about truthlikeness has changed, Tichy'S basic approach has always struck me as the most fruitful and promising. Anyone who reads this book will realise that my debt to him is enormous, and I would like to thank him for everything that I have learnt from him. As we have worked, discussed and corresponded together over the years our ideas on the topic have

PREFACE xi become increasingly entangled. However, I have tried throughout the book to indicate our respective contributions, as well, of course, as those of others. At roughly the same time that Tichy began working on his approach at Otago, Risto Hilpinen and Ilkka Niiniluoto began working on a similar approach in Finland. Hilpinen argued for the importance of likeness in judgements of truthlikeness, and Niiniluoto stressed the importance of giving a rigorous account of this, by means of Hintikka's normal forms. It is encouraging that such very similar discoveries can be made independently by philosophers working in quite different ways. As a realist, I take this to be evidence for the objectivity and solidity of truth, even in philosophy. But though the truth is solid enough, there is not much light about, and it is only occasionally that inquirers, in their stumblings and gropings, simultaneously grasp a portion of the truth, and become familiar with its shape. In the course of the book I outline the major proposals that have been put forward, both within the probability-content programme (Chapters Two and Three) and within the likeness programme (Chapters Three and Four). This part of the book contains an overview of the debate, but obviously it has a perspective, and Chapter Four culminates in what I argue to be the most promising proposal for first-order logic. Moreover, the different theories are presented not so much in historical order, as in the order which best illuminates the argument for the proposal I defend. The basic proposal for first-order truthlikeness can be extended and developed in a number of directions. In some quarters first-order logic is regarded with a quasi-religious awe, and deep suspicion surrounds those who draw attention to its shortcomings. First-order logic is usually thought to be congenial to nominalism (or at least not hopelessly at odds with nominalism), and nominalism, in various disguises, is the favoured philosophy of the day. It was also from Pavel Tichy that I first learnt the necessity for breaking out of the first-order strait-jacket, as well as the liberating pleasure of doing so. Many concepts central to our conceptual scheme (for example, causation, intention, action, purpose) show no inclination to be reduced to first-order surrogates, despite generations of philosophical effort. Thus higher-order frameworks are introduced in Chapter five, and it is shown how a space of possibilities can be generated by a collection which includes higher-order concepts or traits. Perhaps the most novel aspect of the treatment here is the account of truthlikeness for such higher-order frameworks, and the theory of permutative normal forms on which it is based. Chapter Five also extends the basic theory of truthlikeness to a general theory of distance between propositions, and a general

xii PREFACE account of the accuracy of a theory with respect to particular questions. It is widely held that the most serious challenge to this approach to truthlikeness comes from a quite general attack on the notion of likeness -itself. This attack can be mounted in a number of different ways. In David Miller's hands it amounts to the claim that this account of truthlikeness is not language (or translation) invariant. According to Miller, it gives conflicting results for the same pairs of theories expressed in different languages. Miller goes on to argue that if a notion is to have 'any objective significance at all' it must be 'translation invariant'. Chapter Six contains an exhaustive analysis of this argument, and ones closely related to it. Miller does not state explicitly the semantic (or metaphysical) presuppositions of this argument, but it is one of the virtues of the argument that it forces the defenders of truthlikeness to unearth their own semantic and metaphysical assumptions. The argument demands a searching analysis of the identity conditions of propositions, and of states of affairs, as well as of the 'objective significance' of such diverse notions as structure, change, confirmation, disconfirmation, and likeness in general. The conclusions of this analysis may not be particularly palatable to all realists, but they seem to be virtually unavoidable in the defense of truthlikeness, and hence of any realist doctrines (like those of truth and progress mentioned above) which require such a defense. Popper has claimed that this kind of account fails to capture adequately the relationship between content and truthlikeness, and the claim is examined, and repudiated, in Chapter Seven. Other important objections to truthlikeness cluster around the apparent methodological uselessness of the notion. On the one hand, if we know the truth already then the notion is redundant. On the other, if we don't know the truth then it seems that we can't know the degree of truthlikeness of a proposition either. And so in this case the notion is useless-it has no criteria of application. It is shown where the fallacies in this argument, and ones related to it, lurk. It is argued that truthlikeness is the best candidate for the role of epistemic (or cognitive) utility (or value). I define the overall accuracy of a proposition with respect to particular questions, and develop a plausible conjecture concerning the close relationship between degrees of truthlikeness and degrees of overall question answering accuracy. If correct, this conjecture is of considerable importance for both theory and practice. Confidence in the truthlikeness of apparently accurate theories would be justified. And the more truthlike a theory, the more likely it would be to give accurate answers to pressing practical problems. The laws of truthlikeness are quite different from the laws of truth, or the laws of

PREFACE xiii probability and content. Indeed, truthlikeness is, in many ways, a much richer and more complex notion than these. And if the argument of the book is sound then truthlikeness is just as amenable as these other notions to rigorous logical treatment, and at least one sceptical argument against the realist account of inquiry is defeated. There is room for realists to be optimistic. The results should be of interest to all those interested in the notion of truth, and that must include most philosophers. I have tried to make this book as accessible to as many people as possible. A modest acquaintance with introductory first-order logic is assumed, but any material that might appear intimidating is relegated to the Appendix. The unavoidable technicalities that remain in the body of the text are not all that numerous, and tend to be brief. For the most part, provided the reader is willing to take on trust the claims I base on these portions, they can be skipped without detriment to the main line of argument.

ACKNOWLEDGEMENTS There are two people to whom I am especially indebted. I have mentioned in the Preface that my debt to Pavel Tichy is quite evident from the text itself. I am also greatly indebted to John Watkins, who gave me an enormous amount of help while I was working on my doctoral thesis at London University, and subsequently has proved to be a generous correspondent. Both of them have been unstinting in the time and energy they have put into this project. It will also be evident from the text that I have had a long and fruitful correspondence with Ilkka Niiniluoto, and I would like to thank him for that. Although Ilkka and I have often disagreed about many aspects of truthlikeness, he has always received my ideas with an openness and fairness which is as commendable as it is rare. Others from whom I have benefitted greatly by way of both discussion and correspondence include Robert Butts, Jonathan Cohen, Greg Currie, Bob Durrant, Martin Fricke, John Harris, Colin Howson, Theo Kuipers, David Miller, Alan Musgrave, William Newton-Smith, David Pearce, Roy Perrett, Raimo Tuomela, Peter Urbach, Bryan Wilson and John Worrall. I am grateful for permission to copy a graph (p. 157) which originally appeared in the American Journal of Physics, and to reuse some of my own material originally published in Acta Philosophica Fennica, The British Journalfor the Philosophy of Science, and Synthese. Several people have helped in the production of various drafts of the manuscript and of the final copy. I am very grateful for the help of Christine Colbert, Merle Munroe and June O'Donnell. I am particularly grateful for all the help given by Bryan Wilson in producing the final camera-ready copy. There are many people, besides the ones mentioned here, to whom lowe all sorts of debts indirectly connected with this book. I hope that they will forgive me for not mentioning them. I can't imagine that anyone would be the least inclined to attribute my errors to those I have mentioned, but if there is such a person then at least those whom I have not mentioned will be spared that indignity. xiv

NOTATION Apart from those conventions which are almost universal, I employ the following slightly idiosyncratic conventions. Bold face letters are used for particular (specified) non-syntactic objects. Ordinary roman letters, in a symbolic context, stand for particular syntactic items of particular specified languages. Italic letters are used for variables, both variables ranging over syntactic items and variables ranging over non-syntactic items. The following is an incomplete list which should make the conventions clear. A,B,C,... are particular specified frameworks. AI' A 2, A 3,.. (Bl' B 2, B 3,... ) are particular specified propositions over framework A (respectively, framework B). 0, N are particular individuals over framework C. h, r, ware particular (basic) propositions over framework D. WI' W 2, W 3,.. are particular specified worlds over framework D. &, v are, respectively, the conjunction and disjunction functions, which take pairs of classes of worlds to classes of worlds. Xl' x 2, x 3, are the variables common to all first-order languages. h, r, ware particular sentences of language L D F and T are the monadic predicates of language L E, H a dyadic predicate of language L F &, v are the sentential connectives which (when interpreted) stand for the conjunction and disjunction functions respectively. The following letters (sometimes subscripted) are used for variables with the specified ranges: X, Y, Z... range: the individuals of a framework. U, V, W... range: the possible worlds of a framework. A, B, C... range (in different contexts): propositions, or sentences-the context will make it clear. P, Q, R... range (in different contexts): properties, or predicates -the context will make it clear. a, b,... range: terms of a language. xv