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091 Second Philosophy a Naturalistic Method.Pdf This page intentionally left blank Second Philosophy This page intentionally left blank Second Philosophy A naturalistic method Penelope Maddy 1 1 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 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 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 Penelope Maddy 2007 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2007 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 the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Typeset by Laserwords Private Limited, Chennai, India Printed in Great Britain on acid-free paper by Biddles Ltd, King’s Lynn, Norfolk ISBN 978–0–19–927366–9 10987654321 For David This page intentionally left blank Preface The roots of this project trace to my previous book—Naturalism in Math- ematics—in two ways, one foreseen and one not. The first is implicit in Naturalism itself, where typically ‘philosophical’ questions about mathemat- ics are explicitly set aside in single-minded pursuit of purely methodological concerns (see [1997], p. 203). I intended from the start to return to these broader issues, an undertaking that seemed to me to require a preliminary foray into the philosophy of logic before circling back; the result is Part III and the three central sections on mathematics in Part IV. The second came as a surprise: when I set out on Naturalism, I assumed that everyone knew what it is to be a naturalist, that my job was to explain how to extend this idea to mathematics. What I discovered—from reactions to various talks and papers and to the book—was that everyone, naturalist or not, seemed to harbor his or her own firm notion of what ‘naturalism’ requires. To complete the story of Naturalism, I had to make my own firm notion explicit, which eventually led to the Second Philosophy described in Parts I, II, and the remainder of Part IV. Along the way, the nature of word–world relations presented itself as an opportune example for Part II because of the way debates over truth often intermingle with the topics of IV.4. Several papers published since Naturalism contain embryonic versions of discussions found here. Much of ‘Second philosophy’ ([2003]) has made its way into I.1,I.2,I.6,andIV.1, and ‘Mathematical existence’ ([2005b]) makes up a goodly portion of IV.4. Smaller chunks of the survey paper ‘Three forms of naturalism’ ([2005a]) appear in I.6, and of ‘Some naturalistic reflections on set theoretic method’ ([2001a])inIV.2.iii and IV.3. Traces of ‘Three forms’, ‘Logic and the discursive intellect’ ([1999]), ‘Naturalism and the a priori’ ([2000]), and ‘Naturalism: friends and foes’ ([2001b]) survive in III.1, III.1 and III.2,I.4,andI.7 and IV.1, respectively. My thanks to the Indian Council of Philosophical Research, the Association for Symbolic Logic, Oxford University Press, Springer Science and Business Media, the Notre Dame Journal of Formal Logic,and Philosophical Perspectives for permission to use this material. In addition, viii preface ‘A naturalistic look at logic’ ([2002]) constitutes a rough first pass at the position of Part III. Finally, it’s a great pleasure to acknowledge my many intellectual debts. Let me first extend special thanks to John Burgess and Mark Wilson, whose thinking has influenced far more than the specific sections (IV.4 and II.6) where their work is explicitly discussed. Many others have helped in a variety of ways, including Karl Americks, Jody Azzouni, Mark Balaguer, Jeff Barrett, Janet Broughton, Joshua Brown, Mark Colyvan, Christina Conroy, William Demopoulos, Lara Denis, Sean Ebels-Duggan, Hartry Field, Michael Friedman, Sam Hillier, Kent Johnson, Peter Koellner, Joe Lambert, Mary Leng, Cathay Liu, Colin McLarty, David Malament, Ruth Marcus, Patricia Marino, Teri Merrick, Alan Nelson, Charles Parsons, Brendan Purdy, John Rapalino, Brian Rogers, Waldemar Rohloff, Jef- frey Roland, Adina Roskies, Barbara Sarnecka, Sally Sedgwick, Stewart Shapiro, Rory Smead, Kyle Stanford, John Steel, Jamie Tappenden, Carla Valenzuela, Nick White, Crispin Wright, Steve Yablo, and Kevin Zoll- man. I’m particularly grateful to Hillier, Liu, Malament, Purdy, Rapalino, Rogers, Rohloff, Smead, Valenzuela, and Zollman for participating in an informal discussion group that read through the penultimate draft of the entire manuscript and made many good suggestions, and to Malament again, for keeping me honest on the physics and for encouraging words when they were needed most. Thanks finally to Peter Momtchiloff of Oxford University Press for supporting the project from the beginning. Near the end of the Tractatus (in 6.53), Wittgenstein remarks, ‘The right method of philosophy would be this. To say nothing except what can be said, i.e., the propositions of natural science.’ Of course, ‘what can be said’ and ‘the propositions of natural science’ are heavily weighted theoretical terms for Wittgenstein, but if the words ‘to say nothing except ... natural science’ were understood in their ordinary, rough and ready senses, this ‘right method’ would be Second Philosophy. Ever tempted to overstep, Wittgenstein adds ‘and when someone else wished to say something metaphysical, to demonstrate to him that he had given no meaning to certain signs’. The Second Philosopher indulges in no such corrective project: her reaction to extra-scientific philosophy is puzzlement; she asks methodically after its standards and goals, and assesses these by her own lights. Wittgenstein concludes that ‘this method would be unsatisfying to the other—he would not have the feeling that we were teaching him preface ix philosophy’. My hope here is to discredit this last claim, to suggest that the Second Philosopher can address traditionally philosophical questions—and that she can answer them. P. M. Irvine, California July 2006 This page intentionally left blank Contents Introduction 1 Part I. What is Second Philosophy? 9 1. Descartes’s first philosophy 11 2. Neo-Cartesian skepticism 20 3. Hume’s naturalism 37 4. Kant’s transcendentalism 47 5. Carnap’s rational reconstruction 65 6. Quine’s naturalism 83 7. Putnam’s anti-naturalism 97 Part II. The Second Philosopher at Work 113 1. What’slefttodo? 115 2. An illustration: truth and reference 119 3. Reconfiguring the debate 139 4. Disquotation 152 5. Minimalism 166 6. Correlation 175 Part III. A Second Philosophy of Logic 197 1. Naturalistic options 199 2.Kantonlogic 207 3. Undoing the Copernican revolution 225 4. The logical structure of the world 234 5. The logical structure of cognition 245 6. The status of rudimentary logic 271 xii contents 7. From rudimentary to classical logic 282 8. Caveats 299 Part IV. Second Philosophy and Mathematics 303 1. Second philosophy of science 305 2. Mathematics in application 314 3. Second methodology of mathematics 344 4. Second philosophy of mathematics 361 5. Second metaphysics 392 References 412 Index 439 Introduction These days, as more and more philosophers count themselves as naturalists, the term has come to mark little more than a vague science-friendliness. To qualify as unnaturalistic, a contemporary thinker has to insist, for example, that epistemology is an a priori discipline with nothing to learn from empir- ical psychology or that metaphysical intuitions show quantum mechanics to be false. There are those who take such positions, of course, but to lump everybody else under one rubric is clearly too crude a diagnostic. My goal in this book is to delineate and to practice a particularly austere form of naturalism. One minor difficulty is that the term ‘naturalism’ has acquired so many associations over the years that using it tends to invite indignant responses of the form, ‘but that can’t be naturalism! Naturalism has to be like this!’ As my project is to spell out an approach that differs in subtle but fundamental ways from other ‘naturalisms’, it seems best to coin a new term, on the assumption that I will then be permitted to stipulate what I intend it to mean. Thus, ‘Second Philosophy’. A deeper difficulty springs from the lesson won through decades of study in the philosophy of science: there is no hard and fast specification of what ‘science’ must be, no determinate criterion of the form ‘x is science iff ... ’. It follows that there can be no straightforward definition of Second Philosophy along the lines ‘trust only the methods of science’. Thus Second Philosophy, as I understand it, isn’t a set of beliefs, a set of propositions to be affirmed; it has no theory. Since its contours can’t be drawn by outright definition, I resort to the device of introducing a character, a particular sort of idealized inquirer called the Second Philosopher, and proceed by describing her thoughts and practices in a range of contexts; Second Philosophy is then to be understood as the product of her inquiries.
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