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NEW ESSAYS on TARSKI and PHILOSOPHY This Page Intentionally Left Blank New Essays on Tarski and Philosophy NEW ESSAYS ON TARSKI AND PHILOSOPHY This page intentionally left blank New Essays on Tarski and Philosophy Edited by DOUGLAS PATTERSON 1 1 Great Clarendon Street, Oxford 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 the Several Contributors 2008 The moral rights of the authors have been asserted Database right Oxford University Press (maker) First published 2008 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 Data available Typeset by Laserwords Private Ltd, Chennai, India Printed in Great Britain on acid-free paper by Biddles Ltd., King’s Lynn, Norfolk ISBN 978–0–19–929630–9 13579108642 Contents List of Contributors vii 1Introduction 1 Douglas Patterson 2 Tarski and his Polish Predecessors on Truth 21 RomanMurawskiandJanWole´nski 3 Polish Axiomatics and its Truth: On Tarski’s Le´sniewskian Background and the Ajdukiewicz Connection 44 Arianna Betti 4 Tarski’s Conceptual Analysis of Semantical Notions 72 Solomon Feferman 5 Tarski’s Theory of Definition 94 Wilfrid Hodges 6 Tarski’s Convention T and the Concept of Truth 133 Marian David 7 Tarski’s Conception of Meaning 157 Douglas Patterson 8 Tarski, Neurath, and Kokoszynska´ on the Semantic Conception of Truth 192 Paolo Mancosu 9 Tarski’s Nominalism 225 Greg Frost-Arnold 10 Truth, Meaning, and Translation 247 Panu Raatikainen 11 Reflections on Consequence 263 John Etchemendy 12 Tarski’s Thesis 300 Gila Sher 13 Are There Model-Theoretic Logical Truths that are not Logically True? 340 Mario G´omez-Torrente vi Contents 14 Truth on a Tight Budget: Tarski and Nominalism 369 Peter Simons 15 Alternative Logics and the Role of Truth in the Interpretation of Languages 390 Jody Azzouni Index 431 List of Contributors Jody Azzouni, Professor of Philosophy, Tufts University Arianna Betti, Vrije Universiteit Amsterdam Marian David, Professor of Philosophy, University of Notre Dame John Etchemendy,Provost,StanfordUniversity Solomon Feferman, Professor of Mathematics and Philosophy and Patrick Suppes Pro- fessor of Humanities and Social Sciences, Stanford University Greg Frost-Arnold, Assistant Professor of Philosophy, University of Nevada, Las Vegas Mario G´omez-Torrente, Instituto de Investigaciones Filosoficas,´ Universidad Nacional Autonoma´ de Mexico´ Wilfrid Hodges, Professorial Fellow, School of Mathematical Sciences, Queen Mary, University of London Paolo Mancosu, Professor of Philosophy, University of California, Berkeley Roman Murawski, Faculty of Mathematics and Computer Science, Adam Mickiewicz University Douglas Patterson, Associate Professor of Philosophy, Kansas State University Panu Raaikainen, Academy Research Fellow, Academy of Finland, and Docent in The- oretical Philosophy, University of Helsinki Gila Sher, Professor of Philosophy, University of California, San Diego Peter Simons, Professor of Philosophy, University of Leeds Jan Wolenski´ , Jagiellonian University Institute of Philosophy This page intentionally left blank 1 Introduction Douglas Patterson If we go by the manner in which his contributions have been received up to the present day, there are three Alfred Tarskis. One is the pure mathematician and preternaturally clear logician and father of model theory, ‘‘the most methodologic- ally sophisticated definer of all time’’ (Belnap 1993, 132). This is the Tarski known to logicians and very formally inclined philosophers. A second Tarski is known in con- tinental Europe as the most eminent member of the Lvov–Warsaw school of philo- sophers following Kazimerez Twardowski—Stanislaw Le´sniewski, Jan Łukasiewicz, Kazimierez Ajdukiewicz, Tadeusz Kotarbinski,´ and so on (Wolenski´ 1989)—and as a philosopher who was in close contact with movements such as Hilbertian formal- ism (Sinaceur 2001) and the positivism of the Vienna Circle (Szaniawski 1993). The third Tarski is the one known among mainstream philosophers of language in the English speaking world. This Tarski came from nowhere to propose certain technical means of defining truth, means exploited in one way by Davidson (2001) and criti- cized in another by Field (1972). This Tarski taught us that sentences such as ‘‘ ‘snow is white’ is true if and only if snow is white’’ are very important to the theory of truth. This third Tarski also proposed a simple approach to the paradox of the liar, one that provides a convenient foil for more sophisticated accounts, and he held a strange view to the effect that natural languages are ‘‘inconsistent.’’ My aim in assembling this collection of essays is to encourage us to rediscover the real Tarski behind these three appearances. My own journey began with acquaintance with the third, as I read mainstream work in the philosophy of language. I also knew something of the first Tarski from my own study of logic and mathematics. I think I did wonder, as many do, who Tarski was and how he had come to exercise such a large influence, as I knew nothing about his background aside from a few familiar anec- dotes. Things changed for me—prompted, I recall, by a remark of Lionel Shapiro’s to the effect that though many people talk about ‘‘The Concept of Truth in Form- alized Languages’’ few people actually read it—when I sat down, more or less on a whim, to make myself one of the exceptions. What I found was vastly more inter- esting than what I’d been told about. Since then I have been reading and re-reading Tarski, learning what I can about where he came from and how his views developed, and rethinking the significance of what he said. In a way my motives in putting this collection together have been entirely selfish: I wanted to learn more about Tarski, and I have. 1 2 Douglas Patterson More sociably, however, I want to get three mutually isolated groups of scholars talking to one another. I don’t believe that Tarski’s remarks on formal topics from the seminal pre-war years can be understood without attention both to the philosoph- ical and mathematical background in which he worked. To take one example here, Tarski’s presentation of ‘‘Tarski’s Theorem’’ on the indefinability of truth—known today as the result that arithmetic truth is not arithmetically definable, or, a bit more philosophically put, that no language sufficient for expressing a weak version of arithmetic can consistently express basic aspects of its own semantics—is intimately bound up with his views on expressibility and type theory, views Tarski attributes to Le´sniewski and even Husserl. These make the difference between what is now said, which is that arithmetic truth is not arithmetically definable, and what Tarski said at the time, which is that it isn’t definable at all. There are also questions, raised by Gomez-Torrente 2004, as to whether Tarski proves the result usually attributed to the passage, or a different, syntactic result. In the seminal works of the 1930s one finds an emerging body of formal results still embedded in a bygone era. Much has been lost along the way, some well, some not, but we cannot understand the develop- ment of modern logic, a development in which Tarski played a central role, without setting its beginning in proper context. When it comes to the second, genuinely historical Tarski, my hope is to help to rescue him and, even more importantly his teachers, from the obscurity into which they have fallen in the English speaking world. There is no reason why Le´sniewski, Łukasiewicz, Ajdukiewicz, Kotarbinski,´ Twardowski, and their compatriots are not accorded at least the status of Carnap, Reichenbach, Schlick, Neurath, and Hempel. My belief here is that this isn’t really anything more than a legacy of the many misfortunes Poland endured in the twentieth century. Lvov and Warsaw before the Second World War seem poised to play roles equivalent to that of Vienna in the history of philosophy before being cut off by fascism and communism. As a res- ult, in the English speaking world undergraduate and even graduate students learn nothing of the Polish school, and many important texts are walled off by archaic or missing translations. I hope that this work will stimulate interest in Tarski’s pre- decessors. As for the third Tarski, I believe him to be a vastly less able philosopher than the real one. Among other things, I argue here and elsewhere that his approach to the semantic paradoxes is different from, and vastly better than, what is usu- ally attributed to him. He also has things to say about definition that I believe have a good deal to teach us about meaning and analyticity. The arsenal of stock criticisms of Tarski—that his methods of defining truth make contingent truths about the semantics of language into necessary or logical truths, that he was mis- guided to think that languages can be ‘‘inconsistent,’’ that he advocated a simplistic formalization-and-hierarchy approach to the paradoxes—nearly all fail to make con- tact with Tarski’s actual views.
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