GAMES: UNIFYING LOGIC, LANGUAGE, AND PHILOSOPHY LOGIC, EPISTEMOLOGY, AND THE UNITY OF SCIENCE VOLUME 15 Editors Shahid Rahman, University of Lille III, France John Symons, University of Texas at El Paso, U.S.A. Editorial Board Jean Paul van Bendegem, Free University of Brussels, Belgium Johan van Benthem, University of Amsterdam, the Netherlands Jacques Dubucs, University of Paris I-Sorbonne, France Anne Fagot-Largeault Collège de France, France Bas van Fraassen, Princeton University, U.S.A. Dov Gabbay, King’s College London, U.K. Jaakko Hintikka, Boston University, U.S.A. Karel Lambert, University of California, Irvine, U.S.A. Graham Priest, University of Melbourne, Australia Gabriel Sandu, University of Helsinki, Finland Heinrich Wansing, Technical University Dresden, Germany Timothy Williamson, Oxford University, U.K. Logic, Epistemology, and the Unity of Science aims to reconsider the question of the unity of science in light of recent developments in logic. At present, no single logical, semantical or methodological framework dominates the philosophy of science. However, the editors of this series believe that formal techniques like, for example, independence friendly logic, dialogical logics, multimodal logics, game theoretic semantics and linear logics, have the potential to cast new light no basic issues in the discussion of the unity of science. This series provides a venue where philosophers and logicians can apply specific technical insights to fundamental philosophical problems. While the series is open to a wide variety of perspectives, including the study and analysis of argumentation and the critical discussion of the relationship between logic and the philosophy of science, the aim is to provide an integrated picture of the scientific enterprise in all its diversity. For other titles published in this series, go to www.springer.com/series/6936 Games: Unifying Logic, Language, and Philosophy Edited by Ondrej Majer Czech Academy of Sciences, Czech Republic Ahti-Veikko Pietarinen University of Helsinki, Finland Tero Tulenheimo University of Helsinki, Finland ABC Editors Dr. Ondrej Majer Dr. Tero Tulenheimo Academy of Sciences of the University of Helsinki Czech Republic Department of Philosophy Institute of Philosophy Siltavuorenpenger 20 A Jilska 1 FI-00014 Helsinki 110 00 Prague 1 P.O. Box 9 Czech Republic Finland [email protected] [email protected] Dr. Ahti-Veikko Pietarinen University of Helsinki Department of Philosophy Siltavuorenpenger 20 A FI-00014 Helsinki P.O. Box 9 Finland [email protected] Cover image: Adaptation of a Persian astrolabe (brass, 1712–13), from the collection of the Museum of t he History of Science, Oxford. Reproduced by permission. ISBN 978-1-4020-9373-9 e-ISBN 978-1-4020-9374-6 Library of Congress Control Number: 2008938971 All Rights Reserved °c 2009 Springer Science + Business Media B.V. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper 9 8 7 6 5 4 3 2 1 springer.com Contents Introduction ix Ondrej Majer, Ahti-Veikko Pietarinen, and Tero Tulenheimo Part I Philosophical Issues 1 Why Play Logical Games? 3 Mathieu Marion 2 On the Narrow Epistemology of Game-Theoretic Agents 27 Boudewijn de Bruin 3 Interpretation, Coordination and Conformity 37 Hykel Hosni 4 Fallacies as Cognitive Virtues 57 Dov M. Gabbay and John Woods Part II Game-Theoretic Semantics 5 A Strategic Perspective on IF Games 101 Merlijn Sevenster 6 Towards Evaluation Games for Fuzzy Logics 117 Petr Cintula and Ondrej Majer 7 Games, Quantification and Discourse Structure 139 Robin Clark Part III Dialogues 8 From Games to Dialogues and Back 153 Shahid Rahman and Tero Tulenheimo 9 Revisiting Giles’s Game 209 Christian G. Ferm¨uller v vi Contents 10 Implicit Versus Explicit Knowledge in Dialogical Logic 229 Manuel Rebuschi Part IV Computation and Mathematics 11 In the Beginning Was Game Semantics 249 Giorgi Japaridze 12 The Problem of Determinacy of Infinite Games from an Intuitionistic Point of View 351 Wim Veldman Symbol Index 371 Subject Index 373 Name Index 377 Contributing Authors Boudewijn de Bruin Dov M. Gabbay Faculty of Philosophy Department of Computer Science University of Groningen King’s College London Oude Boteringestraat 52 The Strand 9712 GL Groningen London WC2R 2LS The Netherlands England [email protected] UK [email protected] Petr Cintula Hykel Hosni Institute of Computer Science Scuola Normale Superiore Academy of Sciences Piazza dei Cavalieri of the Czech Republic 56100 Pisa Pod Vodarenskou vezi 2 Italy 182 07 Prague 8 [email protected] Czech Republic [email protected] Giorgi Japaridze Department of Computing Sciences Robin Clark Villanova University Department of Linguistics 800 Lancaster Avenue 619 Williams Hall Villanova, Pennsylvania 19085 University of Pennsylvania USA Philadelphia, PA 19104-6305 [email protected] USA [email protected] Mathieu Marion D´epartement de philosophie Christian G. Ferm¨uller Universit´eduQu´ebeca ` Montr´eal Technische Universit¨at Wien Case postale 8888, succursale Favoritenstr. 9-11/E1852 Centre-ville A-1040 Wien Montr´eal, Qu´ebec Austria Canada H3C 3P8 [email protected] [email protected] vii viii Contributing Authors Merlijn Sevenster John Woods Philips Research Department of Philosophy Prof. Holstlaan 4 University of British Columbia 5656 AA Eindhoven 1866 Main Mall E370 The Netherlands Vancouver, BC [email protected] Canada V6T 1Z1 [email protected] Shahid Rahman [email protected] U.F.R. de Philosophie Domaine Universitaire “Pont de Bois” Ondrej Majer Universit´e Lille III Institute of Philosophy 59653 Villeneuve d’Ascq Academy of Sciences France of the Czech Republic [email protected] Jilsk´a 1, 110 00 Prague Manuel Rebuschi Czech Republic Laboratoire d’Histoire des Sciences [email protected] et de Philosophie Archives Henri Poincar´e Ahti-Veikko Pietarinen UMR 7117 CNRS - Nancy-Universit´e Department of Philosophy Universit´eNancy2 P.O. Box 9 23, Bd. Albert Ier-BP 3397. F-54015 00014 University of Helsinki NANCY Cedex Finland France ahti-veikko.pietarinen@helsinki.fi [email protected] Wim Veldman Tero Tulenheimo Institute for Mathematics, Department of Philosophy Astrophysics and Particle Physics Academy of Finland Radboud University Nijmegen P.O. Box 9 P.O. Box 9010 00014 University of Helsinki 6500 GL Nijmegen Finland The Netherlands tero.tulenheimo@helsinki.fi [email protected] Introduction Ondrej Majer, Ahti-Veikko Pietarinen, and Tero Tulenheimo 1 Games and logic in philosophy Recent years have witnessed a growing interest in the unifying methodolo- gies over what have been perceived as pretty disparate logical ‘systems’, or else merely an assortment of formal and mathematical ‘approaches’ to philo- sophical inquiry. This development has largely been fueled by an increasing dissatisfaction to what has earlier been taken to be a straightforward outcome of ‘logical pluralism’ or ‘methodological diversity’. These phrases appear to reflect the everyday chaos of our academic pursuits rather than any genuine attempt to clarify the general principles underlying the miscellaneous ways in which logic appears to us. But the situation is changing. Unity among plurality is emerging in con- temporary studies in logical philosophy and neighbouring disciplines. This is a necessary follow-up to the intensive research into the intricacies of logical systems and methodologies performed over the recent years. The present book suggests one such peculiar but very unrestrained method- ological perspective over the field of logic and its applications in mathematics, language or computation: games. An allegory for opposition, cooperation and coordination, games are also concrete objects of formal study. As a metaphor for argumentation Aristotle’s Topics and its reincarnations such as the scholastic Ars Obligatoria are set up as dialogical duels (Pietarinen, 2003a). Logics exploiting this idea resurface in the twentieth century attempts to clarify the concepts of argument and proof. The game metaphor has re- tained its strength in contemporary theories of computation (Pietarinen, 2003b, Japaridze, this volume), in which computation is recast in terms of the symbio- sis between the Computing System (‘Myself’) and its Environment (‘Nature’). In mathematics, the benefits of doing so were noted decades ago by Stanislaw Ulam (1960), who wrote how amusing it is “to consider how one can ‘gamize’ ix x Introduction various mathematical situations (or perhaps the verb should be ‘paizise’ from the Greek word παιςιη,toplay).” Games as explications of the core philosophical questions concerning the scientific methodologies were on the brink of being born in the writings of the early unificators, including Rudolf Carnap, Otto Neurath, Charles Morris and Carl Gustav Hempel. But they never operationalised the key notions. The term ‘operationalisation’ is apt, since what was attempted was to give meaning to ‘operationalisation’. According to operationalism, a concept is synonymous with the set of operations correlated with it. Influenced by Percy Bridgman’s and Alfred Einstein’s thoughts, the early workers on what