The Realism-Antirealism Debate in the Age of Alternative Logics

Transcription

1 The Realism-Antirealism Debate in the Age of Alternative Logics

2 LOGIC, EPISTEMOLOGY, AND THE UNITY OF SCIENCE VOLUME 23 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 Göran Sundholm, Universiteit Leiden, The Netherlands 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 on 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 further volumes:

3 Shahid Rahman Giuseppe Primiero Mathieu Marion Editors The Realism-Antirealism Debate in the Age of Alternative Logics 123

4 Editors Shahid Rahman Université de Lille, UdL3 CNRS, UMR 8163: STL F Villeneuve d Ascq France shahid.rahman@univ-lille3.fr Mathieu Marion Université du Québec à Montréal Département de philosophie Succursale Centre-Ville 8888 C.P. H3C 3P8 Montreal QC, Canada marion.mathieu@uqam.ca Dr. Giuseppe Primiero FWO, Ghent University Blandijnberg 2 Ghent Belgium IEG Oxford University Oxford UK giuseppe.primiero@ugent.be ISBN e-isbn DOI / Springer Dordrecht Heidelberg London New York Library of Congress Control Number: c 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 Springer is part of Springer Science+Business Media (

5 To the memory of Paul Gochet

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7 Preface In the preface to the first volume of LEUS, the editors of the series pointed out, within the context of the failure of the positivist project of the unity of science, the difference between science as a body of knowledge and science as process by which knowledge is achieved. In fact, the editors suggested that a ban on the logical analysis of science as a dynamic process, which in traditional philosophy was overtaken by gnoseology, produced a gap between sciences and logic (including philosophy of science). In gnoseology the main notion was the one of judgement rather than that of proposition. Judgement delivered the epistemic aspect of logic, namely the relation between an (epistemic) agent and a proposition. This represented the basis of the Kantian approach to logic, which seemed to be in conflict with the post- Fregean approach where only relations between propositions are at stake and where the epistemic aspect is seen as outside logic. As it happens quite often in philosophy, the echoes of the old traditions come back and point to the mistakes of the younger iconoclast movements. This is indeed the case in the relation between logic and knowledge where the inclusion or exclusion of the epistemic moment as linked with the concept of proposition provoked a heated debate since the 1960s. The epistemic approaches, which started to call themselves, following Michael Dummett, antirealism, found their formal argument in the mathematics of Brouwer and intuitionistic logic, while the others persisted with the formal background of the Frege-Tarski tradition, where Cantorian set theory is linked via model theory to classical logic. This picture is, however, incomplete. Already in the 1960s Jaakko Hintikka tried to join both traditions by means of what is now known as explicit epistemic logic, where the epistemic content is introduced into the object language as an operator which yield propositions from propositions rather than as metalogical constraint on the notion of inference. The debate had thus three players: classical logicians, intuitionistic logicians (implicit epistemic logic) and epistemic logicians (explicit epistemic logic), though the mainstream continued to think that the discussion reduces to the discussion between classical and intuitionistic logic. The editors of the present volume think that in these days and age of Alternative Logics, where manifold developments in logic happen in a breathtaking pace, this debate should be revisited. In fact, collaborators to this volume took happily this challenge and responded with new perspectives on the debate from both vii

8 viii Preface the explicit and the implicit point of view, challenging it from the newly arisen perspectives in logic. This volume aims therefore at presenting standard issues of the realism-antirealism debate in a new light, shed from the point of view of different philosophical perspectives. It is therefore appropriate that we open with Patrick Allo s contribution, which analyses the meaning of ambiguous connectives (and in particular of disjunction) from a logical pluralistic viewpoint, in which content is explained in terms of informativeness. Logical pluralism can be understood as the larger conceptual umbrella under which one finds today many different understandings of the realism-antirealism debate. This certainly still grows on Dummett s arguments against truth-conditional semantics, which Neil Kennedy reconstructs and critically analyses; in general, it refers to well known forms of semantic antirealism, which Sanford Shieh characterizes by means of the distinction between epistemically-based and conceptually based ones, and it still triggers today huge debates such as the one on Moorean validities, that Jon Cogburn reconstructs in view of the different old and new interpretations. But antirealism today profits of the influences of many different backgrounds: this is the case for example of Martin-Löf s type theory, which is conceptually and historically located within the larger frame of theories of truth and judgement in Göran Sundholm s contribution, and which meets for the first time belief revision dynamics in Giuseppe Primiero s paper. Departure from classical principles of reasoning is therefore possible in different forms, and whereas Denis Bonnay and Mikaël Cozic place the justification of radical forms of anti-realism in the context of the (to them still unjustified) shift to linear logic, Joseph Vidal-Rosset suggests a larger philosophical frame for the understanding of radical antirealism. Many are therefore the new branches of logic that are called upon in this volume to face non-classical issues raising from an antirealistic perspective: this is the case of modal logic in the interpretations by Reinhard Kahle and Elia Zardini; the anti-realistic inspired defence of realist mathematics by Greg Restall, where (implicit) antirealism is understood as a means to defend logical pluralism: the extension to Paraconsistency, via a defence of a suitable negation connective in the Kripke-Hintikka reconstruction of intuitionistic logic, suggested by Graham Priest, which virtually dialogues with the dialogical interpretation of the same connective given by Shahid Rahman. The relation of antirealism to dialogical logic and game semantics appears also in Mathieu Marion s contribution, where it is considered how to make Dummett s Manifestation Argument work within this new programme, and it is argued that a derived Thesis fits (with appropriate reformulations) within game semantics. Stephen Read, takes the proof theoretical approach to logic of the antirealists to challenge the epistemic constraints of the intuitionists and Francesca Poggiolesi analyses properties of anti-realistic definitions starting from the classical requirements imposed by Lesniewski. Truth is of course always an open field for new interpretations: Alexandre Billon considers the notion of assessment-sensitive truth to provide solutions to semantic paradoxes and Maria Frapolli presents a prosentential account of truth showing that our comprehension of truth and the use we make of truth expressions are strictly independent of our views about the relation between mind and world.

9 Preface ix Some years have passed from the initial proposal to collect a number of contributions from scholars that are reconsidering the realism-antirealism debate from new philosophical, logical and metaphysical perspectives. This has led to different lineups of both authors and editors. What we hope to have achieved through this process is to have selected significant contributions on the different aspects of research on anti-realism done today at academic level, a representative body of work that can be of reference and inspiration for further advancements in this field. Montreal, Canada Ghent, Belgium Lille, France December 2010 Mathieu Marion Giuseppe Primiero Shahid Rahman

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11 Acknowledgements This volume originates from the Workshop (Anti-)Réalismes. Logique et Métaphysique, which took place in Nancy (France), from June 28 to July 2, For that reason, we would like first to express our gratitude to the organizing committee formed by the Laboratoire d Histoire des Sciences et de Philosophie Archives Henri Poincaré, UMR 7117 CNRS, Nancy-Université and the laboratory UMR 8163: Savoirs, Textes, Langage, Université de Lille 3, with special thanks to Gerhard Heinzmann (Nancy 2), Laurent Rollet, Manuel Rebuschi (Nancy 2), Christian Berner (Lille3). The editors would also like to thank Laurent Keiff (UMR:STL), who started this project and later handed it to us. We also would like to mention here the work of the various readers and referees that helped us selecting and improving the contributions to this volume; their silent help is very much appreciated. xi

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13 Contents 1 On When a Disjunction Is Informative... 1 Patrick Allo 2 My Own Truth Alexandre Billon 3 Which Logic for the Radical Anti-realist? Denis Bonnay and Mikaël Cozic 4 Moore s Paradox as an Argument Against Anti-realism Jon Cogburn 5 The Neutrality of Truth in the Debate Realism vs. Anti-realism María J. Frápolli 6 Modalities Without Worlds Reinhard Kahle 7 Antirealism, Meaning and Truth-Conditional Semantics Neil Kennedy 8 Game Semantics and the Manifestation Thesis Mathieu Marion 9 Conservativeness and Eliminability for Anti-Realistic Definitions Francesca Poggiolesi 10 Realism, Antirealism, and Paraconsistency Graham Priest xiii

14 xiv Contents 11 Type-Theoretical Dynamics Giuseppe Primiero 12 Negation in the Logic of First Degree Entailment and Tonk Shahid Rahman 13 Necessary Truth and Proof Stephen Read 14 Anti-realist Classical Logic and Realist Mathematics Greg Restall 15 A Tale of Two Anti-realisms Sanford Shieh 16 A Double Diamond of Judgement Göran Sundholm 17 Stable Philosophical Systems and Radical Anti-realism Joseph Vidal-Rosset 18 Two Diamonds Are More Than One Elia Zardini Index

15 Contributors Patrick Allo Postdoctoral Fellow, Fund for Scientific Research Flanders (Belgium), Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel, Brussels, Belgium; IEG, Oxford University, Oxford, UK, Alexandre Billon Université Lille Nord de France, F Lille, France; UdL3, STL, CNRS, UMR 8163, F Villeneuve d Ascq, France, alexandre.billon@m4x.org Denis Bonnay Université Paris Ouest-Nanterre, Ireph & IHPST, Paris, France, denis.bonnay@ens.fr Jon Cogburn Louisiana State University Baton Rouge, Baton Rouge, LA, USA, joncogburn@yahoo.com Mikaël Cozic Université Val de Marne & IHPST, Paris, France, Mikael.Cozic@ens.fr María J. Frápolli Departamento de Filosofía I, Universidad de Granada, Granada, Spain, frapolli@ugr.es Reinhard Kahle CENTRIA and DM, FCT, Universidade Nova de Lisboa, P Caparica, Portugal, kahle@mat.uc.pt Neil Kennedy Université du Québec à Montréal, Montréal, QC, Canada; Université de Paris 1 IHPST, Paris, France, neil.patrick.kennedy@gmail.com Mathieu Marion Canada Research Chair in the Philosophy of Logic and Mathematics, Université du Québec à Montréal, Montréal, QC, Canada, marion.mathieu@uqam.ca Francesca Poggiolesi CLWF, Vrije Universiteit Brussel, Brussels, Belgium, poggiolesi@gmail.com Graham Priest Departments of Philosophy, University of Melbourne, Melbourne, VIC, Australia; University of St Andrews, St Andrews, UK; The Graduate Center, City University of New York, New York, NY, USA, g.priest@unimelb.edu.au xv

16 xvi Contributors Giuseppe Primiero FWO, Ghent University, Blandijnberg 2, Ghent, Belgium; IEG, Oxford University, Oxford, UK, Shahid Rahman Université de Lille, UdL3, CNRS, UMR 8163: STL, F Villeneuve d Ascq, France, shahid.rahman@univ-lille3.fr Stephen Read University of St Andrews, St Andrews, Scotland, UK, slr@st-andrews.ac.uk Greg Restall School of Historical and Philosophical Studies, Melbourne, VIC, Australia, greg@consequently.org Sanford Shieh Department of Philosophy, Wesleyan University, Middletown, CT 06459, USA, sanford.shieh@wesleyan.edu Göran Sundholm Institute for Philosophy, Leiden University, Leiden, The Netherlands, goran.sundholm@gmail.com Joseph Vidal-Rosset Archives Poincaré, UMR 7117, Nancy, France, joseph.vidal-rosset@univ-nancy2.fr Elia Zardini Department of Philosophy, Northern Institute of Philosophy, University of Aberdeen, Aberdeen, UK, elia.zardini@abdn.ac.uk