The Age of Alternative Logics Assessing Philosophy of Logic and Math
In the last century developments in mathematics, philosophy, physics, computer science, economics and linguistics have proven important for the development of logic. There has been an influx of new ideas, concerns, and logical systems reflecting a great v
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LOGIC, EPISTEMOLOGY, AND THE UNITY OF SCIENCE VOLUME 3
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 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.
The Age of Alternative Logics Assessing Philosophy of Logic and Mathematics Today Edited by
Johan van Benthem ILLC, University of Amsterdam, The Netherlands
Gerhard Heinzmann Archives Henri Poincaré, Nancy University, France
Manuel Rebuschi Archives Henri Poincaré, Nancy University, France
and Henk Visser ILLC, University of Amsterdam, The Netherlands
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN-10 1-4020-5011-9 (HB) ISBN-13 978-1-4020-5011-4 (HB) ISBN-10 1-4020-5012-7 (e-book) ISBN-13 978-1-4020-5012-7 (e-book)
Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands. www.springer.com
Printed on acid-free paper
All Rights Reserved © 2006 Springer 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.
CONTENTS
Acknowledgments
ix
1 Introduction: Alternative Logics and Classical Concerns Johan van Benthem
1
Part I Proof, Knowledge and Computation 2 Epistemic Mo
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