The Argument of Mathematics

Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those a

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Andrew Aberdein Ian J. Dove Editors

The Argument of Mathematics

The Argument of Mathematics

LOGIC, EPISTEMOLOGY, AND THE UNITY OF SCIENCE VOLUME 30

Editors Shahid Rahman, University of Lille III, France John Symons, University of Kansas, U.S.A. Managing Editor Ali Abasnezhad, University of Lille III, France

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, Ruhr-University Bochum, 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: http://www.springer.com/series/6936

Andrew Aberdein • Ian J. Dove Editors

The Argument of Mathematics

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Editors Andrew Aberdein Department of Humanities and Communication Florida Institute of Technology Melbourne, FL, USA

Ian J. Dove Department of Philosophy University of Nevada, Las Vegas Las Vegas, NV, USA

ISBN 978-94-007-6533-7 ISBN 978-94-007-6534-4 (eBook) DOI 10.1007/978-94-007-6534-4 Springer Dordrecht Heidelberg New York London Library of Congress Control Number: 2013941250 © Springer Science+Business Media Dordrecht 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection wi

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