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"This book is about philosophy, mathematics and logic, giving a philosophical account of Pluralism which is a family of positions in the philosophy of mathematics. There are four parts to this book, beginning with a look at motivations for Pluralism by way of Realism, Maddy's Naturalism, Shapiro's Structuralism and Formalism. In the second part of this book the author covers: the philosophical presentation of Pluralism; using a formal theory of logic metaphorically; rigour and proof for the Pluralist; and mathematical fixtures. In the third part the author goes on to focus on the transcendental presentation of Pluralism, and in part four looks at applications of Pluralism, such as a Pluralist approach to proof in mathematics and how Pluralism works in regard to together-inconsistent philosophies of mathematics. The book finishes with suggestions for further Pluralist enquiry. In this work the author takes a deeply radical approach in developing a new position that will either convert readers, or act as a strong warning to treat the word "pluralism" with care."--Page 4 de la couverture.
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Logic, Epistemology, and the Unity of Science 32 Michèle Friend Pluralism in Mathematics: A New Position in Philosophy of Mathematics Pluralism in Mathematics: A New Position in Philosophy of Mathematics LOGIC, EPISTEMOLOGY, AND THE UNITY OF SCIENCE VOLUME 32 Editors Shahid Rahman, University of Lille III, France John Symons, University of Texas at El Paso, USA 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, Coll`ege de France, France G¨oran Sundholm, Universiteit Leiden, The Netherlands 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. For further volumes: http://www.springer.com/series/6936 Mich`ele Friend Pluralism in Mathematics: A New Position in Philosophy of Mathematics 123 Mich`ele Friend The George Washington University Washington, DC, USA ISBN 978-94-007-7057-7 ISBN 978-94-007-7058-4 (eBook) DOI 10.1007/978-94-007-7058-4 Springer Dordrecht Heidelberg New York London Library of Congress Control Number: 2013953900 © Springer Science+Business Media Dordrecht 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, speci