From a Geometrical Point of View A Study of the History and Philosop
From a Geometrical Point of View explores historical and philosophical aspects of category theory, trying therewith to expose its significance in the mathematical landscape. The main thesis is that Klein’s Erlangen program in geometry is in fact a particu
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LOGIC, EPISTEMOLOGY, AND THE UNITY OF SCIENCE VOLUME 14
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, Coll`ege 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.
For further volumes: http://www.springer.com/series/6936
From a Geometrical Point of View A Study of the History and Philosophy of Category Theory by
Jean-Pierre Marquis University of Montreal, QC, Canada
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Dr. Jean-Pierre Marquis University of Montreal Department of Philosophy C.P. 6218, succ. Centre-ville Montreal QC Canada H3C 3J7 [email protected]
Cover image: Adaptation of a Persian astrolabe (brass, 1712–13), from the collection of the Museum of the History of Science, Oxford. Reproduced by permission.
ISBN 978-1-4020-9383-8
e-ISBN 978-1-4020-9384-5
Library of Congress Control Number: 2008938359 c Springer Science+Business Media B.V. 2009 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
A` Marie, pour tout, tout simplement.
Acknowledgements
I thank Mike Barr, Marta Bunge, Andr´e Joyal, Jim Lambek, Michael Makkai, Gonzalo Reyes,
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