The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics
This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical. The first section covers the history of these ideas in philosophy. Chapter one, entitled ‘The co
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John L. Bell
The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics
THE WESTERN ONTARIO SERIES IN PHILOSOPHY OF SCIENCE A SERIES OF BOOKS IN PHILOSOPHY OF SCIENCE , METHODOLOGY , EPISTEMOLOGY , LOGIC , HISTORY OF SCIENCE , AND RELATED FIELDS
Managing Editors ROBERT DI SALLE
University of Western Ontario, Canada STATHIS PSILLIOS
University of Athens Assistant Editors DAVID DEVIDI
Philosophy of Mathematics, University of Waterloo WAYNE MYRVOLD
Foundations of Physics, University of Western Ontario Editorial Board JOHN L. BELL, University of Western Ontario YEMINA BEN-MENAHEM, Hebrew University of Jerusalem JEFFREY BUB, University of Maryland PETER CLARK, St. Andrews University JACK COPELAND, University of Canterbury, New Zealand JANET FOLINA, Macalester College MICHAEL FRIEDMAN, Stanford University CHRISTOPHER A. FUCHS, University of Massachusetts MICHAEL HALLETT, McGill University WILLIAM HARPER, University of Western Ontario CLIFFORD A. HOOKER, University of Newcastle, Australia JÜRGEN MITTELSTRASS, Universität Konstanz THOMAS UEBEL, University of Manchester VOLUME 82
More information about this series at http://www.springer.com/series/6686
John L. Bell
The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics
John L. Bell Department of Philosophy University of Western Ontario London, ON, Canada
ISSN 1566-659X ISSN 2215-1974 (electronic) The Western Ontario Series in Philosophy of Science ISBN 978-3-030-18706-4 ISBN 978-3-030-18707-1 (eBook) https://doi.org/10.1007/978-3-030-18707-1 © Springer Nature Switzerland AG 2019 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. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
This book has a double purpose: first, to trace the histor
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