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Albert Lautman (1908-1944) was a French philosopher of mathematics whose work played a crucial role in the history of contemporary French philosophy. His ideas have had an enormous influence on key contemporary thinkers including Gilles Deleuze and Alain Badiou, for whom he is a major touchstone in the development of their own engagements with mathematics. Mathematics, Ideas and the Physical Real presents the first English translation of Lautman's published works between 1933 and his death in 1944. Rather than being preoccupied with the relation of mathematics to logic or with the problems of foundation, which have dominated philosophical reflection on mathematics, Lautman undertakes to develop an understanding of the broader structure of mathematics and its evolution. The two powerful ideas that are constants throughout his work, and which have dominated subsequent developments in mathematics, are the concept of mathematical structure and the idea of the essential unity underlying the apparent multiplicity of mathematical disciplines. This collection of his major writings offers readers a much-needed insight into his influence on the development of mathematics and philosophy.
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MATHEMATICS, IDEAS AND THE PHYSICAL REAL
Also available from Continuum: Being and Event, Alain Badiou Conditions, Alain Badiou Infinite Thought, Alain Badiou Logics of Worlds, Alain Badiou Theoretical Writings, Alain Badiou Theory of the Subject, Alain Badiou Cinema I, Gilles Deleuze Cinema II, Gilles Deleuze Dialogues II, Gilles Deleuze Difference and Repetition, Gilles Deleuze The Fold, Gilles Deleuze Foucault, Gilles Deleuze The Fold, Gilles Deleuze Future Christ, François Laruelle Francis Bacon, Gilles Deleuze Kant’s Critical Philosophy, Gilles Deleuze Nietzsche and Philosophy, Gilles Deleuze Of Habit, Félix Ravaisson Proust and Signs, Gilles Deleuze Logic of Sense, Gilles Deleuze Ant-Oedipus, Gilles Deleuze and Félix Guattari A Thousand Plateaues, Gilles Deleuze and Félix Guattari Seeing the Invisible, Michel Henry Future Christ, François Laruelle Essay on Transcendental Philosophy, Salomon Maimon After Finitude, Quentin Meillassoux Time for Revolution, Antonio Negri Philosophies of Difference, François Laruelle Politics of Aesthetics, Jacques Rancière The Five Senses, Michel Serres Art and Fear, Paul Virilio Negative Horizon, Paul Virilio
MATHEMATICS, IDEAS AND THE PHYSICAL REAL Albert Lautman
Translated by Simon B. Duffy
Continuum International Publishing Group The Tower Building 80 Maiden Lane 11 York Road Suite 704 London SE1 7NX New York NY 10038 www.continuumbooks.com Originally published in French as Les mathématiques, les idées et le réel physique © Librairie Philosophique J. VRIN, 2006 This English language edition © the Continuum International Publishing Group, 2011 All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage or retrieval system, without prior permission in writing from the publishers. British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. EISBN 978-1-4411-4433-1
Library of Congress Cataloging-in-Publication Data Lautman, Albert, 1908–1944. [Mathématiques, les idées et le réel physique. English] Mathematics, ideas, and the physical real / Albert Lautman; translated by Simon B. Duffy. p. cm. “Originally published in French as Les Mathématiques, les idées et le réel physique. Librairie Philosophique, J. VRIN, 2006”–T.p. verso. Includes bibliographical references and index. ISBN-13: 978-1-4411-4656-4 ISBN-10: 1-4411-4656-3 ISBN-13: 978-1-4411-2344-2 (pbk.) ISBN-10: 1-4411-2344-X (pbk.) 1. Mathematics–Philosophy. I. Duffy, Simon B. II. Title. QA8.4.L37613 2010 510.1–dc22 20