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Alain Badiou - SOK PDF

636 Pages·2009·1.97 MB·English
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Page 1 LOGICS OF WORLDS 10:57:11:03:09 Page 1 Page 2 Also available from Continuum: Being and Event, Alain Badiou Conditions, Alain Badiou Infinite Thought, Alain Badiou Theory of the Subject, Alain Badiou After Finitude, Quentin Meillassoux The Politics of Aesthetics, Jacques Rancière Art and Fear, Paul Virilio Negative Horizon, Paul Virilio Desert Screen, Paul Virilio 10:57:11:03:09 Page 2 Page 3 LOGICS OF WORLDS BEING AND EVENT, 2 Alain Badiou Translated by Alberto Toscano 10:57:11:03:09 Page 3 Page 4 This work is published with the support of the French Ministry of Culture – Centre National du Livre. Continuum 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 Logiques des mondes © Editions du Seuil, 2006 This English language translation © Continuum 2009 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. ISBN-10:HB:0–8264–9470–6 ISBN-13:HB:978–0–8264–9470–2 Library of Congress Cataloging-in-Publication Data Badiou, Alain. [Logiques des mondes. English] Logics of worlds / Alain Badiou ; translated by Alberto Toscano. p. cm. Includes bibliographic references (p. ) and index. ISBN 978–0–8264–9470–2 1. Ontology. 2. Subjectivity. 3. Truth. I. Title. B2430.B273L6413 2009 194—dc22 2008036972 Typeset by RefineCatch Limited, Bungay, Suffolk Printed and bound in Great Britain by MPG Books Ltd, Bodmin, Cornwall 10:57:11:03:09 Page 4 Page 5 To Françoise Badiou 10:57:11:03:09 Page 5 Page 6 10:57:11:03:09 Page 6 Page 7 Contents Translator’s Note xv Preface 1 1 Democratic materialism and materialist dialectic 1 2 For a didactics of eternal truths 9 3 Mathematical example: numbers 10 4 Artistic example: horses 16 5 Political example: the state revolutionary (equality and terror) 20 6 Amorous example: from Virgil to Berlioz 28 7 Distinctive features of truths, persuasive features of freedom 33 8 Body, appearing, Greater Logic 35 Technical Note 41 Book I Formal Theory of the Subject (Meta-physics) 43 1 Introduction 45 2 Referents and operations of the faithful subject 50 3 Deduction of the reactive subject: reactionary novelties 54 4 The obscure subject: full body and occultation of the present 58 vii 16:04:11:03:09 Page 7 Page 8 LOGICS OF WORLDS 5 The four subjective destinations 62 6 The final question 67 7 Truth-procedures and figures of the subject 69 8 Typology 72 Scholium: A Musical Variant of the Metaphysics of the Subject 79 Foreword to Books II, III and IV: The Greater Logic 91 Book II Greater Logic, 1. The Transcendental 97 Introduction 99 1 Necessity of a transcendental organization of the situations of being 101 2 Exposition of the transcendental 102 3 The origin of negation 104 Section 1 The Concept of Transcendental 109 1 Inexistence of the Whole 109 2 Derivation of the thinking of a multiple on the basis of that of another multiple 111 3 A being is thinkable only insofar as it belongs to a world 113 4 Appearing and the transcendental 118 5 It must be possible to think, in a world, what does not appear within that world 122 6 The conjunction of two apparents in a world 125 7 Regional stability of worlds: the envelope 128 8 The conjunction between a being-there and a region of its world 131 9 Dependence: the measure of the link between two beings in a world 133 10 The reverse of an apparent in the world 135 11 There exists a maximal degree of appearance in a world 138 12 What is the reverse of a maximal degree of appearance? 139 viii 10:57:11:03:09 Page 8 Page 9 CONTENTS Section 2 Hegel 141 1 Hegel and the question of the Whole 141 2 Being-there and logic of the world 144 3 Hegel cannot allow a minimal determination 147 4 The appearing of negation 149 Section 3 Algebra of the Transcendental 153 1 Inexistence of the Whole: to affirm the existence of a set of all sets is intrinsically contradictory 153 2 Function of appearing and formal definition of the transcendental 155 3 Equivalence-structure and order-structure 157 4 First transcendental operation: the minimum or zero 159 5 Second transcendental operation: conjunction 160 6 Third transcendental operation: the envelope 163 7 Conjunction of a being-there and an envelope: distributivity of ∩ with regard to Σ 165 8 Transcendental algebra 166 9 Definitions and properties of the reverse of a transcendental degree 167 10 In every transcendental, the reverse of the minimum µ is a maximal degree of appearance (M) for the world whose logic is governed by that transcendental 169 11 Definition and properties of the dependence of one transcendental on another 171 Section 4 Greater Logic and Ordinary Logic 173 1 Semantics: truth-values 175 2 Syntax: conjunction (‘and’), implication (‘if ... then’), negation, alternative (‘or’) 176 3 The existential quantifier 178 4 The universal quantifier 180 ix 10:57:11:03:09 Page 9 Page 10 LOGICS OF WORLDS Section 5 Classical Worlds 183 1 What is a classical world? 183 2 Transcendental properties of the world of ontology 185 3 Formal properties of classical worlds 187 Appendix: Demonstration of the Equivalence of the Three Characteristic Properties of a Classical World 189 Book III Greater Logic, 2. The Object 191 Introduction 193 Section 1 For a New Thinking of the Object 199 1 Transcendental indexing: the phenomenon 199 2 The phenomenon: second approach 204 3 Existence 207 4 Analytic of phenomena: component and atom of appearing 211 5 Real atoms 217 6 Definition of an object 220 7 Atomic logic, 1: the localization of the One 221 8 Atomic logic, 2: compatibility and order 225 9 Atomic logic, 3: real synthesis 229 Section 2 Kant 231 Section 3 Atomic Logic 243 1 Function of appearing 243 2 The phenomenon 245 3 Existence 246 4 Phenomenal component and atom of appearing 247 5 Real atom and postulate of materialism 250 6 Definition of the object 251 7 Atomic logic, 1: localizations 252 8 Atomic logic, 2: compatibility 255 9 Atomic logic, 3: order 257 x 10:57:11:03:09 Page 10

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Being and Event, Alain Badiou. Conditions, Alain Badiou. Infinite Thought, Alain Badiou. Theory of the Subject, Alain Badiou. After Finitude, Quentin Meillassoux.
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