Logics of Worlds (Being and Event, 2)

636 Pages·2008·1.97 MB·English

by  Alain Badiou

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LOGICS OF WORLDS
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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
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LOGICS OF WORLDS
BEING AND EVENT, 2
Alain Badiou
Translated by Alberto Toscano
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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
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To Françoise Badiou
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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
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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
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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
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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
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