Badiou's Being and Event and the Mathematics of Set Theory

289 Pages·2015·1.114 MB·English

by  Burhanuddin Baki

Badiou’s Being and Event and
the Mathematics of Set Theory
Also available from Bloomsbury
Alain Badiou: Live Theory, Oliver Feltham
Badiou’s Being and Event, Christopher Norris
Being and Event, Alain Badiou (translated by Oliver Feltham)
Conditions, Alain Badiou (translated by Steven Corcoran)
Infinite Thought, Alain Badiou
Intensive Science and Virtual Philosophy, Manuel DeLanda
Logics of Worlds: Being and Event II, Alain Badiou
(translated by Alberto Toscano)
Mathematics of the Transcendental, Alain Badiou
(translated by A. J. Bartlett and Alex Ling)
Theoretical Writings, Alain Badiou
(translated and edited by Ray Brassier and Alberto Toscano)
Theory of the Subject, Alain Badiou (translated by Bruno Bosteels)
Think Again: Alain Badiou and the Future of Philosophy,
edited by Peter Hallward
Badiou’s Being and Event and
the Mathematics of Set Theory
By
Burhanuddin Baki
Bloomsbury Academic
An imprint of Bloomsbury Publishing Plc
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First published 2015
© Burhanuddin Baki, 2015
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
ISBN: HB: 978-1-4725-2445-4
ePDF: 978-1-4725-7872-3
ePub: 978-1-4725-7871-6
Library of Congress Cataloging-in-Publication Data
Baki, Burhanuddin, author.
Badiou’s Being and event and the mathematics of set theory/Burhanuddin Baki.
pages cm
Summary: “Alain Badiou’s Being and Event continues to impact philosophical investigations into the
question of Being. By exploring the central role set theory plays in this influential work, Burhanuddin
Baki presents the first extended study of Badiou’s use of mathematics in Being and Event. Adopting a
clear, straightforward approach, Baki gathers together and explains the technical details of the relevant
high-level mathematics in Being and Event. He examines Badiou’s philosophical framework in close
detail, showing exactly how it is ‘conditioned’ by the technical mathematics. Clarifying the relevant
details of Badiou’s mathematics, Baki looks at the four core topics Badiou employs from set
theory: the formal axiomatic system of ZFC; cardinal and ordinal numbers; Kurt G
ISBN 978-1-4725-2445-4 (hardback) – ISBN 978-1-4725-7871-6 (epub) – ISBN 978-1-4725-7872-3 (epdf)
1. Badiou, Alain. L’Être et l’Événement. 2. Set Theory. 3. Ontology. 4. Events (Philosophy) I. Title.
B2430.B273E8733 2014
111–dc23
2014021234
Typeset by Deanta Global Publishing Services, Chennai, India
Contents
List of Figures and Tables vi
Acknowledgements vii
Note on Abbreviations, Citations and Translations viii
Introduction 1
1 Mathematics = Ontology 11
2 Ontology of Axiomatic Set Theory 35
3 Metaontology of Situations and Presentation 65
4 Metaontology of the State and Representation 105
5 Ontology and Metaontology of the Cardinal and Ordinal Numbers 125
6 Ontology and Metaontology of the Constructible 151
7 Ontology of Forcing and Generic Sets 169
8 Metaontology of the Subject, Truth, the Event and Intervention 195
Epilogue 243
Notes 251
References 257
Index 261
List of Figures and Tables
Figure 3.1 From Being to beings via the count-as-one 89
Figure 4.1 The triad of domain-representation-veridicy 113
Figure 8.1 The ground model M (before forcing) 209
Figure 8.2 The generic extension N (after forcing) 210
Figure 8.3 The Cantor decision tree 220
Figure 8.4 From Being to beings via the count-as-one; from the event
to truth via subjectivation 242
Table 8.1 Example of the first four generic enquiries 219
Acknowledgements
This book could not have been written without the guidance, generosity and
friendship of my mentors Christopher Norris and Steven Connor. My thanks
also to Christopher Fynsk for being a great teacher during my early years as
a philosopher. I would like to thank my father, Baki Bakar; my mother, Maria
Jomel; my brother, Aminuddin; and my sisters, Nursyuhada and Nur’Ata’ain,
for their support. I would also like to express my gratitude to Professor Tan Sri
Dato’ Dzulkifli Abdul Razak, and also to the people at the Tunku Abdul Rahman
Sarawak Foundation for their help and guidance in securing the funding for
my research, particularly Tan Sri Datuk Amar Adenan Satem. Thanks also to
Fabio Gironi, Oliver Kullman, Zachary Luke Fraser, Tzuchien Tho, Anindya
Bhattacharya, Justin Clemens, Will Potter, John Dance, Alberto Toscano and
Olivier Feltham for their comments and discussions. My gratitude also goes to
Peter Hallward, Peter Gan Chong Beng, Lok Chong Hoe, Nazalan Najimudin,
Mashhor Mansor and Dato’ Rosihan Ali. Finally, I am most grateful to Anita
Singh at Deanta Global, as well as Emma Brady, Andrew Wardell, David Barker
and Colleen Coalter at Bloomsbury Publishing for their wonderful guidance
and assistance.
I dedicate this work to my maternal grandmother Hajjah Chik bt. Jol who
passed away during the period of my writing this book.
Note on Abbreviations, Citations
and Translations
I rely mostly on Oliver Feltham’s text Being and Event for the English translation
of my citations from Alain Badiou’s L’Être et L’Événement. Abbreviations for
three frequently cited texts by Badiou, where also I rely on the current English
translations, are as follows:
BE Being and Event (trans. Oliver Feltham, 2005)
MP Manifesto for Philosophy (trans. Norman Madarasz, 1999)
TW Theoretical Writings (trans. Ray Brassier and Alberto Toscano, 2004)
Introduction
Anyone sufficiently informed about the current scene in contemporary philo-
sophical thought will no doubt bear witness to the explosive surge of global
interest in the work of Alain Badiou. We need not go further than observing the
enormous popularity of his written works; the extremely active publishing industry
dedicated to translating his texts; the hundreds of listeners attending his public
lectures or viewing online recordings of them; and the exponential growth in the
amount of books, journal articles, conferences, courses, editorials, manifestos,
art works, blog posts, podcasts and tweets devoted to explaining, appropriating,
praising, criticizing and critiquing his philosophy. Many introductions to this
philosophy often begin by repeating the proposal that Alain Badiou is, since the
death of Jacques Derrida in 2004, probably the most important living French
philosopher and, along with Slavoj Žižek and Jürgen Habermas, possibly the
most important living European philosopher. All of this provides adequate
proof that anyone attempting to engage with the contemporaneity of intellectual
thought must find some way to reckon, either positively or negatively, though
never indifferently, with the imposing forcefulness of Alain Badiou’s oeuvre.
Anyone who knows enough about the reception of this oeuvre will no doubt
be aware of the well-accepted proposition among scholars that Being and Event
[L’Être et L’Événement], Alain Badiou’s major treatise published in 1988, is his
masterpiece. Peter Hallward even went as far as to proclaim it as ‘the most
ambitious and most compelling single philosophical work written in France
since Sartre’s Critique de la raison dialectique’ (2003, xxi). And anyone who
knows about Being and Event will no doubt be informed about its innovative,
even revolutionary, deployment of mathematical thinking to reconfigure the
entire landscape of our present investigations into the most central philosophical
issues, from various discipline-specific questions in science, art, history, politics,
economics, sociology, psychoanalysis and theology to problems concerning the
philosophy of language, truth, subjectivity, knowledge, ethics and, above all,
ontology. Being and Event seizes results from modern mathematics, specifically
from the field of nineteenth- to twentieth-century set theory, to construct an