The Concept of Model: An Introduction to the Materialist Epistemology of Mathematics (Transmission)

183 Pages·2007·1.59 MB·English

by  Alain Badiou

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The Concept of Model
TRANSMISSION
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Transmission republishes
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that re-examine classical
philosophical thought.
Transmission is the name
for what takes place.
The Concept of Model
An Introduction to the
Materialist Epistemology of Mathematics
Alain Badiou
Edited and translated by
Zachary Luke Fraser and Tzuchien Tho
re.press
PO Box 75, Seddon, 3011, Melbourne, Australia
http://www.re-press.org
© re.press 2007
This work is ‘Open Access’, published under a creative commons license which means that
you are free to copy, distribute, display, and perform the work as long as you clearly attribute
the work to the authors, that you do not use this work for any commercial gain in any form
and that you in no way alter, transform or build on the work outside of its use in normal aca-
demic scholarship without express permission of the author and the publisher of this volume.
Furthermore, for any reuse or distribution, you must make clear to others the license terms of
this work. For more information see the details of the creative commons licence at this web-
site: http://creativecommons.org/licenses/by-nc-nd/2.5/
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Cataloguing-in-Publication Data
A catalogue record for this book is available from the Library of Congress
National Library of Australia Cataloguing-in-Publication Data
Badiou, Alain.
[Le Concept de modèle. English.]
The concept of model : an introduction to the materialist
epistemology of mathematics.
Bibliography.
ISBN 9780980305234 (pbk.).
1. Model theory. 2. Mathematics - Philosophy. I. Title.
(Series : Transmission).
510
Designed and Typeset by A&R
Printed on-demand in Australia, the United Kingdom and the United States
This book is produced sustainably using plantation timber, and printed in the destination
market on demand reducing wastage and excess transport.
Contents
Acknowledgements vii
INtroDuCtIoN
The Category of Formalization:
From Epistemological Break to Truth Procedure xiii
by Zachary Luke Fraser
I. Ideology and Epistemological Break xiv
II. Formalization: Subtraction and Forcing xxv
III. On Objectless Materialisms xxxiv
IV. Structural Materialism xxxvi
V. Ontological Materialism xxxix
VI. ‘The Chief Defect of All Hitherto Existing Materialism’ xliv
VII. From Machinic Psychosis to Subjective Fidelity:
‘Marque et manque’, and L’être et l’événement xlvi
VIII. The Structure of Philosophical Intervention,
and its Use of Formal Inscription lvii
IX. Note on the Translation lxi
the CoNCePt of MoDeL
translated by Zachary Luke Fraser
Foreword 3
1. A Few Preliminaries Concerning Ideology 5
2. On the Theses to be Defended in the Sequel 9
3. On Certain Uses of Models that are Not in Question Here 10
4. On a Purely Ideological Use of the Word ‘Model’ 14
5. The Scientific Concept of Model and the Neo-positivist
Doctrine of Science 18
6. Construction of the Concept of Model:
I. Syntactic preliminaries 23
7. Construction of the Concept of Model:
II. Fundamental aspects of semantics 29
8. Construction of the Concept of Model:
III. Some games with the example 35
9. The Category of Model and Mathematical Experimentation 42
10. The Category of Model and the Historical Time of
Mathematical Production 48
Appendix 56
§1: The goal 56
§ 2: Description of the apparatus PS 56
§ 3: Every theorem of PS is purely logical 57
§ 4: Deduction theorem 58
§ 5: The relative consistency of certain extensions of PS 61
§ 6: The scope of the completeness theorem 61
§ 7: The Lindenbaum lemma 62
§ 8: The completeness theorem 64
[Supplement] 72
Syntax 72
Semantics 74
AN INtervIew wIth ALAIN BADIou
The Concept of Model, Forty Years Later:
An Interview with Alain Badiou 79
conducted & translated by Tzuchien Tho
Bibliography 107
About the Authors 113
Acknowledgements
First of all, I thank Shan Mackenzie-Fraser, my wife and friend; it’s far
too little to say that your encouragement, patience and love made this
project possible, but it’s a start. Thanks, too, to my brilliant children,
Ruis, Kai, Hinahni and Sophie; someday, I’ll tell you all about the diffi-
cult marriage of formal semantics and the class struggle that kept your fa-
ther busy back in the summer of 2007. My gratitude also goes to my par-
ents, Zach and Marion Fraser, whose enduring support and confidence,
babysitting shifts and ribbings, helped me get this book to press. I also
wish to thank my comrade and collaborator, Tzuchien Tho, who, above
and beyond the achievements explicitly registered in this book, spent
countless hours running around Hell’s creation to track down obscure
documents, transcribe and translate long-forgotten videotapes, and wait
repeatedly for appointments with Beckettian personages in Kafkaesque
environs. I am grateful, as well, to the numerous men and women who
assisted in reading torturously awkward drafts of this translation: Rohit
Dalvi, who, some years back, suggested that I write a master’s thesis on
Badiou’s thought, and who, when that project tangentially spawned a
rough translation of the Le Concept de modèle (which at the time was
little more than an exercise and a hobbyhorse), surprised me by saying
that it wouldn’t be inconceivable to publish the thing; Gillman Payette
and Stephanie Dick, who made up two thirds of a short lived philosophy
of mathematics reading group that dedicated more than half its meetings
to The Concept of Model; and Gordon McOuat, who offered consistently
helpful feedback on early drafts of this translation, despite his distaste for
all things Althusserian. I would also like to thank the aforementioned
circle of translators and scholars that helped bring this text to fruition,
particularly: Ray Brassier, Oliver Feltham, Robin Mackay, and Alberto
Toscano. Thanks also to Adam Bartlett, Paul Ashton and Justin Clemens
at re.press, whose camaraderie and commitment have made this entire
project a pleasure to be a part of, and whose fidelity to ideals higher than
vii
the marketplace has made it an honour. Finally, thanks to Alain Badiou,
both for giving my questions and critiques the dignity worthy of prob-
lems demanding solutions, and, of course, for writing.
Zachary Luke Fraser
Conditions for the possibility of philosophical work are always split be-
tween the alimentation of daily life and the clinamatic impact of friend-
ship. Both are aleatory by nature and their ranking cannot but be arbi-
trary. Zachary Luke Fraser extended a hand to me in camaraderie and
partnership; what he sometimes received was a fist full of criticism and
immature scribbling. I owe him gratitude and apology in equal amounts.
Amy Anderson’s evolving praxis of our shared fidelity to the amorous
truth condition has pushed me to continuously re-examine the indiscern-
ible in being. The last year would not have been possible without her and
Mr. Marx’s continuous encouragement. I thank Mr. Tu Chiang-shiang
for a love of books and Mr. Tu Nai-ping for teaching me the undesirabil-
ity of a merely nutritive life. Madame Liu Yue-chiao has always been a
stronghold and never asks anything in return. My parents, Tho Kee-ping
and Tu Hsiu-chen, taught me how to ‘zuo-ren’, roughly translated as ‘be
human’, a gift that can neither be repaid nor returned. David and Karen
Anderson have shown me a degree of grace that I have not experienced
before. I thank Bruno Besana, Oliver Feltham, François Farellacci, Colin
Mcquillan, Nate Holdren, Brian Howell for camaraderie and friendship,
and O. Bradley Bassler for late night clarifications on incompleteness.
Alain Badiou can be blamed for the number of youths corrupted by his
philosophical practice. Forty years after Le Concept de modèle, I consider
myself lucky to have been perverted.
Tzuchien Tho
viii