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

by Alain Badiou, Zachary Luke Fraser (Translator), Tzuchien Tho (Translator)

The Concept of Model is the first of Alain Badiou's early books to be translated fully into English. With this publication English readers finally have access to a crucial work by one of the world's greatest living philosophers. Written on the eve of the events of May 1968, The Concept of Model provides a solid mathematical basis for a rationalist materialism. Badiou's concept of model distinguishes itself from both logical positivism and empiricism by introducing a new form of break into the hitherto implicated realms of science and ideology, and establishing a new way to understand their disjunctive relation. Readers coming to Badiou for the first time will be struck by the clarity and force of his presentation, and the key place that The Concept of Model enjoys in the overall development of Badiou's thought will enable readers already familiar with his work to discern the lineaments of his later radical developments. This translation is accompanied by a stunning new interview with Badiou in which he elaborates on the connections between his early and most recent thought. "This book is indispensable for those seeking to understand Alain Badiou's philosophical project, and for anyone interested in investigating real points of contact between the analytic and continental traditions." - Ray Brassier, Middlesex University

Genres: Philosophy, Mathematics

180 pages, Paperback

First published January 1, 1969

About the author

Alain Badiou, Ph.D., born in Rabat, Morocco in 1937, holds the Rene Descartes Chair at the European Graduate School EGS. Alain Badiou was a student at the École Normale Supérieure in the 1950s. He taught at the University of Paris VIII (Vincennes-Saint Denis) from 1969 until 1999, when he returned to ENS as the Chair of the philosophy department. He continues to teach a popular seminar at the Collège International de Philosophie, on topics ranging from the great 'antiphilosophers' (Saint-Paul, Nietzsche, Wittgenstein, Lacan) to the major conceptual innovations of the twentieth century. Much of Badiou's life has been shaped by his dedication to the consequences of the May 1968 revolt in Paris. Long a leading member of Union des jeunesses communistes de France (marxistes-léninistes), he remains with Sylvain Lazarus and Natacha Michel at the center of L'Organisation Politique, a post-party organization concerned with direct popular intervention in a wide range of issues (including immigration, labor, and housing). He is the author of several successful novels and plays as well as more than a dozen philosophical works.

Trained as a mathematician, Alain Badiou is one of the most original French philosophers today. Influenced by Plato, Georg Wilhelm Friedrich Hegel, Jacques Lacan and Gilles Deleuze, he is an outspoken critic of both the analytic as well as the postmodern schools of thoughts. His philosophy seeks to expose and make sense of the potential of radical innovation (revolution, invention, transfiguration) in every situation.

Reviews

[Matthew · Rating 4 out of 5]

Badiou's first book, from presentations written for (and partially delivered in) Althusser's Philosophy Course for Scientists. It is, among other things, a nice record of Badiou's early period, at his closest to Althusser ("I was still an Althusserian at the time," he says in the concluding interview, although Balibar and Macherey have both gone on record disputing the use of this term...), Bachelard, and Canguilhem. The book builds nicely off of Althusser's course ("Philosophy and the Spontaneous Philosophy of the Scientists"), as Badiou picks up on a gauntlet tossed by Althusser: Althusser says that the concept of "models" in science is ideological, and Badiou's deft philosophical intervention separates the various streams--ideological and scientific--caught up in the concept/notion of "model." Another wonderful element is Badiou's forceful critique of Levi-Strauss--another fine piece of evidence (as if more were really needed) that Althusser and his circle were never "structuralists" in the strict sense.

Overall, I will say that while I always really enjoy reading Badiou (but then, I also always thought that symbolic logic and set theory were fun...), I generally find it a vaguely stultifying experience. That is to say, I understand what is being said, but very rarely feel like a) I have anything to say in response; or that b) I can use Badiou's analysis of a subject/situation/etc. to "do" anything further. [I will readily admit that this is my problem, and not a problem with Badiou's writing per se.] This text, however, at least seemed to contribute to a larger project (other than the project of "Reading Badiou") for me, in the sense that I could at least see the benefit in drawing on this work (albeit among others!) in my own work on science and ideology.

Finally, though buried in the background, the context of this work is fascinating. Not only the fact that it was given during--and interrupted by--the events of May '68, but further, that it was Badiou's contribution to the course in which Balibar, Macherey, Fichant, and Pecheux were participants, and which was furthermore attended by (among about 300 others) Julia Kristeva and Philippe Sollers.

[Shulamith Farhi · Rating 5 out of 5]

All 3 parts of this volume reward careful reading.

(1) The introduction brings the uninitiated up to speed, presenting the text as the inauguration of a materialist epistemology, treating the seemingly ideal object of mathematical inscriptions. Badiou's 'scriptural materialism' is presented in admirably jargon-free prose - the intro is one of the best primers on this period of his work.

(2) The text itself is an interesting intervention (the term 'theoreticist' is appropriate - one has to care about theory for its own sake to grasp the stakes) into ideological uses of models and modelling. Badiou's distinction between ideological notions, philosophical categories and scientific concepts is useful, and his analysis of Levi-Strauss' structuralist bricolage (somewhat controversially translated as 'patchwork') and Carnap's logical positivist representation (with surprising resonances to the broader 'critique of representation') as bourgeois epistemology remain fruitful today.

(3) The interview following the text covers a lot of ground. Highlights include Badiou's reflections on models and Platonic participation in ideas (p92-3), his elaboration of the concept of formalization and his responses to the questions that point out potential inconsistencies in his work.

In general, this is a text I wish I had read earlier, and that I would warmly recommend to anyone wishing to understand the earliest, and perhaps most radical (theoretically speaking), phase of Badiou's work.

[William · Rating 5 out of 5]

Badiou presents a simple picture of mathematics, where it follows what might be called a scientific method, with models being the grist for experimenting on formal systems that those models instantiate. No doubt this picture is influenced by Bourbaki. This description of mathematical practice is then used to argue that positivist model-oriented philosophy of science more-or-less puts the cart before the horse by reversing the terms of the relationship. This is tied into a more general Marxist observation that model-first approaches might be inclined to prioritize representation over asking questions that would involve modelling interventions in the model system. He suggests a modelling approach that prioritizes interventions equal to representations would be better for scientific practice and would enable science to go beyond idealist positivist conceptions of science.

I buy that at least parts of mathematics have the described form. I think that there is an independent case in this text that models should focus on interventions as much as the task of bare representation. I am not sure I buy the idea of using set theoretic models as a metaphor for scientific models, but perhaps that was more of a salient point against the background of logical positivism, which Badiou addresses himself to often. Some of his philosophical interpretations of mathematics are a bit off (e.g. that the independence of choice from ZF calms all fears about using it), however they're mostly forgivable.

Good book, well worth a read for an introduction to a more grounded approach to philosophy of mathematics, chase with Fernando Zalamea if you can handle algebraic topology and/or modern algebra.

[AG · Rating 5 out of 5]

Don’t skip the interview at the end of this! Badiou’s elaboration of the continuities and discontinuities between his earlier formalism and his mature work is essential for those invested in his project and the legacy of the Althusserian camp.

[Karlo Mikhail · Rating 3 out of 5]

I'm sure I missed lots of technical stuff. I have to read this again.

[Nick Black]

How did I see this randomly among the GoodReads search results and immediately know John.Bova would have read it, awarding 5 stars? Hehehehe you're growing predictable, goodreads buddy -- no way would you have missed something with "concept of model" in the title! =D This looks fascinating but not for right now, maybe a 2010 read.

[Ian Slagle · Rating 4 out of 5]

This one is an interesting read, very different from modern understanding, though not necessarily in a way I agree. I will always appreciate an application of group theory where maybe it doesn't quite belong.