Nothingness & Event

Aside from a bit of formatting that remains to be done, I've just finished my article for MonoKL's upcoming special issue on Badiou. It's essentially an extraction (and condensation) from my MA thesis, which I wrote a few years ago on Sartre and Badiou. Though I see it as being, more than anything else, a sort of formal experiment on philosophical materials (I have a hard time drawing anything, I don't know, self-subsistent out of it) it might be of some interest to the readers of this blog.

The gist of the paper is to demonstrate a strict structural similarity between the form of the Badiousian event and that of the Sartrean for-itself, and then use this homology as a means to splice together the two structures, as a way of fleshing out the skeletal theory of the subject in Being and Event with the dynamics of lack that emerge from the immediate structures of the for-itself in Being and Nothingness. Pure scholasticism, really, but I had fun constructing it.

The paper can be found HERE.

Paul Livingston's THE POLITICS OF LOGIC

So long as academic presses continue to jail our books behind prices like this, I consider anyone who's not making their work available online to be a fool. Paul Livingston, who is not a fool, has just released his excellent book, The Politics of Logic, to you, dear readers. [UPDATE: THE MANUSCRIPT IS NO LONGER AVAILABLE AT THIS URL. PAUL CAN, HOWEVER, BE REACHED HERE.] The book is a fascinating piece of work, which conscripts the conceptual achievements of analytic philosophy -- and, in particular, of that artery of analytic philosophy that has developed a sustained and brilliant reflection on the aporias of structure and language -- to the ends of compiling and illuminating an "orientation of thought" that can compete with Badiou on Badiou's own territory -- what Livingston dubs the "paradoxico-critical orientation". The main gist is something like this: what Gödel's incompleteness theorems throw into dramatic relief is not a simple obligation to accept incompleteness (of any formal system capable of expressing arithmetic, etc.), but the need to make a decision between inconsistency and incompleteness. Badiou's conditioning of his philosophy by mathematics, and principally by the metamathematical and foundational results of Gödel, Skolem, Cohen and others, elides this decision, and so passes over the possibility of the capacity for a rigorous -- and "complete" -- but essentially inconsistent discipline of formal thought to condition philosophy. Against Badiou's vision of the absolutely multiple, Livingston aims to deploy a vision of the paradoxical one, while retaining the ideal of conceiving radical situational change through the lens of formal thought. To this end, the book interweaves a sympathetic and subtle, but at bottom antagonistic reading of Badiou's work with a meditation on the foundations of mathematics and logic, and an invigorating synthesis of Wittgenstein and Agamben, Gödel and Derrida, and others.

Now go and read it [LINK BROKEN] for free.

Mexico City Seminars on Mathematical Logic, Badiou & Girard

The slides for the seminars (which are predominantly in Spanish, or something resembling Spanish) are available HERE.

The dominant theme in all three seminars was the gap between syntax and semantics, conceived as site for conceptual and mathematical invention rather than as a call to mimicry. This took us from a study of Badiou's Concept of Model (read in the light of Althusser's critique of the "mirror myth of knowledge" in the introduction to Reading Capital, and as a more or less successful attempt to elaborate and refine this critique in order to intervene against the empiricist use of the logico-mathematical theory of models), a case study of the Löwenheim-Skolem theorem (the first really significant theorem dealing with the concept of model, and also the one which opened the abyss between syntax and semantics, and produced the concept of "non-standard" models), in Seminar 1, to a examination, in Seminar 2, of Badiou's category of "forcing", focussing on how it draws on the two mathematical "conditions" of Robinson's method for producing non-standard models for analysis (as analysed in Badiou's early text, "La Subversion infinitesimale"), and, of course, Paul Cohen's "forcing" technique in the controlled production of models for set theory, which was the key condition for the theory of truth and subjectivity in Being and Event. Seminar 3 dealt with Girard's work, and its conceptual and historical context. We looked at his critique of Tarski-style semantics, and his more or less tacit philosophical concepts of blind spot and of logic as essentially 'productive' -- themes which helped to link this material back to Althusser, etc. The shift from a set-theoretic paradigm to a procedural one -- the neglect of which would make Girard's project almost impossible to understand -- was examined in terms of the move from a set-theoretic conception of functions to a conception informed by the lambda calculus. A bit of time, not much, was spent on the parallel difference between Tarskian and denotational semantics (where what is modelled is the dynamics of proofs, not mere 'provability' -- the notion which semantic 'truth' roughly and imperfectly captures, in a garment which leaves nothing to the imagination and yet is far too bulky). We moved from there through the the sequent calculi and the Curry-Howard isomorphism (the isomorphism between proofs (in the sequent calculus, or natural deduction systems) and programmes (in the lambda calculus, the Turing machine formalism, or any actual computer), and so on, to linear logic, looking at the subtle tensions which emerge in our understanding of logic as we direct our attention to its hidden symmetries, its procedural aspects, etc. Another important conceptual distinction that we dealt with was that between "typed" and "untyped" systems -- focussing again on the lambda calculus, but with the intention of asking (in light of the Curry-Howard isomorphism) what an untyped logic might look like.

(Explanation, by way of example: in the untyped lambda calculus, every lambda term -- every programme or function -- can interact with every other lambda term, even if the result is a non-terminating procedure (a 'crash') -- "plus 1", for example, can act not only on the numerals for which it was designed, but even on functions which have nothing to do with numbers. The result's not always pretty, but something always happens. The untyped lambda universe is a wild world, and this leads to some very strange facts -- such as every function possessing a fixed point (for all F there exists an X such that F(X) = X) even if this fixed point is monstrous. In the typed lambda calculus, by contrast, everything is domesticated: the functions are saddled with a "superegoic" apparatus of types (Girard's metaphor, I think, if not Joinet's) which limits interaction, and allows terms to act only upon terms of the appropriate "type". The upshot is that every function eventually "terminates" or reaches "normal form" -- nothing crashes -- in the typed calculus, but the control by which this peace is won seems a bit artificial, or at least superficial, and doesn't really seem to proceed from the deeper structure of the calculus.)

[ADDENDUM: What is a 'type' in logic, you ask? A type is the name of a proposition. "A & B", for example, is a proposition of type A&B. The Curry-Howard isomorphism maps proofs to programmes, and propositions to types of programmes. So the question, "What would an untyped logic look like?" becomes something like "Can we do logic without casting our propositions in types prior to the demonstrative work that explicates them and tests them for consequences?" Can we have a logic where we don't begin with a battery of atomic sentences and pre-fabricated connectives? That's the gist of it.]

Finally, we looked at ludics, which is just such a logic (an untyped logic, that is), and which in Girard's eyes succeeds in sublating the gap between syntax and semantics. This section was pretty much improvised. I'll try and write something more precise about and thorough it soon, and post it here. [ADDENDUM: For now, I'll just say: cut-elimination, the algorithmic procedure by which appeals to lemmas are eliminated from a proof, rendering the proof wholly explicit, without 'subroutines', is the key. Cut-elimination is always possible for classical logic, always yields a unique result for intuitionistic and linear logic, but only in ludics does the dynamic of cut-elimination find its full scope, becoming the real engine of the entire system. In 'pre-ludic' logics, many characteristically 'semantic' properties can be expressed in terms of syntactic properties of cut-free proofs. Ludic 'interaction' -- a generalized form of cut-elimination -- reaches into crannies that ordinary cut-elimination can't.] In the meantime, curious readers can find some of my rough sketches of this subject matter (in English this time) here and here.

I'm happy to say that the seminars went extremely well, better than I could have hoped. I'm incredibly grateful for the boundless hospitality and generosity of Carlos Gomez, the Lacanian psychoanalyst who not only, through some incomprehensible faculty of persuasion, convinced the Department of Mathematics and Physics to invite me to come give the seminars, but ensured that my wife and I received full royal treatment while in the city. (And what a city!)

The participants in the seminars were few, but brilliant, and I left with several loose threads which I hope to follow up soon in my research. Among the most interesting of these concerned the sense that should be read into Girard's project for a "transcendental syntax" -- of which ludics is just one adumbration -- with one participant, named Cristina, pointing out that this sounds like Deleuze's conception of the transcendental more than anything (productive of what it conditions, untyped or 'wild', not already sorted into kinds, not resembling the conditioned -- unlike the Tarskian "meta"). This is something I'll have to look at more closely, so, readers, where should I start for a clear treatment of Deleuze's concept of the transcendental? Deleuze has always been someone I've liked quite a bit, but who I've read more or less casually. I'm thinking that Difference and Repetition would be the key text on this topic, but I welcome other suggestions.

Taller Sobre Badiou y la Lógica Matemática en la Ciudad de México

As I mentioned in an earlier post, I will be holding a three-seminar workshop this Tuesday and Wednesday at La Universidad Iberoamericana, in Mexico City. The seminars will be held in a combination of English and Spanish (I took the trouble to putting together my slides in Spanish, but will probably swing back and forth between the two languages as necessary. It's been a while since I my Spanish was at a fluent conversational level). I'll post my powerpoint slides to the blog after the seminars, if anyone's interested.

1. Sobre El Concepto de Modelo de Alain Badiou, (martes 10 de mayo, de 9am a 10:30 am y de 11 am a 12 pm)


2. El Concepto y La Categoría de Forcing (Forzamiento), de La Subversión Infinitesimal al Ser y el Acontecimiento, (Miércoles 11 mayo, de 9 am a 10:45 am)


3. El Proyecto Lógico de Jean-Yves Girard, como Radicalización Lógico-Matemático de la Critica de el 'Espejo-Mito' de Saber Criticado por Althusser y Badiou, y como una Condición Contemporánea para la Filosofía, (Miércoles 11 mayo, de 11:15am a 1:00pm)

LECTURAS PARA LOS SEMINARIOS

El seminario donde el text se va usar se indica en abrazaderas, en la forma [S#].

Textos citados por negritos son fuertemente recomendados. Los otros son algo opcionales.

Unos de estes textos se pueden encontrar al sitio de Jean-Yves Girard: http://iml.univ-mrs.fr/~girard/Articles.html

o el sitio dedicado a los Cahiers pour l’analyse: http://www.web.mdx.ac.uk/cahiers/

Althusser, Louis. “Prefacio: De El Capital a la filosofía de Marx,” in Para leer el Capital. Buenos Aires: Siglo XXI. [S1]

Althusser, Louis. Curso de filosofía para científicos (introducción: Filosofía y filosofía espontánea de los científicos, 1967). [S1]

Badiou, Alain. 2009 (1969). El Concepto de modelo: Introducción a una epistemología materialista de las matemáticas. Trad. Vera Waksman. Buenos Aires: La Bestia Equilátera. [S1, S2, S3]

———. 1967. La Subversion infinitesimale. En Cahiers pour l’analyse, Vol. 9. [S1]

———. 1968. Marque et manque: à propos de zéro. En Cahiers pour l’analyse, Vol. 10. [S2, S3]

———. 1999 (1988). El Ser y el acontecimiento. Trad. R. Cerdeiras et al. Buenos Aires: Manantial. Meditaciones 31, 33, 34, 35, 36. [S2]

Cohen, Paul. 2008 (1966). Set Theory and the Continuum Hypothesis. Mineola, NY: Dover. [S2]

Miller, Jacques-Alain. 1987 (1967). Acción de la estructura. En Matemas I. Buenos Aires: Manantial. (En francés: Action de la structure. En Cahiers pour l’analyse, Vol. 9.) [S2]

Girard, Jean-Yves. Proofs & Types. Trans. P. Taylor & Y. Lafont. Cambridge: Cambridge University Press, 1989. Vean especialmente Chapters 1-5. [S3]

———. Linear Logic, Theoretical Computer Science, London Mathematical 50:1, pp. 1-102, 1987. Restored by Pierre Boudes. [S3]

———. On the meaning of logical rules I: syntax vs. semantics, Computational Logic, eds Berger and Schwichtenberg, pp. 215-272, SV, Heidelberg, 1999. [S3]

———. Locus Solum, Mathematical Structures in Computer Science 11, pp. 301-506, 2001. (Vean la “Dictionary”, en particular.) [S3]

———. Le fantôme de la transparence, pour les 60 ans de Giuseppe Longo.
 Identité, égalité, isomorphie ; ou ego, individu, espèce. D'après une exposé à la réunion LIGC opus 10, Firenze, villa Finaly, 18 Septembre 2009. [S3]

———. La syntaxe transcendantale, manifeste, Février 2011. [S3]

(Todos éstos textos de Girard son para examinar ligeramente. No se preocupen por los detalles muy difícils o técnicos. Están disponible a http://iml.univ-mrs.fr/~girard/Articles.html)

Joinet, Jean-Baptiste. 2009. ‘Introduction’ a J-B. Joinet y S. Tronçon (eds.), Ouvrir la logique au monde: Philosophie et mathématique de l’interaction. Paris: Hermann. [S3]

Everything you needed to know about forcing, but were afraid to ask Alain Badiou

Hat tip to Fabio at Hypertiling and Tzuchien Tho for bringing this to my attention. Wish I could be there. If the reason you can't attend this magnificent, London-based workshop is that you'll be in Mexico City this May, stay tuned...

===================


A Set Theory Postgraduate Workshop for Readers of Being and Event or: Everything You Needed to Know about Forcing but were Afraid to Ask Alain Badiou

24 May, 31 May and 7 June 2011 in Room G03, 28 Russell Square

As part of its ongoing Seminar Series on Mathematics for the Humanities and Cultural Studies, the London Consortium will hold a series of three postgraduate students workshops that aims to discuss and provide a quick overview of some of the mathematics that needs to be known in order to follow the use of set theory
in Alain Badiou’s Being and Event [L'Être et l'Événement]. The main focus of these ‘bootcamps’ will be on introducing and discussing, in a friendly manner, the technicalities concerning the “mathematical bulwarks” mentioned in Badiou’s philosophical masterpiece:
(1) the Zermelo-Fraenkel Axioms of Set Theory
(2) the Theory of Ordinal and Cardinal Numbers
(3) Kurt Gödel and Paul Cohen’s work on Consistency and Independence.

Particular attention will be paid towards providing a sufficiently detailed, rigorous and clear explication of Paul Cohen’s technique of forcing and generic models, a mathematical result that Peter Hallward has called “the single most important postulate” in the whole of Being and Event. If time permits, we might also be touching on some recent mathematical developments in the field as well as trying to understand how Badiou contributes towards the contemporary re-intervention of mathematical thinking into philosophy.

The workshops will be held in room G03 at 28 Russell Square, Bloomsbury, London. The intended audience are postgraduate students or researchers who are interested in understanding Badiou’s philosophy but who lack the mathematical background. There are no assigned compulsory readings for the bootcamps,
and there are no pre-requisites save for some minimal familiarity with mathematics at the pre-university level. The sessions are free and open to the public but please register by sending your name, email and affiliation to forcing.badiou@gmx.com so as to give us an idea of the numbers since the classroom size, unfortunately, will be limited.

Workshop Convener: Burhanuddin Baki

Schedule and List of Topics

Session I (Tuesday, 24 May)

2-4pm – Basic Mathematics and Short Introduction to Forcing
Short Introduction to Badiou’s Being and Event; Basic Arithmetic, Abstract Algebra and First-Order Logic;
Idea of Mathematical Proof; Induction; Naïve Set Theory, Cantor’s Theorem and Russell’s Paradox

6-8pm – Zermelo-Fraenkel Set Theory
Zermelo-Fraenkel Axioms plus the Axiom of Choice (ZFC); Peano Axioms of Arithmetic; Gödel’s
Incompleteness Theorems; Being and Event Parts I, II, IV and V; Some Alternative Axiomatizations of
Mathematics and Set Theory

Session II (Tuesday, 31 May)

2-4pm – Cardinal and Ordinal Numbers
Cardinal Numbers; Well-Orderings; Ordinal Numbers; Continuum Hypothesis; Being and Event Part III
and Meditation 26; Introduction to Surreal Numbers

6-8pm – Kurt Gödel and the Constructible Hierarchy
Some Relevant Model Theory; Formal Semantics of Situations; Formal Semantics of Events; Gödel’s
Completeness Theorem; Compactness Theorem; Löwenheim-Skolem Theorem and Paradox; Transfinite
Induction; Cumulative and Constructible Hierarchies; Axiom of Constructibility; Gödel’s Proof of
Consistency; Being and Event Meditation 29; Introduction to Large and Inaccessible Cardinals

Session III (Tuesday, 7 June)

2-4pm – Paul Cohen, Forcing and Generic Models
General Machinery of Forcing; Analogy between Forcing and Field Extensions; Cohen’s Proof of
Independence

6-8pm – Beyond Cohen’s Forcing
Cohen’s Proof of Independence (con’t); Being and Event Meditations 33, 34 & 36; Forcing in terms of
Kripkean Semantics; Forcing in terms of Boolean-valued models; Forcing Axioms and Generic
Absoluteness; Introduction to Categorial Logic and Topos Theory; Forcing in terms of Topos Theory;
Short Introduction to Forcing in Badiou’s The Logics of Worlds

Suggested Introductory Reading List

Avigad, J. (2004). “Forcing in Proof Theory”. http://www.andrew.cmu.edu/user/avigad/Papers/forcing.pdf.
Badiou, A. (2007). Being and Event. Translated by Oliver Feltham. London: Continuum.
Badiou, A. (2007). The Concept of Model. Translated by Zachary Fraser & Tzuchien Tho. Victoria: re:press.
Badiou, A. (2008). Number and Numbers. Translated by Robin Mackay: Cambridge: Polity.
Badiou, A. (2009). The Logics of Worlds. Translated by Alberto Toscano. London: Continuum.
Bowden, S. (2005). “Alain Badiou: From Ontology to Politics and Back”.

http://jffp.pitt.edu/ojs/index.php/jffp/article/view/244/238.

Chow, T. (2004). “Forcing for Dummies”. http://math.mit.edu/~tchow/mathstuff/forcingdum.
Chow, T. (2008). “A Beginner’s Guide to Forcing”. http://arxiv.org/abs/0712.1320.
Cohen, P. (2002). “The Discovery of Forcing”.

http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rmjm/1181070

010.
Cohen, P. (2008). Set Theory and the Continuum Hypothesis. New York: Dover.
Crossley, J., et. al. (1991). What is Mathematical Logic?. Mineola: Dover.
Devlin, K. (1991). The Joy of Sets: Fundamentals of Contemporary Set Theory. New York: Springer.
Doxiadis, A., et. al. (2009). Logicomix: An Epic Search for Truth. Bloomsbury Publishing PLC.
Easwaran, K. (2007). ” A Cheerful Introduction to Forcing and the Continuum Hypothesis”.

http://arxiv.org/abs/0712.2279.

Fraser, Z. (2006). “The Law of the Subject: Alain Badiou, Luitzen Brouwer and the Kripkean Analyses of
Forcing and the Heyting Calculus”. http://www.cosmosandhistory.org/index.php/journal/article/view/30.
Goldblatt, R. (2006). Topoi: The Categorial Analysis of Logic. Mineola: Dover.
Hallward, P. (2003). Badiou: A Subject to Truth. Minneapolis: U. of Minnesota Press.
Halmos, P. (1974). Naive Set Theory. New York: Springer.
Jech, T. (2004). Set Theory: The Third Millennium Edition, Revised and Expanded. New York: Springer-Verlag.
Jech, T. (2008). “What is Forcing?”. http://www.ams.org/notices/200806/tx080600692p.pdf.
Kanamori, A. “Cohen and Set Theory”. Bull. Symbolic Logic 13(3) (2008), 351-78.
Kunen, K. (1992). Set Theory: An Introduction to Independence Proofs. New York: North Holland.
Norris, C. (2009). Badiou’s Being and Event. London: Continuum.
Pluth, E. (2010). Badiou: A Philosophy of the New. Cambridge: Polity Press.
Potter, M. (2004). Set Theory and its Philosophy. Oxford: Oxford U. Press.
Smullyan, R. & M. Fitting. (2010). Set Theory and the Continuum Problem. Mineola: Dover.
Tiles, M. (1989). The Philosophy of Set Theory. Mineola: Dover.

The London Consortium is a multi-disciplinary graduate programme in Humanities and Cultural Studies. We are a collaboration between five of London’s most dynamic cultural and educational institutions: the Architectural Association, Birkbeck College (University of London), the Institute of Contemporary Arts, the Science Museum, and Tate.

SUTURE ENTRY

Would you look at that? It looks like I forgot an entry. [[UPDATE: It seems I hadn't forgotten it at all---it was published on this blog back on March 5th. Somehow, due to my clumsy bloghandling, it disappeared, probably while I was trying to do some editing to it. As my wife put it, the suture unravelled somehow...]]

New and original material coming soon, by the way. Probably something like an overview of a series of seminars I'm going to be giving in Mexico City next month (on May 10th and 11th -- details to come!) on Badiou's Concept of Model and use of the forcing concept, before launching into desperate attempt to break out of Badiou's work with some reflection on Jean-Yves Girard's research programme in mathematical logic, the subject of my current research.

For now, though, I bring you SUTURE. Again.

===========================================
BADIOU DICTIONARY
SUTURE entry

The word ‘suture’ takes on three distinct meanings in Badiou’s texts. These do not mark distinct periods in the evolution of a single category so much as three different categories whose association under the same name perhaps signals nothing more interesting than synonymy—though some hesitation in accepting this conclusion is no doubt appropriate. To keep things as clear as possible, we will label these categories ideological suture, ontological suture, and philosophical suture, and we will deal with them in turn.

Ideological Suture

The word ‘suture’, in a sense which Badiou will diagnose as exclusively ideological in scope, first appears in Badiou’s work in late 1960s. It was the subject of an intense debate amongst the members of Le Cercle d’épistémologie (the working group behind Les Cahiers pour l’Analyse), which was polarized by the positions of Jacques-Alain Miller on one side, and Alain Badiou on the other. The first move was Miller’s. His contribution to the first issue Les Cahiers pour l’Analyse, ‘Suture (elements for a logic of the signifier)’, he sought to extract the concept of suture from the implicit state it enjoyed in Lacan’s teachings. By Miller’s reading, Lacan had recourse to the word ‘suture’ on a handful of occasions to name the covering of an essential lack in discourse, by way of an short-circuiting of heterogeneous orders (the imaginary and the symbolic, for instance), an operation that serves to constitute the subject by installing it in a chain of signifiers. Miller’s gambit, above and beyond his effort at exegesis, is to show that the operation of suture is at work even in those discourses where we expect it least, claiming to detect it in Gottlob Frege’s rigorously anti-psychologistic attempt to derive the laws of arithmetic from the foundations of pure logic. The focus of the article is Frege’s definition of zero as ‘the Number which belongs to the concept “not identical with itself”’ which, according to Frege’s earlier definition of a Number as a set of concepts whose extensions are equal, comes down to defining zero as the set of concepts F whose objects can be put in a one-to-one correspondence with the objects describable as ‘not identical to themselves’. On Miller’s reading, it is the exigency to preserve ‘the field of truth’ in which arithmetic must be inscribed that forces Frege to consider the extension of the concept ‘not identical to itself’ to be empty—for this field would suffer ‘absolute subversion’ if a term, being non-self-identical, could not be substituted for itself it the signifying chain (Miller 28-9). (This slippage from an object to the mark that indicates it goes unnoticed by Miller—a thread that Badiou will later seize upon in both MM and NN.) This definition, Miller claims, ‘summons and rejects’ (Miller 32) the non-self-identical subject, whose unconscious effects can be detected in the Fregean operation of succession (the ‘plus one’) that takes us from one number to another. That operation, Miller argues, functions only insofar as it is possible for the non-identical (the subject), lacking from the field of truth, to be ‘noted 0 and counted for 1’ (Miller 31). He grounds this argument on Frege’s definitions of one and the successor: Frege defines one as ‘the number of the extension of the concept: identical with zero’ (Frege §77, p.90), and defines the successor of n as the Number of the concept ‘member of the series of natural numbers ending with n’ (Frege §79, p.92)—a definition which could only yield n itself the zero which belongs to each of these series were not, again and again, counted as one. But this ‘counting of zero for one’, by Miller’s lights, depends entirely on the suturing of the subject that engenders the field of logical truth. It is therefore the subject that makes succession tick—but a subject manifested only in the suturation of its lack and so a condemned to miscognition on logic’s behalf.

Badiou will have none of this. The counterargument he delivers in ‘Mark and Lack: On Zero’ (which appears in the tenth and final volume of the Cahiers) can be condensed as follows:

(1) Scientific discourse in general, and mathematical logic in particular, is not a unitary field of discourse or ‘field of truth’ at all. It must be conceived, instead, in terms of multiple stratified apparatuses of inscription.

(2) At no point does any discursive operation in any of these strata have any occasion or need to invoke a radical, unthinkable ‘outside’. What looks like an invocation of ‘lack’—the statement that the concept ‘not-identical-to-itself’, for example, has an empty extension—is nothing but a referral to an anterior stratum of the discourse. No scientific inscription enjoys the paradoxical status of ‘cancelling itself out’, as Miller supposed to take place in the Fregean invocation of the ‘non-self-identical’. Analysing Frege’s definition of zero, for instance, we should see the inscription, on a particular stratum (which Badiou terms the ‘mechanism of concatenation’, or ‘M2’, and whose task is merely to assemble grammatical expressions), of the predicate ‘x is not identical to x’ as a perfectly stable inscription (which indeed presupposes the self-identity of the mark ‘x’ in a perfectly consistent fashion and without the slightest ambiguity). It is only on another stratum (M3, the ‘mechanism of derivation’, which sorts the output of M2 into theorems and non-theorems) that the system ‘rejects’ the existential quantification of ‘x is not identical to x’ as a non-theorem. In no sense does M3 cancel out the productions of M2, or summon them only to reject them: it receives these productions as its raw material, and operates on them in a fashion altogether different what we find in M2. On a subsequent stratum (M4), the predicate 0 can then be defined in terms of the predicate whose extension was shown to be empty, and so on. What transpires in all of this is not, and cannot be, the ephemeral invocation of the non-self-identical subject, or a wound in discourse obscured by the scar of the letter, but a stable relay between fully positive strata the assemblage of which ‘lacks nothing it does not produce elsewhere’ (MM 151), a rule which, Badiou affirms, holds good for all of science.

(3) Not only does the stratification of the scientific signifier exclude suture from science, it suffices to foreclose the subject from scientific discourse altogether, and this is the secret of science’s universality: Science is a ‘psychosis of no subject, and hence of all: congenitally universal, shared delirium, one has only to maintain oneself within it in order to be no-one, anonymously dispersed in the hierarchy of orders’ (MM 161).

(4) Rigorous stratification and foreclosure of subjective suturation are not just accidental features of science, but what constitute science as science. It is they that give form to the notion of the epistemological break, the continuous struggle by which science separates itself from ideology.

(5) ‘The concept of suture,’ therefore, ‘is not a concept of the signifier in general, but rather the characteristic property of the signifying order wherein the subject comes to be barred – namely, ideology’ (MM 162).

This is not to say that suturation never happens when scientists speak. It occurs repeatedly – but these occurrences are nevertheless extrinsic to science in itself. The suturing of scientific discourse is what occurs in the continual establishment of epistemological obstacles, the destruction of which is the sciences’ incessant task. This dialectic of stratification and suturation, or of science and ideology, is elaborated in the appendix to ‘Mark and Lack,’ in a detailed case study of Gödel’s first incompleteness theorem—a study which implicitly attacks Lacan’s attempt to exploit this theorem in ‘Science and Truth’. (See entry on ideology for more details.)

Ontological Suture

Upon mathematics’ ontological baptism, at the beginning of Being and Event, the word ‘suture’ makes a prominent return. It comes to serve two functions: to name the empty umbilicus that links each situation to being by way of the void that haunts it (‘I term void of a situation this suture to being’ (BE 55)), and to christen being with the ‘proper name’ Ø, the mathematical sign of the empty set. Given the rigour and severity of his attack on Miller’s application of the notion of suture to mathematical discourse, Badiou’s abrupt decision to declare Ø set theory’s ‘suture-to-being’ (BE 66) – in a sense ‘which will always remain enigmatic’ (BE 59) – may strike the reader as surprising. More surprising still is that no link, positive or negative, is drawn between the then-falsified Millerian thesis that the subject’s inconsistency is sutured by the arithmetical 0, and the now-affirmed thesis that being’s inconsistency is sutured by the set-theoretical Ø. Even in Number and Numbers, where Miller’s thesis comes in for a second round of attacks, we find the new metaontological suture-thesis affirmed with innocence throughout the book (see NN Chapter 3).

When pressed on this point, Badiou responds that between these two theses, the word ‘suture’ ‘changes its meaning’: it is no longer a question of invoking the void of the (Lacanian) subject, but the void of being as radical inconsistency. This was not in doubt. But the argument deployed in ‘Mark and Lack’ against applicability of the notion of suture to the Fregean 0 nowhere depends on the identification of lack, or radical inconsistency, with the subject. If the argument is sound then it will remain so under the uniform substitution of ‘being’ for ‘subject’, and one cannot use this substitution to flee the difficulties encountered by Miller: we cannot avoid seeing that ‘the torch which lights the abyss, and seals it up, is itself an abyss.’ If the meaning of ‘suture’ in Being and Event differs from the meaning of ‘suture’ in ‘Mark and Lack’ only with respect to the terms it relates—subject then, being now—then the Badiou of 1988 and after remains hostage to the Badiou of ’69, and the stratified psychosis of mathematics will absolve itself from ontology as relentlessly as it does from ideology, foreclosing being as radically as it does subjectivity.

Philosophical Suture

There is a third sense in which Badiou uses the word ‘suture’, which is not so obscurely entangled nor obviously connected with its older usage, though certain structural similarities can still be observed: here, it names a particular – potentially disastrous – way in which philosophy may relate itself to one of its conditions. The relation of conditioning that the philosopher is charged with maintaining between extra-philosophical disciplines (truth procedures) and her own collapses into a relation of suture when, by way of destratification, the philosopher confuses these two disciplines with one another. It is helpful to make a distinction here, according to which partner in the suture achieves dominance. The dominance of the condition—such as the poetic condition dominates the late Heidegger and his pupil, Gadamer, the political condition dominates certain strains of Marxist thought, the scientific condition dominates Carnap and Hempel, and the amorous condition dominates Levinas and Irigaray—is indicated by its hegemony over the philosophical category of truth and its capture of philosophical rationality. No other modes of truth but those of the condition, sutured in dominance, are recognized, and the philosopher measures her reasoning by strictures proper to the conditioning discipline. This renders philosophy incapable of fulfilling its mandate, which is to construct a systematic compossibilization of heterogeneous truths. The dominant position in a suture may also be occupied by philosophy. When this occurs, philosophy takes itself as producer of truths – the kind of truths, moreover, that ought to be entrusted to an external condition. When this takes place, the threat of disaster looms large, and so I refer the reader to the entry on that concept.

VOID ENTRY

This entry completes the series of BADIOU DICTIONARY drafts that Form & Formalism has been bringing you for the last week (unless Tzuchien feels like tossing a few onto the blog), but keep an eye out for the book itself, which should (I think) be coming out at some point within the year. In it, you'll find entries on a slew of Badiousian vocabulary, written by some of the best scholars in the field. If nothing's changed since I last heard, we can expect entries from Nina Power, Tzuchien Tho, Anindya "Bat" Bhattaryya (who I've been waiting to see publish something on Badiou for ages; back in the days of the "Badiou-Dispatch" mailing list, everything he had to say about Badiou's work, and especially its use of mathematics, was profoundly clarifying), Alberto Toscano, both Brunos (Bosteels and Besana), Justin Clemens, Jelica Riha, A.J. Bartlett, Fabien Tarby, Michael Burns, Alenk Zupancic, Dominiek Hoens, Ozren Pupovac, and the editor of the volume, Steve Corcoran, along with a few I've probably forgotten or overlooked. (I welcome corrections on this point.)

That said, here's the entry: last but least, the VOID...

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BADIOU DICTIONARY

VOID ENTRY

Z.L. FRASER

            The word ‘void’ is surprisingly equivocal in Badiou’s writings. Leaving aside the non-ontological, ‘operational’ notion of the void that Badiou discusses in his first Manifesto (where ‘the void’ figures as the empty place in which a philosophy receives the truths of its time), we can discern, in Badiou’s work, at least four distinct senses of ‘void’:

1.     The void as the ultimate ground of ontological identity.

2.     The void as pure, non-self-identical, inconsistent multiplicity.

3.     The void as the emptiness of the count-as-one, itself.

4.     The void as the ‘gap’ between presentation and what-is-presented.

These senses are not always easy to untangle. Sense 1 is the one most readily divined from the empty set (Ø) of ZF. The identity between any two sets is determined by the axiom of extensionality, which simply states that ‘two’ sets are identical if they have all the same elements. Since a set is never anything but a set of sets, this criterion implies a regress: before the identity of a set can be established, we must first establish the identity of its elements by looking at its elements, and so on. The only stopping point to this regress is Ø, whose existence is asserted by the axiom of the empty set, and which, alone, is immediately self-identical. The void, in this sense, figures as the ‘prime matter’ from which presentation is composed; every presentational multiplicity is conceived as ‘a modality-according-to-the-one [selon-de-l’un] of the void itself’ (BE 57).

According to Sense 2, the void is thought as a sheer chaos of self-differentiation – the plethos of being-without-unity that appears in the ‘dream’ evoked at the end of the Parmenides. The void is that aspect of every situation that is still-uncounted, and which inheres in every presentation as the invisible but ineffaceable residuum of inconsistency, a ‘yet-to-be-counted, which causes the structured presentation to waver towards the phantom of inconsistency’ (BE 66). This sense, too, resonates with the set-theoretic Ø – as witnessed by the theorem that Ø is a subset of every set – but at the price of a slight ambiguity: Ø is, mathematically speaking, a perfectly consistent set, neither eluding identification nor threatening the stability of the sets in which it inheres. And so it is that, ‘with the inconsistency (of the void), we are at the point where it is equivocally consistent and inconsistent […] the question of knowing whether it consists or not is split by the pure mark (Ø).’[i]

While these first two senses of ‘void’ seem capable of enjoying a strained harmony as interpretations of the empty set, Sense 3 seems to speak of something else altogether. There is no straightforward set-theoretic formulation of the notion of ‘the emptiness of set-formation’. If there is dissonance here, it is unheard by Badiou, for whom

it comes down to exactly the same thing to say that the nothing [the void] is the operation of the count – which, as source of the one, is not itself counted [Sense 3] – and to say that the nothing is the pure multiple upon which the count operates – which ‘in itself’, as non-counted, is quite distinct from how it turns out according to the count [Sense 2].

            The nothing [the void] names that undecidable of presentation which is its unpresentable, distributed between the pure inertia of the domain of the multiple, and the pure transparency of the operation thanks to which there is oneness [d’où procède qu’il y ait de l’un]. The nothing is as much that of structure, thus of consistency, as that of the pure multiple, thus of inconsistency. (BE 55; emphasis added)

Here, yet another thought of the void emerges, playing on the equivocity of ‘between’ (which can indicate either a distribution or an interval): The void is, now, ‘the imperceptible gap, cancelled then renewed, between presentation as structure and presentation as structured-presentation, between the one as result and the one as operation, between presented consistency and inconsistency as what-will-have-been-presented’ (BE 54; trans. modified): this is Sense 4 in our list. It is not at all clear how this conception of the void is related to the empty set (unless we imagine it to mark a suture in Miller’s sense). Here, Badiou seems to be naming something like the sheer moment of differentiation that must be supposed to hold sway between a set and its elements—a moment which, structurally, recalls nothing so much as the nothingness that, to Sartre’s eyes, interposes itself between impersonal consciousness and its objects, and which arises as an ‘impalpable fissure’ that arises in the heart of consciousness in the event of its reflexive presentation.[ii]

I would argue that it is this notion of the void that allows us to make productive and non-trivial sense of Badiou’s thesis that

for the void to become localisable at the level of presentation, and thus for a certain type of intrasituational assumption of being qua being to occur, there must be a dysfunction of the count, resulting from an excess-of-one. The event will be this ultra-one of chance, on the basis of which the void of a situation may be retroactively discerned (BE 56; trans. modified).

One way of explaining this thesis would be to show how an ‘event’, a moment when presentation folds back on itself, breaking with the axiom of foundation and foiling the extensional regime of ontological identity, formally replicates what Sartre called ‘the immediate structures of the for-itself’.[iii] The void—the ‘nothingness’—which erupts in such circumstances is not described by a set theoretical ontology, but a Sartrean one—one capable of systematically articulating the relation between the ‘void’ exposed by an event and the form of subjectivity to which an event gives rise (including its dimensions of temporality, possibility, normativity, and liberty). What remains lacking is a univocal concept through which these various senses of ‘void’ can be synthesized.

See also: EVENT, ONTOLOGY, ONE, SUBJECT, STRUCTURE, SET THEORY, SUTURE, SARTRE

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[i] Badiou & Tzuchien Tho, ‘The Concept of Model, Forty Years Later: An Interview with Alain Badiou’, in CM, p. 99.

[ii] Jean-Paul Sartre (1956), Being and Nothingness: An Essay in Phenomenological Ontology, trans. Hazel E. Barnes, New York, Philosophical Library, pp.77-8

[iii] Cf. Sartre, Being and Nothingness, esp. Part II, Chapter I, Section I.

ONE ENTRY

Today, Form & Formalism brings you an entry on the notion of 'The One' in Badiou's work (focussing more or less exclusively on Being and Event). This text may or may not turn up in the BADIOU DICTIONARY, alongside the others I've been posting. An entry on 'The One', it turns out, had already been commissioned from another author (I'm not sure who), and so this entry is really just an understudy. I wasn't planning on preparing an entry on this concept at all, in fact, but just happened to stumble across it in a pile of scraps I had left over from my contribution to BADIOU: KEY CONCEPTS (the word limit on that text had been lowered at the last minute, and so I ended up with plenty of scraps on the cutting room floor---just as well, I suppose, as the short essay was starting to bristle with tangents). After a bit of pruning and scrubbing, the piece seemed to stand up fairly well as a dictionary entry, and so here it is:

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BADIOU DICTIONARY

ENTRY ON ‘THE ONE’
Z.L. FRASER

Being and Event begins with an announcement of the book’s inaugural decision: that ‘the one is not’ (23). There is no One, no self-sustaining unity, in being, but only the count-as-one, the non-self-sufficient operation of unification. There is no unity-in-itself, because every unity is a unity of something, something that differs from the operation of unification. This decision is no less fundamental for Badiou’s philosophy than his well-known equation of mathematics with ontology, and their metaontological meanings are deeply entangled; any attempt to isolate one from the other would mutilate the sense that Badiou gives its twin.

Through the prism of set theory, the non-being of the One refracts into three distinct ontological bans: (1) the prohibition of an ‘All’, or a set of all sets (by the ZF axioms, the supposition of such a set’s existence leads directly into the embrace of the Russell paradox)—an important corollary of this ban is that is no ‘set theoretical universe’ against which the various models of set theory can be measured, and so every coherent interpretation of the axioms will be pathological or ‘non-standard’ to some extent—there is no such thing as the standard model of set theory—a fact we must bear in mind when grappling with Cohen’s results, among others; (2) the ban on atomic elements, or units that are not themselves sets (ZF makes no provisions for unities that are not unities-of-something—with the possible exception of the void, into which the axiom of extensionality would collapse any putative ‘atoms’); and, we could add, (3) a self-unifying unity, a set that counts-as-one itself alone; schematically, the set W such that W = {W} (this set, which would in any case evade identification by the axiom of extensionality, is expressly forbidden by the axiom of foundation). 

Note that there exist axiomatizations of set theory which violate each of the three impossibilities by which we have translated, ‘the One is not’. There are set theories with a universal set V, such that for all e, e Î V (the One as All, as set of all sets);[i] there are set theories with urelements, elements u such that no element e belongs to u, but which are nevertheless distinct from the empty set (the One as atom, as a unity that is not a unity-of-something);[ii] and there are set theories with hypersets, sets X such that X Î X, or X Î A₁ Î … Î A_n Î X (the One as counting-itself-as-one, as self-presentation).[iii]

It is the identification of ontology not simply with mathematics but with a particular version of set theory (ZF) that therefore helps to motivate the decision that the One is not. Observing the existence of other One-affirming set theories emphasizes the particularity of this decision. The converse motivation—of the decision to identify mathematics with ontology by the decision on the non-being of the one—is somewhat murkier, but Badiou insists upon it. It is because the One is not, Badiou argues, that we must resist any temptation to subject being qua being to the unity of a concept. Subtracted from unity, ontology can articulate the sayable of being only by means of a non-conceptual regime of axioms, which regulate the construction of pure multiplicities without having recourse to any definition of multiplicity (BE 29). But why insist that concepts cannot deploy themselves axiomatically, by way of definitions that are purely implicit?[iv] Even if this is granted, nothing prevents a reversal of the argument. What, for instance, keeps an opponent from objecting to the placement of being-without-oneness under the ‘formal unity’ of an axiomatic, rather than submitting it to ‘the mobile multiplicity of the concept’?

See also: MULTIPLICITY, MODEL, SET THEORY, ONTOLOGY, INFINITY, VOID

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[i] See Willard Van Orman Quine, ‘New Foundations for Mathematical Logic,’ American Mathematical Monthly 44 (1937), pp. 70-80.

[ii] See Ernst Zermelo, ‘Investigations in the Foundations of Set Theory I’, trans. Stefan Mengelberg, in Jean van Heijenoort, ed. From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, Cambridge, Harvard University Press, 1967, pp. 183–198. Zermelo’s axiomatization of set theory with urelements, originally published in 1908, actually pre-dates the Zermelo-Fraenkel axiomatic which does without urelements and recognizes only sets as existent.

[iii] See Aczel, Peter. Non-well-founded sets. Stanford: CSLI, 1988.

[iv] Replying to Frege’s accusation that an axiomatic operating with undefined terms is conceptually vacuous, the same Hilbert we met at the beginning of this chapter argues that, on the contrary,

If one is looking for other definitions of a ‘point’, e.g., through paraphrase in terms of extensionless, etc., then I must indeed oppose such attempts in the most decisive way; one is looking for something one can never find because there is nothing there; and everything gets lost and becomes vague and tangled and degenerates into a game of hide-and-seek. […T]o try to give a definition of a point in three lines [of text] is to my mind an impossibility, for only the whole structure of axioms yields a complete definition. Every axiom contributes something to the definition, and hence every new axiom changes the concept. (Hilbert, Letter to Frege, dated December 29^th, 1899, pp. 39-40; e.a.)

It’s strange that Badiou would, without argument, reshackle the concept to the Fregean notion of definition, after arguing (some twenty years prior to writing Being and Event),

that the concepts of a science are necessarily of undefined words; that a definition is never anything more than the introduction of an abbreviating symbol; that, consequently, the regularity of the concept’s efficacy depends on the transparency of the code in which it figures, which is to say, on its virtual mathematization. (Badiou, ‘(Re)commencement de la materialisme dialectique,’ p.464, n.28; e.a.)

Do ‘concepts’ deployed in this fashion refasten discourse to the One? On what grounds could we even give an answer to this question?

Our series of entries for the BADIOU DICTIONARY will conclude tomorrow with THE VOID, so stay tuned!

IDEOLOGY ENTRY

Here it is:
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BADIOU DICTIONARY

IDEOLOGY ENTRY

Z.L. FRASER

            Badiou’s most explicit meditations on the topic of ideology appear in a series of texts written over the course of a decade or so, stretching from the late ’60s to the late ’70s. The series divides in two: the first sequence, all composed prior to the events of May ’68, aim to think ideology as that from which thought subtracts itself, impurely and interminably, whether through aesthetic process or epistemological break. The second sequence, in which a faithful articulation of the uprising’s consequences is at stake, and in which political rebellion comes to actively condition Badiou’s philosophy, aim to think ideology itself as a mode of struggle and process of scission.

Ideology: Before ’68

In 1967’s ‘The (Re)commencement of Dialectical Materialism’, Badiou distils a highly schematic concept of ideology from his teacher’s work, breaking ideology into the three imaginary functions of repetition, totalization and placement, which serve

(1)  to institute the repetition of immediate givens in a ‘system of representations […] thereby produc[ing] an effect of recognition [reconnaissance] rather than cognition [connaissance]’ (RMD 449);

(2)  to establish this repetitional system within the horizon of a totalized lifeworld, ‘a normative complex that legitimates the phenomenal given (what Marx calls appearance),’ engendering ‘the feeling of the theoretical. The imaginary thus announces itself in the relation to the ‘world’ as a unifying pressure’ (RMD 450-1).

(3)  to interpellate both individuals and scientific concepts (crossbred with ideological notions) into the horizons of that lifeworld (RMD 450, 450 n.19).

In the background of these three functions is what any Marxist analysis must take to be the ideology’s ultimate aim, which is ‘to serve the needs of a class’ (RMD 451, n.19) – by which is meant, however tacitly, the dominant class. Badiou’s earliest works have little to say about this most basic function of ideology, and even less to say about Althusser’s quiet conflation of ideology tout court with the category of dominant ideology – but this complacency (which, it should be noted, is not uninterrupted – The Concept of Model (1968) marks an important, but ultimately inadequate, exception) will not survive the rebellion mounted in Of Ideology, to which I will return in a moment.

In his first theoretical publication, ‘The Autonomy of the Aesthetic Process’ (1966 – written in ’65), Badiou describes how art, though it does not tear a hole in ideology as science does, nevertheless serves to subtract thought from ideological domination by capturing the latter in ‘the discordant unity of a form: exhibited as content, ideology speaks of what, in itself, it cannot speak: its contours, its limits,’ (APE 80) decentring the specular relation that ideology works to preserve, and exposing the audience to the ‘outside’ surface of ideology’s infinite enclosure:

If ideology produces the imaginary reflection of reality, the aesthetic effect responds by producing ideology as imaginary reality. One could say that art repeats, in the real, the ideological repetition of that real. Even if this reversal does not produce the real, it realizes its reflection. (APE 81)

If ideologies, as Badiou suggests in The Concept of Model, play themselves out as continuous variations on absent themes (CM 7), then the point of the aesthetic process is to expose those themes in their presence themes by capturing them in their form.

            The second mode by which thought subtracts itself from ideology is science, conceived as a sequence of epistemological breaks. Ideology confronts scientific practice in the form of what Bachelard termed epistemological obstacles. In ‘Mark and Lack: On Zero’ (1969 – written in ’67), Badiou contends that epistemological obstacles affect scientific discourse in the form of an unstable suture of the scientific signifier (see entry on suture). Epistemological breaks must therefore act on structure of the signifier itself: they demand a labour of formalization, desuturing and stratifying the scientific signifier, assembling it in an inhuman machine that tears through the fabric of ideological enclosure. The structure of the scientific signifier comes to foreclose every ideological recuperation, but this radical dissonance with ideology is not accidental. It is the constitutive engine of scientific practice:

it is not because it is ‘open’ that science has cause to deploy itself (although openness governs the possibility of this deployment); it is because ideology is incapable of being satisfied with this openness. Forging the impracticable image of a closed discourse and exhorting science to submit to it, ideology sees its own order returned to it in the unrecognizable form of the new concept; the reconfiguration through which science, treating its ideological interpellation as material, ceaselessly displaces the breach that it opens in the former. (MM 173)

Science thus proceeds in an endless dialectical alternation of scientific rupture and ideological recapture – a dialectic that structurally corresponds to that which Badiou will later describe as taking place between truth and knowledge.[i]

            Ideology is the ubiquitous medium of thought and practice, within and against which art and science operate. Philosophy’s task cannot, therefore, be one of purifying thought – whether scientific, artistic or philosophical – of ideology. Its task, as formulated in The Concept of Model, following the direction of Althusser’s ‘Philosophy and the Spontaneous Philosophy of Scientists’, is to draw abstract lines of demarcation between ideology and the subtractive practices it unstably envelops – but this demarcation is not an end in itself. It is carried out for the sake of new ideological-scientific syntheses. In fact, the Badiou of 1968 defines philosophy as ‘the ideological recovery of science,’ the manufacture of ‘categories, denot[ing] ‘inexistent’ objects in which the work of the [scientific] concept and the repetition of the [ideological] notion are combined’ (CM 9). It is clear that this vocation is futile so long as the category of ideology, itself, remains undivided – subsumed, root and branch, under the category of dominant ideology. The philosophical necessity of this division is already legible in The Concept of Model, whose attempt to trace ‘a line of demarcation’ between the scientific concept of model and its bourgeois-ideological recapture is explicitly oriented towards readying the concept’s ‘effective integration into proletarian ideology’ (CM 48). But the theory of this division is not yet clear, and so, for want of a clear articulation of the difference between dominant and resistant ideologies, The Concept of Model can only end with this promissory note.

Ideology: After ’68

            The reader of Badiou’s post-’88 works may recognize in the aesthetic process and the epistemological break an anticipation of the later conception of art and science as truth procedures. Only after ’68 does the third condition arrive in full force, and it is the entrance of political rebellion onto the scene that will force the division of the category of ideology that is needed if the philosophical fabrication of categories is to be justified. This fission comes to a head in a 1976 pamphlet, coauthored with François Balmès under the title, Of Ideology. Badiou and Balmès’ first (and powerfully Sartrean) move is to insist on the transparency of ideology: 

We must have done with the ‘theory’ of ideology ‘in general’ as imaginary representation and interpellation of individuals as subjects […] Ideology is essentially reflection, and in this sense, far from being an agent of dissimulation, it is exactly what it looks like: it is that in which the material order (which is to say, the relations of exploitation) is effectively enunciated, in a fashion that is approximate, but nonetheless real. (DI 19)

Following a merciless critique of the Althusserian theory of ideology (within which Badiou’s initial reflections on the topic took shape), Balmès and Badiou lay down the rudiments of a properly Marxist and militant theory of ideology. They begin by drawing a line between the ideology of the exploiters (the ‘dominant ideology’) and the ideology of the exploited. There can be a ‘dominant ideology’ only where there are people who are dominated, and those who are dominated will resist, whether powerfully or weakly: It is from the standpoint of this resistance that the concept of ideology must be formulated. In resisting domination, the exploited form a more or less systematic representation of the real and antagonistic class relations that exploit them. This representation contains the germ of the ideology of the exploited class – the germ of an ideology of resistance. It is in a resistance to the ideological resistance of domination that the dominant ideology takes shape, struggling, not to deny the existence of contradictory class relations – which could only be a product of blindness or stupidity – but to downplay their antagonistic character. Its platform is threefold:

(i)    Its first move is to contend that ‘[e]very apparent antagonism is at best a difference, and at worst a non-antagonistic (and reconcilable) contradiction.’ (DI 40)

(ii)  Its second is to maintain that ‘[e]very difference is in itself inessential: identity is the law of being, not, of course, in real social relations, but in the ceremonial register of regulated comparisons before destiny, before God, before the municipal ballot-box.’ (DI 40)

(iii) Its ‘third procedure is the externalization of the antagonism: to the supposedly unified body politic [corps social] a term ‘outside of class’ [hors-classe] is opposed, and posited as heterogeneous: the foreigner (chauvinism), the Jew (anti-Semitism), the Arab (racism), etc. The procedures of transference are themselves riveted [chevillées] over an exasperation of the principal contradiction.’ (DI 40; n.27)

Resisting this resistance of resistance to domination, the ideology of the exploited may become an active ideology of rebellion. To do so, ‘revolt must produce an inversion and reversal of values: for it, it’s the differential identity of the dominant ideology that’s the exception, and it is antagonism that is the rule. It is equality that’s concrete, and hierarchy exists abstractly’ (DI 41). In this exponentiation of resistance the communist invariants take shape: egalitarian, anti-proprietary and anti-statist convictions, which, Badiou and Balmès argue, are not specific to proletarian revolt, but genuinely universal, legible in every real mass revolt against class exploitation (DI 66-67). These invariants comprise the contents of resistant ideology, and not necessarily its form, which it as a rule is inherits from the ideology of the dominant class (the communist invariants inscribed in Müntzer’s peasant rebellion, for instance, were couched in a religious form inherited from the ideology of the landowning class).

This division between content and form – with the form of an ideology deriving from the ideology it resists, and its contents reflecting the real class forces that drive it – supplies Badiou and Balmès with a straightforward way of accounting for false consciousness. ‘Illusion and false consciousness,’ they write,

concern the form of representations, and not their content. That a small-time union boss might hold the sincere conviction that he speaks in the name of the working class, and even has the backing of a tawdry Marxism, when he bends over backwards to liquidate a mass revolt, that’s false consciousness – but only so far as the formal side of the question goes. The truth is, our little revisionist is invested by the force of the bourgeois class, which his thought quite adequately reflects. (DI 32)

It is here that the Marxist formation of a proletarian party becomes crucial to the organization of revolt, in its function of welding the correct ideas of the masses – the invariant, communist contents of mass revolt – to the scientific form of Marxism. It is this that sets the proletariat – the organized proletariat – apart from the exploited classes of the past, for while it ‘is not the inventor of ideological resistance, it is its first logician’ (DI 128).

SEE ALSO: SUTURE, FORCING, MODEL, SPLACE, ENCYCLOPAEDIA, REPRESENTATION, STATE, HISTORY, CAPITALISM

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[i] For details on this correspondence, see Z.L. Fraser, Translator’s Introduction to Alain Badiou, The Concept of Model, (Melbourne: re.press, 2007), § VII in particular.