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August 25, 2005
Existence and Mathematics: the two Pauls
Translation of Maquerelle du Vrai, 13 June 2005 - Text by Guillaume Destivère
(Reading of L’Être et l’Événement (EE) by Alain Badiou: Preliminary considerations.)
By the term “subject”, as Alain Badiou generally uses it, we should understand the part of ourselves or the traits of our existence which, perhaps, deserve to be saved: our immortal part. It is in this sense that the problem of existence becomes for Badiou a problem of the subject or of subjects, at the same time that the philosophy of existence becomes a theory of the subject.
Badiou often remarks on the importance which the thought of Lacan has had for him, insofar as Lacan’s writings and seminars can be read as a series of theoretical (and atheistic) elaborations treating of that part of ourselves that is susceptible - “if it exists” - to being saved by the psychoanalytic cure; the “subject” of the unconscious. In this way Badiou inscribes Lacan in a discontinuous lineage of thinkers of existence which passes, notably, through Pascal (the catholic) and Kierkegaard (the protestant), those “anti-philosophers” struggling with the thought of a subject of faith.
With the result that the journey through Lacan, in the final analysis, establishes nothing more decisive than one might have expected from the start. In EE, the theory of the subject articulates the subject in terms of fidelity (there is no subject except as subject of a fidelity), proposes that a fidelity which saves is a truth, and relates every truth to an event-miracle of which it is the (quasi-)cause. Thus it is christian salvation which seems to be in play: every event is something of a “christ”, every truth a little “church”, and there are no subjects other than our “works”; the best of ourselves is always that which we dedicate to this or that truth. Thus Badiou’s reading of Lacan must also be read as a repetition of Saint Paul. This working-through of one which becomes a repetition of the other in a formal scheme is an important feature of Alain Badiou’s philosophy of existence, as “theory of the subject”.
But theologians ought not to rejoice too hastily. Because the second feature of a theory of the subject as philosophy of existence is that the formal scheme, the “theory”, destroys unicity. If there is a formal theory of salvation, it is that there are essentially many orders of salvation, many events-miracles, and just as many associated truth-churches, which realise the scheme. Badiou says that there are truths in science, in politics, in love and in art. Four is the Platonist number of his pluralism. And if there are no religious truths, this is without doubt because religious fidelity itself does not support the plural, by the very definition of its “monotheism”. A very remarkable case of a paradigm which finds itself excluded from his schema. Thus, whatever the role of Saint Paul and of Christianity in Alain Badiou’s work, philosophy always circulates between modern mathematics, revolutionary politics, our love stories and artistic schools, as the pimp of truth, the procuress of encounters with truth.
Thus subtracted from the Christian paradigm, “event, truth, subject” would constitute nothing more than an empty and wholly arbitrary schema if Alain Badiou, perhaps “by hazard of bibliographical and technical research on the couplet discrete/continuous”, had not made the encounter which was to change everything, and dispossess at a stroke all christianism from his scheme. This encounter was that of “catholic” in the form of the “indiscernible”, of the “universal” under the sign of the “generic” of Paul of Tarsus, under the name of Paul Cohen. The first Christian theologian invented the universal, the last great theorist of sets reinvented it far distant from all theological context. This is the Cohen-event of which EE is the orchestration. The whole philosophy of existence is referred, at a single stroke, back to mathematics. The theological paradigms that one still finds in Théorie du sujet (Badiou’s previous important book) do not survive in EE except for Pascal, the destroyer of all jesuitisms, at the same time as the theory of the subject demands an immense detour through Zermelo-Fraenkel set theory, until the method of “forcing” where Cohen’s “generic” finds its mathematical sense.
Since the paulinian universal appears in the shape of generic sets, the church of a truth must “be” a generic “set”. The sense of being (the sense of the verb to be) becomes: being-multiple. Not only for truth-churches (those beings which save), but for every being: each and every being relates back to one (or many?) multiple-forms, at the same time as set theory articulates everything that one can say about the pure multiple as being-qua-being. Badiou’s formula according to which “mathematics is ontology” cannot, from the very start, say anything other. It finds its necessity in the meeting of the two Pauls, of the catholic and the generic, as a complex thinking of an existential and mathematical “universal singularity”.
One might perhaps accuse this reading of not following Badiou to the letter. In his introduction, he has the air rather of taking as his point of departure a Lacanian inspiration concerning the mathematical real. But how can the chance occurrences of the bibliographical researches on the discrete and the continuous, how do whatever intrinsic “obstacles” (which the problem of the continuum certainly is in set theory) become all at once the sign of “the impossible proper to mathematics”? Why not a logical theorem of Gödel’s, which might lead us to a formula which one hears from time to time; that first-order logic is ontology? Why not any undecidable statement from some field other than pure logic or set theory?
We believe that Badiou’s system doubtless finds that the continuum as impasse of formalisation in some sense converges with the Lacanian real and set theory (a promised metonymy of 2600 years of mathematics), but also that this sense is subordinated to the more profound shock of the two Pauls and to the didactic exigencies of Cohen’s invention. Badiou subtracts from the church theologian what he adds to the mathematician of the generic and of forcing; a catholic concept of truth.
This operation is already in effect before EE begins. When he begins to meditate, the philosopher doesn’t already have evangelists at hand, nor Lacan’s Écrits, but Set Theory, Kunen’s manual, which will condition the principle steps of his ascension to the essence of truths, to the schema and the multiple-form of that which merits being lived.
In this context, the Heideggerian resonances of Badiou’s title can no longer deceive us. Heidegger being indeed “the last universally recognizable philosopher”, he tramps along towards nowhere, a book of poems in his hand, whilst Badiou jumps four steps at a time up the staircase of set-theoretical rationality. Not without being threatened many times, it is true, by disquieting phantoms which lend to the whole of his meditiation something of a Mallarméan drama.
Posted by robin at August 25, 2005 02:11 PM