-Excerpt from Peter Hallward's Badiou: A Subject To Truth, 101-103.
"In set-theoretical terms, the naming of the void is accomplished through what is know as the null set axiom. This axiom simply postulates the existence of a set (a multiplicity) that has no elements. From this existence all mathematical things derive, except itself. While most of the other axioms of set theory govern the manipulation of already existing sets, the axiom of the void is exceptional in that upon it and it alone rests the whole derivation of presentation as such. All multiples are multiples of multiples, with the one exception of this 'multiple of nothing.' In other words, though to exist is to belong to a set, the axiomatic foundation of existence is itself the exception that establishes this rule: the null set axiom states, in effect, that 'there exists that to which no existence can be said to belong.' There exists a presentation of the unpresentable, and this unpresentable is nothing other that the very be-ing of (all other) presentation. Or again, in terms that will please readers with a taste for paradox: 'Being allows itself to be named, in the ontological situation, as that whose existence does not exist' (EE, 80-81).
To put this another way, if inconsistency itself can never be presented (can never belong to a situation), what can be presented of inconsistency is just the mark of its unpresentability, that is, its name. Every naming takes place under the structural constraints of that place. In the fully depoeticized set-theoretical situation itself, that 'the void is what can only be said or grasped as pure name' (PM, 167) means that the void is simply an empty sign or letter--by convention, the letter ∅. In terms of the theory, this letter indicates the existence of an empty set, and its own literal existence, its existence as a letter, is exhausted by this indication. ∅ is thus not properly the name of inconsistency 'in itself,' but the name of inconsistency according to a particular situation, that is, as it is presented in ontology (EE, 68). The only privilege of this particular name, the ontologival name, is that it presents the be-ing of naming at its most subtractive or abstract. Ontology demonstrates that, considered in its be-ing, and whatever the situation, the name of the void is a name normally deprived of all meaning and resonance, a name for anonymous namelessness as such.
By thus founding his ontology of the letter ∅, Badiou can fairly claim to fulfill Lacan's great program: 'It is in this instance de la lettre, to use Lacan's expression, an agency [instance] indicated here by the mark of the void, that unfolds thought without One.... Thus is accomplished the equivalence of being and the letter, once we subtract ourselves from the normative power of the One.' Through the nonmediation of the letter ∅, the imposition of an empty mark, so indeed 'being and nothingness are the same thing' (B, 37). On this condition, a fully univocal ontology--an ontology without any reference to the transcendent and without any reliance on figural approximation--can absorb the finite withing the infinite, can be entirely 'actual,' and can fully absolve itself from any 'poeticization.' We need only accept that 'the sole power that can be aligned with that of being is the power of the letter (puissance de la lettre).' In its quite literal insistence of the void, Badiou's ontology is perhaps the only consistent formulation of Lacan's purely symbolic register, in which 'nothing exists except on an assumed foundation of absence. Nothing exists except insofar as it does not exist.'
Now since it cannot be counted as one, the void clearly belongs to no situation. But--and this is an essential difference--it is for the same reason included in every situation. As the suture to its being, the void is an empty but universally included subset or part of any set. Why? Remember that to be included in a set, that is, to be a part or subset of a set, is to have no elements that are not themselves included in the set. So, if set F is not a part of another set, E, it must be because there are elements of F that are not elements of E. But the empty set has no elements. It is thus impossible for it not to be a part of E: 'The empty set is "universally" included, because nothing in it can block or prevent such inclusion.' Containing nothing, with no belongings or 'roots' of its own (nothing underneath it, nothing supporting it), the void is thus a kind of ontological vagrant. The void is 'the without-place of every place' (CT, 200); it is 'neither local nor global, but scattered everywhere, in no place and in every place.' It is precisely as nothing, as void, that 'inconsistency roams through the whole of a situation' (EE, 68,71). And, by the same token, while the void itself is not one-ifiable, it is certainly 'unique.' One void cannot differ from another, since it contains no element (no local point) that might indicate this difference.' Inconsistency is not only everywhere; it is the being of everything.
The essential point is this: the void is included in every part of a situation, but since it can never belong anywhere in a situation, what is 'in' the void can never be known or presented within that situation. A situation cannot encounter its own void. Set theory itself cannot in any meaningful sense know what lies 'under' the proper name ∅: an axiom provides only an implicit definition of what establishes. The normal regime of a situation is structured in precisely such a way as to preserve an essential ignorance or 'unconciousness' [inconscience] of its void. And it is impossible, Badiou insists, to combat this sturctural ignorance so long as the situation is dominated by business as usual, however apparently compassionate or democratic that business might be: 'The void of Being can only occur at the surface of a situation by way of an event' (D, 115), and we shall see that 'what allows a genuine event to be at the origin of a truth, which is the only thing that can be for all, and that can be eternally, is precisely the fact that it relates to the particularity of a situation only from the basis of its void., [which] is the absolute neutrality of being' (E, 65)."
Abbreviations:
EE - L'Etre et l'evenement (Badiou) Being and Event
PM- Petit manuel d'inesthetique (Badiou) Handbook of Inaesthics
B- Beckett: L'increvable desir (Badiou) NO ENGLISH TRANSLATION
CT- Court Traite d' ontolgie transitoire (Badiou) NO ENGLISH TRANSLATION
D- Gilles Deleuze: "La clameur de l'Etre" (Badiou) Deleuze: The Clamor of Being
E- L'Ethique: Essai sur la conscience du mal (Badiou) Ethics: An Essay On The Understanding of Evil
Peter Hallward, Badiou: A Subject To Truth, 101-103.
No comments:
Post a Comment