Same

Le boulet n’est pas passé loin

Published on Mar 31, 2013

Cinema re-cords the cut which is (k)not.

Conditions: Spring Breakers, Film Socialisme, Notre Musique, For Zoohky, and Semi-auto colours, diagrams from Alain Badiou’s Theory of the Subject, Second Manifesto for Philosophy, and a passage from Logics of Worlds. Kanye West as Aimé Pache.

*****

“I confess to having experienced some very difficult moments after reading this message. Not only did it cast doubt on the generality of the postulate of materialism, but also on the entire theory of the event! After all, in Book V an event is defined by its capacity to ‘sublate’ the inexistent of an object. I started thinking of the terrible case of Frege, whose entire reduction of mathematics to logic, a theoretical edifice patiently constructed over a number of years, was brought down by a small proof by Russell (I allude to it at the beginning of Book II).

The night between the 19 and 20 had me poring over my notes and the relevant literature. At last, on January 20, at 6.29 pm, I was able to send Guillaume the following blistering reply:

Let us agree to call ‘canonical classical exposition’ of a set A the following set: A* = [∅, {{x}/x ∈ A}], that is the set constituted on the one hand by the void, on the other by the singletons of the elements of A.

We will then call ‘canonical transcendental indexing of A*’ the function of A* ⋅ A* on T0= (0, 1) so defined: Id(x, y) = 1 if and only if the multiples x and y share a common element: ∃z [(z ∈ x) and (z ∈ y)].
We can easily recognize that (A*, Id) is an object. For every non-empty atom is real, since it is prescribed by the appropriate singleton, while the empty atom is prescribed by ∅.
The proper inexistent of this object is of course ∅. We have in effect Id(∅, x) = 0 for every x, and therefore also E∅ = 0.

We can therefore say that, to the extent that one absolutely wants to represent a pure multiplicity A as object—which we could call an ‘onto-logical objectivation’—this object is really A*. Or, to put it in a different way: in ontology considered as a world (which mathematics does not oblige us to do, since it deals with being ‘without appearance’, or non- localized being), a pure multiplicity is objectivated in terms of its canonical classical exposition, which is in turn marked by its canonical indexing.

The more arcane aspects of this affair involve the existence of an isomorphism between the universe (the topos, in effect) of sets indexed with no regard for the postulate of materialism and the universe (the topos) of the sets indexed with the postulate of materialism. The clue to this isomorphism is contained in the above tactic.

Missed by a hair’s breadth.”

Logics of Worlds p 548 Alain Badiou