In the previous post, I discussed Meillassoux's attempt to refute Humean anxiety about causality. The die can produce numbers from 1-6, but it would be a fallacy to say it could become a potted plant because this possibility is not given. Alain Badiou's [i]Logics of Worlds[/i] offers another route.In Book 2, Section 1, Badiou lays out the transcendental structure of determinate worlds. Worlds are local spaces that form the background of entities, and entities form points within these worlds. He argues that all appearing is governed by a handful of operators such as the envelope and conjunction.
Now, sub-section 5 concerns the ability to think, within a world, that which does not appear within that world. In other words, my ability to think the lack of tarantulas currently appearing in the world of my apartment.
His first argument is fairly straight-forward and continues on the basis of his destruction of the chimerical set-of-all-sets. If it were impossible to think the non-appearance of a being, than every being would have to appear in every world, and suddenly we would have a universe again.
LoW's complicated relationship to phenomenology appears in his second argument. If each being is being-there, than this includes the logical possibility of not-being-there. He will refer to this as a zero-degree of appearing. Again, straight forward.
The third argument is much more technical. Let's examine it in detail, and begin by quoting the function of the transcendental:
"At the core of the transcendental questions lies the evaluation of the degrees of identity or difference between a multiple and itself, or between a being-there and other beings. The transcendental must therefore make possible the 'more' and the 'less.' There must exist values of identity which indicate, for a given world, to what extent a multiple-being is identical to itself or to some other being of the same world." (p. 102-103)
So, the transcendental governs how identical X is, or different from, Y - as well as itself, X. X is more or less identical to X, and more or less different from Y. If X does not appear in a world at all - if tarantulas do not appear in my apartment - than X/hairy spiders must have a zero-level of identity with the beings within the world/my apartment. Thank God.
The third argument relies on this. Any evaluation of identity - saying that X has a strong value of identity to itself or Y - implies that this value could be nil. X could appear quite strongly, or it could appear not at all.
The value of these three arguments is that they do not rely on sense perception or on a calculation of probabilities. Remember Hume's problem: why is the world a consistent place, given that the structure of cause and effect is not empirical? Sense perception only tells us that every time we have seen the cue ball strike the 8 ball, they have interacted in such an such a manner. We can't ground necessity, and if we lose necessity, we end up with an infinite number of possibilities for the 8 ball - why should it not transform into a potted plant?
Well, we can say that not every possibility can exist in a world, because that would make that world the universe. We can also say that while we can think the sudden appearance of a potted plant in the pool-world, we have the corresponding ability to think of it not being there at all. We also have the ability to think the plant's nil-level of appearance - the possible plant has no conjunction with the pool ball.
This does not make the 8 ball-plant transformation impossible, but it shows that, once we stop thinking in terms of infinite probability, than it is no longer really thinkable.
