…stripped-down, given in the course of a remark on Sartre. The context is relatively arbitrary; the argument isn’t.
[…] Contra Priest and others, I’m not embracing paradox or dialetheism, so when I say that X is a witness to the proposition “P is contradictory”, and deploy this syntax in discussing the relation of the event of pure reflection to the ontological thesis that the in-itself-for-itself is a contradiction, I mean first of all that it negates that ideal. It doesn’t paradoxically both-negate-and-affirm it or show it to be contradictory-but-assertable or anything like that. At this point, rather, the spell is broken, even if we don’t know how (yet) to put the breaking of the spell to use, or to say “positively” what is there negatively shown. To the extent, though, that the ideal shown to be contradictory seems to be an inevitable posit of reason, we have to look more closely at what is being affirmed and what is being negated. For one thing, there is nothing contradictory about reason’s having to posit a hypothesis which falls to reductio. In fact, I have an argument (let’s call it the “Argument for Negative Foundations”) that any single true genuinely ontological proposition has to be negative in precisely this way. It has to have the form, “X does not exist” (where X is some name for the Absolute). Why? Because meaning is differential. The only way to provide a characterization is by contrast, by drawing a distinction, and with what can Being be contrasted? Only with what essentially does not exist. The ancients were therefore by no means mistaken to maintain that a characterization of being must proceed by way of reference to a perfect being; they simply mistook the sign, taking for theology what is properly atheology. This is why it is valid for Sartre to maintain the structural, ontological importance of the nonexistence of God, despite the apparently reactive position that it seems, to the friends of some supposedly-pure affirmation, to leave him in, and why the corresponding post-Cantorian form of the same proposition, is at the head or heart of each of Badiou’s major works. (As you can see, my preferred solution to the problems of reason’s dissatisfaction and delimitation is neither Kantian, nor Hegelian, nor Heideggerian.)