We can do a purely logical exercise concerning the presidential pools, in France this year, in the States next year. Are these pools events? Is there in them a political truth? What is the logical context? Classical? Certainly not. Nobody thinks that with Segolene Royal or Hillary Clinton, the poor African or Mexican worker will become a new political hero. So the choice is between intuitionistic or paraconsistent. My own conviction is that pools, today, in our world, are always of the third type: false event, paraconsistency. Seeming like a contradiction, but being like an identity. But everybody knows that I am an ultraleftist. So after all, you can be courageous intuitionistic men and women.
Badiou, “The Three Negations”
I really need to understand Badiou’s relationship to paraconsistent and dialethic logics, because they would seem to be something that would be a major problem for Badiou, if they’re not addressed well enough.
This would also be a problem for Meillassoux, who holds on strongly to the principle of non-contradiction.