Kant vs Cantor?
Somebody once argued that Badiou should not be considered a Kantian; but perhaps this is to oversimplify. Badiou’s metaphysics is not Kant’s, certainly, but there is, perhaps, a more fundamental similarity. Kant’s system derives entirely from asking, “given that reason can give us knowledge, what must the world be like?” From this, Kant derives the mechanism of nature, and from that, he derives the identity of morality and freedom. Badiou begins by taking Kant’s question as his own, with the decision that being is what is knowable by reason. Hence the importance of maths for Badiou, because set theory is the most sophisticated system we have for making ontology rationally comprehensible. What I’m not sure about is how closely Badiou follows Kant at this point: is ontology, because it can be rationally understood by set theory, therefore a deterministic or mechanistic system which the Event, like the moral subject, stands outside of? Or is Badiou’s use of Cantor intended to remove this dualism, to show that the world need not be mechanistic to be knowable, and so to restore morality and freedom to the phenomenal world?