Lacan and Badiou: Logic of the Pas-Tout

The fact that statements about "nothing" are, or are always equivalent to, a universal statement raises the question of a non-universalizable, non-completable nothing. Lacan’s pas-tout is an attempt to logically capture this incompleteness that can never be completed. While the pas-tout is relevant to the field of sexuation, its logic can be considered independent of it. This logic is, of course, a "deviant" logic, and for this reason raises questions about how it is to be interpreted. Alain Badiou criticizes Lacan for adopting a pre-Cantorian attitude towards the infinite and for advocating the strictures of intuitionism. I argue that Lacan is not an intuitionist but a constructivist about mathematics. I also consider Jacques-Alain Miller’s suggestion that Lacan’s pastout can be considered a variant of the Aristotelian negative particular statement, "Not all As are B" or "Not every A is B"