I accord no fundamental importance to Badiou’s allegorical hermeneutics of technical developments in set theory. Without the allegorisation they do not amount to much, and it is the allegorical version of his concepts that is in rivality with those of Lyotard, Deleuze, and Feyerabend. Laruelle is very interesting on this point, showing how Badiou’s mathematism is tantamount to the simplification of the more radical reconceptualisations made possible by quantum theory.
Feyerabend too shows how complementarity can be generalised within a framework that is far more pluralist and far more diachronic than Badiou has ever been capable of elaborating. Further, Deleuze and Guattari’s theory of assemblages is totally in line with Niels Bohr’s generalised version of complementarity, where Badiou’s multiples signify rather the triumph of spatialised thinking. Bohr is a much more radical thinker than Cantor.
Badiou would like the “central” question of modern philosophy to be that of finite and infinite understood in a set-theoretic sense, but that question is a distraction from the dialectic of the one and the many, where he is far from satisfactory. All this was gently pointed out to him by Desanti and Lyotard at the moment of publication of BEING AND EVENT.
I like Badiou most in his more wide-ranging seminars like “What is it to live?” (2003-2004) and in his “wisdom of life” essays, where he is like a modern day Schopenhauer. He employs a vocabulary that is resonant both philosophically and poetically, without his imposing technical apparatus. This allows him to attain great concision, and to liberate the meaning contained in the various objects of his reflection: films, books, axioms, equations, poems.