Alain Badiou is probably the leading living philosopher in France today. He is a very complex figure who writes well-organized, multidimensional books and says things that are sometimes quite insightful, but who takes a number of fundamental positions that I find utterly antithetical. To oversimplify in the extreme, I read him as a sort of sophisticated existentialist who learned a few lessons from structuralism.
One thing I appreciate is that unlike some others of his generation, he unapologetically identifies himself as a philosopher in the classical sense. I also like the fact that he overtly puts a high value on reasoning (though I think he is at root a deeply irrationalist voluntarist decisionist of a Sartrean Maoist Schmittean sort). I appreciate his sharp-tongued social criticism, but think he draws some very wrong conclusions about the way forward (again in a voluntarist direction). I like the way he integrates diverse interests like mathematics and literature, but strongly disagree with his particular philosophy of mathematics.
Badiou has promoted a useful clarification of abstraction as a kind of subtraction.
His first big book was Being and Event. I believe the emphasis on Being is misguided, as is that on set theory. His highly original attempt to redefine events, truths, and subjects that we actually care about as limited to the exceptional cases is quite fascinating, but ultimately spoiled by a rather arbitrary canonization of particular exceptions, and by the voluntarist root agenda.
His early Theory of the Subject included elements of a sort of Lacanian Maoist reading of Hegel. I believe Slavoj Žižek attended the original seminars on which it was based, and got significant inspiration there. At this stage, Badiou was emphasizing the scission of the subject in Lacan, while attempting to relate it to the more general Maoist “One divides into Two” dogma.
While I think Lacan deserves serious consideration in spite of the antics of some of his followers, I regard “One divides into Two” as a subtheoretical atrocity that would undo all of Hegel’s careful work to develop a concept of determinate negation, and that also completely reverses the thrust of Engels’ quite reasonable account of the conditional, relative status of opposites in Anti-Dühring. “One divides into Two” reduces dialectic to crude talk about opposed forces. Badiou still defends this. (See also 1968; Antiphilosophy; Johnston’s Pippin; Weak Nature Alone; Democracy and Social Justice.)
I am even more disturbed by Badiou’s apparent strong sympathy for the work of the political and legal theorist Carl Schmitt, who was an ardent Nazi, and wrote key legal opinions legitimizing Nazi actions. Schmitt’s Nazi involvement seems much worse than Heidegger’s, and his thought far less mitigating. I just read a couple of secondary accounts of Schmitt for the first time — a bunch of stuff about will and enemies. There are more lessons here about the political evils of voluntarism. Badiou’s explicit references to Schmitt are apparently only the tip of an iceberg. I now realize there are many more implicit resonances in his texts.