Some of Badiou’s criticisms of Deleuze can be rejected because he sometimes seems to be taking Deleuze’s system for a bad application of a « set-theoretic » approach.
However, Deleuze is not trying to think in terms of sets and failing, he is attempting something different. Specifically, Deleuze’s « multiplicities » are not sets.
A better comparison between the two comes from a number of positive concepts that Badiou proposes without even having Deleuze in mind but that retroactively can give clarity and insight on neglected aspects of Deleuze’s work.
In particular, the words « infinite » and « infinity » (along with their Deleuzian synonyms: absolute, the outside, the plane of consistency) abound in Deleuze’s work, especially in WHAT IS PHILOSOPHY? But there is a certain confusion in the concepts underlying the words.
Badiou’s typology of four different sorts of infinity, which he draws from recent set theory, can bring some clarity to this confusion. In his « Immanence of Truths project Badiou distinguishes
(1) inaccessible infinites
(2) infinites by resistance to division
(3) infinites by immanent power
(4) infinites by increasing proximity to the absolute.
In Deleuze we can find
(1) the outside further than any exteriority
(2) resistance prior to stratification and segmentation
(3) immanent affirmative powers (becomings, affects, intensities) on the plane of consistency
(4) deterritorialisation approaching the « absolute horizon ».
AGENT SWARM 