The problem that Badiou raises with Deleuze’s philosophy is one of place and not of sense. Badiou has already said (in METAPHYSICS OF REAL HAPPINESS) that for him “sense” in Deleuze corresponds to “truth” in his own system.Badiou argues that Deleuze posits an “absolute place” that is both unifying and totalizing.
We have seen that in WHAT IS PHILOSOPHY? Deleuze and Guattari talk of a plane that is a “reservoir”, “reserve” or “absolute horizon”.
Previously, in RHIZOME they criticised the notion of the Eternal Return as introducing a “supplementary”, or transcendent, dimension, implicitly criticising Deleuze’s earlier philosophy expressed in DIFFERENCE AND REPETITION.
The hunt for transcendences is unceasing, so it is a continuation of the same process when Badiou uncovers and rejects a subjacent unifying and totalising instance in the notion of the plane of immanence. This is an onto-theological element, turning immanence into the Presence of a plane.
I think that this needs further argument, but I certainly do not belong to the “Deleuze can do no wrong” school that will just paste on any ad hoc explanation that comes to mind to cover over any serious objection.
My hypothesis is that Badiou is involved in a slow becoming-Deleuzian. Unfortunately we will never see the possible fourth volume in his BEING AND EVENT series, which could be called: “ONTOLOGY OF PLURALISM: Deleuze as Educator”.
In considering Badiou’s critique of Deleuze one should in a first approach forget about the mathematics. Badiou explicates mathematics (specifically set theory) as foundational for ontology (this is his scientism) but his actual use of it is metaphorical. The main question is: is Deleuze misreading himself when he critiques the eternal return?
IBadiou captures very well the moment of totalisation in Deleuze and Guattari’s thought that can be criticised, as does Laruelle. This is Latour’s critique too. Unfortunately, Badiou regresses from this insight into a real problem in Deleuze’s system with his foundational use of maths.
But we cannot remain fixated on one phase of the historical process. Deleuze died 22 years ago, when he was 70. Badiou is writing today, he is 80, and he is still evolving. Despite his wrong-headedness and his “weirdness”, he is a more legitimate inheritor of Deleuze than the Anglophone business machine academics who dominate the discussion of Deleuze in English.