PLURALISM vs ABSOLUTISM
There seems to be a conflict (or « agon ») between hypothesis 1 (pluralism) and hypothesis 2 (absolutism) in Deleuze’s work. Deleuze is conscious of the conflict and has tried out various solutions.
In his DIFFERENCE AND REPETITION the answer he proposes is the Eternal Return seen as the return of difference, but already in LOGIC OF SENSE he is changing as he gives much less importance to difference and more importance to multiplicity in that work.
In LOGIC OF SENSE the concept of « sense » is proposed as a solution to this conflict as sense is both plural and resonates within a single event in the régime of Aion. It is what both assures and destabilises signification, making it fluid, open, and non-totalisable in a system. Sense has the further advantage of being testable, since Deleuze associates sense and « use » in LOGIC OF SENSE. He also says that we are to incarnate the virtual event in our bodies to be worthy of the event. This constitutes a test both of our « worthiness » and of the sense that we have extracted from the event.
Later, in A THOUSAND PLATEAUS he abandons the Eternal Return as unifying concept, as providing a transcendent instance or supplementary dimension that overcodes the plane of immanence.
In WHAT IS PHILOSOPHY? Deleuze’s solution is to maintain an absolute as « horizon » so as to treat the One-All as an unattainable outside, open and always under construction, and in that sense non-totalisable. But this is a weak solution and may not be enough to save him from relativism.
POETRY vs FORMALISM
As to Deleuze’s poeticity, in my article I was indirectly referring to Badiou’s idea that philosophy’s language is hybrid, torn between the rigorous proofs and formalisation of logic and mathematics on the one hand and the more imagistic language of poetry on the other.
Compared to Badiou’s very thorough and explicit exploration of the formalisms of logic and mathematics Deleuze’s language, while not devoid of formal inspiration and direct exposition comes across as much less formal, more allusive, implicit, and indirect and more poetic.
This poeticity is not necessarily a handicap, and I think we need both. Poeticity is tied toe subjectivation and to perception. One needs to perceive, non-philosophically, the infinite in a proposition (science) and in percepts and affects (art). One can generalise this idea in terms of perceiving the infinites also in situations/states of things, in ourselves and in the world.
LANGUAGE OF THE INFINITE
In WHAT IS PHILOSOPHY? Deleuze recognises the need to elaborate a language of the infinite to articulate these perceptions, in the sense that he gives us a rich vocabulary for talking about the infinite in various ways, in various domains.
Badiou feels the need to give greater clarity and differentiation to this sort of language in making use of the mathematics of large cardinals in his THE IMMANENCE OF TRUTHS, a book that truly impressed me and revolutionised my thought.
So Badiou is in a position to say that science (as matheme) does not renounce the infinite but develops it in new and surprising ways. Deleuze would have to reply that this is not strictly speaking a case of the « conceptual » infinite but merely of the functional infinite, as he makes a sharp demarcation between the concepts of philosophy and the functions of science.
I think that this sort of sharp demarcation between science and philosophy is a mistake, and that it does not even cohere very well with the rest of Deleuze’s philosophy. Taken at face value it would be methodologically disastrous.
For example this demarcation it would forbid, or at least discourage, Zizek’s appeal to quantum mechanics, which is one of the most interesting aspects of his ontological explorations.
Deleuze’s idea of empirical testability in philosophy, in WHAT IS PHILOSOPHY?, is based on his transcendental empiricism, and so is still too internalist and autarchic. Yet, at the same same, this transcendental aspect means that experience is already formalised for Deleuze, only in a different way than Badiou’s mathematical formalisation.
So we cannot give a clea-rcut judgement of the sort « Deleuze is right and Badiou wrong » or vice versa. The real question is pragmatic and heuristic: in some situations a more poetic approach is most useful, and in others a more mathematical approach may be more appropriate.
Badiou in THE IMMANENCE OF TRUTHS has demonstrated the advantages of a greater exploration of mathematical formalisms. Similarly Deleuze in WHAT IS PHILOSOPHY? has demonstrated the value of a poetic formalism that tends towards the inform without being absorbed by it.
Note: I am indebted to a discussion with Ed Leenders for helping me to clarify my ideas.