I left off the last post asking what Badiou gets out of his reliance upon Zermelo-Fraenkel axiomatic transitivity, given its crippling exclusion of pathic interaction. His characterization of ontology in terms of the inconsistent multiplicity of ordinals is certainly capable of describing the possibility of existential novelty (or emergence), but performs poorly for novelty itself. For similar reasons, Levi Bryant claims that Badiou makes a category mistake by confusing essence with existence, Badiou’s set theoretical truths describing only the former. But, Bryant concedes, it is quite a powerful description of essence. Here I want to talk a bit about just why it is such a powerful description of essence.
Usually during winter break I try to get a scholarly project started. I tend to flounder until the last few days of the break, when the ideas seem miraculously to come together. Then the semester begins. Any project begun during break quickly dissipates, and if I’m lucky, I can pick up the pieces and turn it into something else a little later on. But during this break, I went in a slightly different direction. I simply spent much of my off time rereading Alain Badiou’s Number and Numbers.
I had read and cited Number and Numbers before, but always had the nagging sense that I had under-read it. The first time through, I read it as the 240 page book it appeared to be. This time, I read it as the 900 page tome it really is. Number and Numbers is one of Badiou’s least celebrated books, but it’s my favorite. It is to the Being and Event books what the Prolegomena is to Critique of Pure Reason. It’s a stripped down book of pure ideas without much meditation on their implications. But like the surreal numbers Badiou champions, it’s a dense, dense fabric. It’s the thought process of a genius on full display, but it also gives us a glimpse of Badiou the teacher. What he gives the reader is difficult, but he’s gentle and generous in the delivery. Credit here must also go to Robin Mackay for the beautiful translation.