Following in the spirit of book reviews written about books that do not exist, I offer here -- no doubt at my own peril -- a series of observations in anticipation of Alain Badiou’s forthcoming Being and Event 3: The Immanence of Truths, a book that does not yet exist but will exist at some point in the future.
1. Alain Badiou has been interested in poetry and literature throughout his long career. Yet in recent years he seems to be turning more closely to poetry. Such a turn presents something of a problem for Badiou, a Platonist, given Plato’s skepticism toward poetry and concomitant preference for mathematics. But what is poetry? And what is math? For Badiou poetry is a marker for the event, for life, for the real, for what Jacques Lacan called “the impossible.” By contrast, mathematics is the space of the precise letter, of argument, of proof, of learning and training (after the original Greek meaning of mathēsis), of formal abstraction in its most rigorous articulation. Already notorious for his defense of mathematics as ontology, Badiou has become a bit more evenhanded on the question of the matheme versus the poem, preferring instead to describe philosophy as poised “between” poetry and mathematics, not simply privileging the latter.
2. In its essence, poetry is an attempt to touch the real continuum of life. And, as Badiou argues, there is no poem that does not in some basic way describe an event. While at the same time mathematics is an attempt to abstract away from the real continuum into the realm of consistency, name, rule, and identity. Still, the contrast is perhaps overstated. Poetry is impossible to define in its totality without reference to rule and rhythm, figuration and abstraction. Likewise mathematics spans both domains. There has existed since the ancients a mathematics of the real continuum as well as a mathematics of the proper name and rule. The former is a mathematics of pure difference while the latter a mathematics of pure identity; the former a math of time -- indeed directly in time -- while the latter formalizes time to a sufficient degree as to be able to purge it entirely, replacing time with space.