Badiou's Number: A Critique of Mathematics as Ontology

Abstract

1. Being and Event When an English translation of Being and Event appeared in 2005, Alain Badiou took the opportunity to reminisce about the initial French publication some twenty years before: “at that moment I was quite aware of having written a ‘great’ book of philosophy.” He located that greatness in four “affirmations” and one “radical thesis.” Affirmation one: “Situations are nothing more, in their being, than pure multiplicity.” Two: “The structure of situations does not, in itself, deliver any truths. By consequence, nothing normative can be drawn from the simple realist examination of the becoming of things. . . . A truth is solely constituted by rupturing with the order which supports it, never as an effect of that order.” This type of truth-constituting rupture Badiou calls “the event.” Three: “A subject is nothing more than an active fidelity to the event of truth.” Four: “The being of a truth, proving itself an exception to any pre-constituted predicate of the situation in which that truth is deployed, is to be called ‘generic.’” A truth is a “generic procedure. And to be a Subject (and not a simple individual animal) is to be a local active dimension of such a procedure.” Finally, the “radical thesis”: “Insofar as being, qua being, is nothing other than pure multiplicity, it is legitimate to say that ontology, the science of being qua being, is nothing other than mathematics itself.”2 The thesis is indeed radical. Using language borrowed from set theory (Georg Cantor’s multiplicity, Paul Cohen’s generic) Badiou is, throughout, asserting that sets and their properties are there, regardless of whether