Brian Anthony Smith
Abstract: This essay is an examination of the limits of the model of the subject that Badiou establishes in Being and Event. This will concentrate on both Being and Event, and the later ethical developments introduced in Ethics: An Essay on the Understanding of Evil. My aim will be to show that there is a possible subjective figure, based on the independence of the Axiom of Choice, which remains unexamined in both these works. The introduction of this new subjective figure not only complicates Badiou’s ethical categories of Good and Evil, but it also raises questions about the nature of the subject in general in his philosophy.
Keywords: Badiou; Axiom of Choice; Subject; Individual; Non-constructible Sets; Temporality
The figure of the subject in Badiou’s Being and Event is key to understanding the link between his revival of a systematic ontology, in the form of set theoretical mathematics, and his wider philosophical and ethical concerns. Through a critical examination of the subject, as it appears in Being and Event, and an evaluation of the categories of subjective Good and Evil, developed in his book Ethics: an Essay on the Understanding of Evil, I hope to probe the limits of this subjective model and to propose a new subjective figure that appears possible, but unexamined, in either of these works.
My analysis will focus on two main points: first, Badiou’s use of the Axiom of Choice, as a key factor in his philosophy that allows for the possibility of a subject, and, second, his selective use of set theoretical forcing, which concentrates mainly on the independence of the Continuum Hypothesis.
Badiou’s ethics is based on the capacity of individuals to distinguish themselves from their finite animal nature and to become immortal; to become immortal is to become a subject (E 12, 132). What constitutes this singular ability, our rationality, is the use of mathematics (E 132). Specifically it is the Axiom of Choice that elevates the human animal to the level of a potential subject. This axiom expresses an individual’s freedom, a freedom equivalent to the affirmation of pure chance.  It is this capacity that allows an individual to affirm its chance encounter with an event; the moment of this affirmation is called intervention and marks the birth of a subject (BE Meditations 20 and 22).
The importance of the Axiom of Choice is clear; it provides the connection between the individual, the event and the subject. It defines the individual and provides the condition under which subjectivity is possible.