The Limits of The Subject in Badiou’s Being and Event
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.
Badiou’s appeal to Paul Cohen’s theory of forcing is predominately directed toward his proof of the independence of Georg Cantor’s Continuum Hypothesis. But in Cohen’s book, Set Theory and the Continuum Hypothesis, the method of forcing is used equally to prove the independence of the Axiom of Choice. For Badiou, the Continuum Hypothesis is a restrictive theorem of ontology; it confines ontology to the merely constructible and neuters the individual by reducing the power of the Axiom of Choice (BE Meditations 28 and 9). Under such a restriction the Axiom of Choice loses its independence as an axiom and becomes a theorem, a mere consequence of the system (BE 305-7). Cohen’s theory of forcing is important as it shows that it is possible to construct a model of set theory in which the Continuum Hypothesis fails, thus liberating us from its restrictive bonds. In the process it not only reinstates the full power of the Axiom of Choice, the freedom of the individual, but also, through the use of this axiom, a subject emerges.
The mathematical theory of forcing, as it is applied to the Continuum Hypothesis, provides Badiou with the paradigmatic model for the subjective response to an event. The subjective process emancipates the individual, through a correct use of their freedom in the face of an event, from some restrictive condition of their situation. This production of a truth introduces true novelty that expands, or extends, the subject’s situation. This forms the basis of Badiou’s theory of ethics. Subjective endeavour, forcing the truth of an event, forms the positive concept of the Good and ‘It is from our positive capability for Good… that we are to identify Evil’ (E 16). The range of types of Evil can be identified with false, abortive or totalizing activities that try to subvert a truth procedure, the Good being the practice of the virtues of discernment, courage and moderation (E 91). The subject remains faithful to the event and its consequences.
The clarity and decisive character of Badiou’s ethics is refreshing, but is it the case that the subject is always intrinsically good? What would happen if we examined the consequences of a valid subjective process, based on the mathematical model of forcing, which instead of liberating an individual, in the process of their subjective action, condemned them? I think the independence of the Axiom of Choice provides such an occasion. What would be the consequences of forcing a situation in which the Axiom of Choice fails, in which the freedom of the individual is denied and the competence of the subject questioned?