Abstract
Why think about set theory as part of legal studies? In particular, is there value in reading works by Alain Badiou, such as Being and Event,1 as speaking to law? This is the general question considered by this essay. By “law” I mean to designate juridical law, unless otherwise indicated. Being and Event makes many claims and distinctions. I focus on a few: first, the claim that equates mathematics with ontology; second, the distinction made among the one, the multiple, and multiplicities. In this regard, Badiou observes that traditional western metaphysics conceived of a multiple as dependent on the concept of the one. He identifies the work of mathematician Paul Cohen as providing a conceptual framework for thinking about multiplicities independent of reliance on the concept of the one (i.e. without the need for a prior concept of individuals). Cohen’s innovation was to introduce the technique of “forcing” to prove that the traditional axioms of set theory are consistent with the negation of the continuum hypothesis.4 Previously, Kurt Godel had proved that the traditional axioms of set theory are consistent with the truth of the continuum hypothesis.5 Together, the results of Godel