Mathematics and the Theory of Multiplicities: Badiou and Deleuze Revisited

Deleuze once wrote tha t “encounters between independent thinkers always occur in a blind zone,” and this is certainly true of the encounter between Alain Badiou and Gilles Deleuze.’ In 1988, Badiou published Being and Event, which attempted to develop an ”ontology of the multiple” derived from the mathematical model of axiomatic set theory.2 Soon afterward, he tells us, he realized-no doubt correctly-that his primary philosophical rival in this regard was Deleuze, who similarly held that “philosophy is a theory of m~ltiplicit ies,”~ but whose own concept of multiplicities was derived from different mathematical sources and entailed a different conception of ontology itself. In 1997, Badiou published a study of Deleuze entitled Deleuze: The Clamor of Being, in which he confronted his rival directly and attempted to set forth their fundamental differences. The study, Badiou tells us in the introduction, was occasioned by a n exchange of letters he had with Deleuze between 1992 and 1994, which focused directly on the concept of “multiplicity” and the specific problem of “an immanent conceptualization of the m~l t ip l e . ”~ On the opening page of the book, Badiou notes tha t ”Deleuze’s preferences were for differential calculus and Riemannian manifolds ... [whereas] I preferred algebra and setsn5-1eading the reader to expect, in what follows, a comparison of Deleuze’s and Badiou’s notions of multiplicity based in part, at least, on these differing mathematical sources. Yet as one reads the remainder of Deleuze: The Clamor of Being, one quickly discovers that Badiou in fact adopted a quite different strategy in approaching Deleuze. Despite the