Mathematics and the Theory of Multiplicities: Deleuze and Badiou Revisited

Deleuze once wrote that “encounters between independent thinkers always occur in a blind zone,” and this is certainly true of the encounter between Badiou and Deleuze.In 1988, Badiou published his book Being and Event, which attempted to develop an “ontology of the multiple” derived from the mathematical model of axiomatic set theory.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 multiplicities,”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 its introduction, was occasioned by an 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 multiple.”On the opening page of the book, Badiou notes that “Deleuze’s preferences were for differential calculus and Riemannian manifolds . . . [whereas] I preferred algebra and sets”—leading 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 announced intention, the book does not contain a single discussion of Deleuze’s theory of multiplicities; it avoids the topic entirely.