# Structure: Multiplicity and Multiple in Deleuze and Badiou

## Abstract

This Chapter attends to multiplicity as structure in Deleuze’s and Badiou’s works, structures that are not articulated according to traditional philosophical conceptions of ‘the many,’ but are rather associated with mathematical paradigms. Bernhard Riemann’s continuous manifoldness and certain of its operational accompaniments inform Deleuze’s work, which I show in his account of the virtual Idea in *Difference and Repetition* and to the account of smooth and striated spaces in Plateau “1440: the Smooth and the Striated” in *A Thousand Plateaus.* Georg Cantor’s distinction of *inconsistent* from *consistent* multiples are at the foundation of Badiou’s ontology; Zermelo’s axiom of separation solves a problem (crystallized in Russell’s Paradox) about any possible relation between inconsistent and consistent multiples. Badiou’s work in *Being and Event* and a short description of inconsistent multiplicity in *Briefings on Existence* are the texts under investigation here.

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