One of the most attractive, problematic, and astonishing features of Badiou’s ontology is his strictly extensional understanding of sets or multiplicities. A set is not defined by its members sharing a common predicate or quality, nor by the relations among members of the set. Rather, a set is defined strictly by its extension or the members that belong to that set. From the standpoint of 20th Century French and German Continental philosophy, this thesis cannot but be a heresy, for the predominant trend in Continental thought has been a relational conception of entities. Whether we are speaking of language as a diacritical set of negative oppositions as defended by the structuralists and the post-structuralists, or Heidegger’s being-in-the-world where entities, the ready-to-hand, are defined by the relational networks to which they belong, the predominant trend has been to treat beings as bundles of relations such that the entity is nothing apart…