Sets, Set Sizes, and Infinity in Badiou's Being and Event

This paper argues that Cantorian transfinite cardinality is not a necessary assumption for the ontological claims in Badiou’s L’Être et l’Événement (Vol. 1). The necessary structure for Badiou’s mathematical ontology in this work was only the ordinality of sets. The method for reckoning the sizes of sets was only assumed to follow the standard Cantorian measure. In the face of different and compelling forms of measuring non-finite sets (following Benci and Di Nasso, and Mancosu), it is argued that Badiou’s project can indeed accommodate this pluralism of measurement. In turn, this plurality of measurement implies that Badiou’s insistence on the “subtraction of the one”, the move to affirm the unconditioned being of the “inconsistent multiple”, results in the virtuality of the one, a pluralism of counting that further complicates the relationship between the one and the multiple in the post-Cantorian era.