Alain Badiou’s work has in many ways set the terms on which the relation between mathematics and philosophy is conceived today within contemporary European philosophy. Badiou attempts an asymptotic approach to contemporary mathematics from within set theory, setting up a division between set theory as ‘real mathematics’ and category theory as mere ‘logic’, between the ‘strong’ singularity of ontological decision and the ‘weak’ elucidation of possible choices. I wish to interrogate this reduction, focussing on a argument of Badiou’s contrasting the singularity of the void (as sign) in set theory with the ‘equivocal’ void of category theory: the empty diagram.