The skeptical reader may still be wondering, How exactly does the mathematical discourse relate or apply to the actual, material situations it purports to describe? How precisely do we move from the purely void-based multiples presented in ontology, which are all “qualitatively very indistinct,” to the qualitative variety of historical situations? To be sure, we know that Badiou “in no way declares that being is mathematical, that is, composed of mathematical objectivities.” Nevertheless, his conviction is that the substance of material or historical situations offers no significant resistance to their mathematization, and that insofar as they can be thought, all situations are to be subtracted from the uncertain domains of substance, perception, and the object.
Badiou: A Subject To Truth. p 105