The burden of proof is upon Badiou from the moment that another system exists that has 15 modes of veridiction. The pro-Badiousian jury has no jurisdiction except inside its own paradigm. I am speaking of the form of the paradigm and finding it wanting. The answer that “noone has ever made us a plausible case for accepting another candidate” is circular.
The “other candidates” are being usefully employed elsewhere, that is enough to show up the limitations. In other words if jury there were, it would be Badiou’s system on the docks of the pluralist court. Fortunately the metaphors of the tribunal or of the job interview are not pertinent to an attempt at democratic dialogue.
Once again, it is not a question of being for or against “four” or “two”, nor is it a question of forcibly importing alien “procedurish-looking things” into Badiou’s system. My worry is over the reflexive elevation, perennisation and legitimation of a rather quirky selection of truth procedures to the status of the only possible configuration of the contemporary situation of truths.
Badiou falls into a form essentialism. For example, the matheme is not the same thing as the science of mathematics, but constitutes their pretended speculative essence. From a materialist point of view this can only correspond to the extraction from a heterogeneous assemblage of one tendency placed above all its other elements as their unitary hegemonic essence.