Abstrakt
Badiou's philosophy draws upon mathematics as its scientific condition. The "axiomatic decision" for mathematics can be interpreted as a historically conditioned choice responding to contemporary sophistry that dismissed the concept of truth.
However, various sections of mathematics (set theory, category theory, and theory of great cardinals) are selected for a condition of philosophy to become. This multi-conditioning is a symptom of a lacuna in Badiou's philosophy that emerged with relating philosophy to this or that section of mathematics.
The lacuna is explained with Easton's theorem as the effect of the relation between philosophy (metastructure) and a section of mathematics (the presented situation). Easton's theorem indicates ontological limits of mathematics.
The door is open for the relating of philosophy to non-mathematical science (Marxism and Lacanian psychoanalysis).