What does Badiou's philosophy offer the philosopher? He has developed a compelling array of concepts that militants, whether political or scientific, amorous or artistic, can apply to their disciplines in order to see them in new light. Crucially, the utility of Badiou's philosophy for each of these practices, scholarly and militant, owes much to its foundation on a series of axiomatic decisions. The abruptness of its axiomatic base grants the scholar a freedom to examine it as self-contained system, logically isolated from its exterior, yet also gives it its remarkable mobility, letting it be transported and applied to domains quite foreign to those of its initial construction.

This coupling of autonomy and mobility is precisely what the pioneers of the axiomatic method sought through the axiomatization and formalization of mathematics.