On the Mathematical Foundation of Alain Badiou’s Philosophical Thoughts

Badiou considers that mathematics is an ontology and a science of being qua being. Based on modern analytical philosophy and later thoughts of Heidegger, he creates his own ontology. The mathematical foundation of Badiou's philosophical thoughts originates from the set theory of Cantor and Paul Cohen. Integrating the thoughts of Sartre and the doctrine of Anglo-Saxon school represented by Wittgenstein, Badiou proposes a conception of "situation", which refers to the place that event happens and a field of multiplicity. According to the difference between set and power set, he divides structure into situation and state of situation, and he finally creates his special philosophical thoughts by grafting set theory on philosophy. Badiou reckons Heidegger doesn't distinguish mathematics from science, while what he engages in is to surpass the anti-science thoughts of Heidegger.