Subject and Set Theoretical Foundations of Subject in Badiou's Thought

Abstract

Frege's project to reduce arithmetic to logic and the development of axiomatic set theory to eliminate the paradoxes that emerged in this Project and the changes caused by attempts to prove Cantor's continuum hypothesis within the boundaries of axiomatic set theory have also transformed the way of making philosophy. One of the thinkers that this transformation can be followed is Alain Badiou. According to him, in the classical way of thinking, there is no explanation for a new thought to be born out of the truth regime with an event. Neither in Plato and Aristotle nor in Kant can there be a place for the process of such an incident and the subjectivation of a person loyally attached to this event. But Badiou, who claims that set theory is the new ontology, thinks that this ontology makes room for the subject and has the opportunity to explain how it is possible. Badiou argued that people who were the perpetrators of the coming of a new truth into existence, who faithfully connected humanity to events that carried humanity to a new historical moment by changing politics, science and art, became the subject of being separated from the animal-human. Based on this subject theory, while grounding the historical of man, it paved the way for proposing brand new theses in the field of ethics and politics.