수학적 존재론과 철학 : 알랭 바디우의 『존재와 사건』에 대한 수학적 비판에 대한 답변

Abstract

Alain Badiou’s Being and Event develops an ontology based on the axiomatic set theory. Polish mathematician Maciej Malicki criticized the book for its mathematical flaws. However, most of Malicki’s critiques stem from a misunderstanding of Badiou's philosophical project, and some critiques can be sufficiently answered in the set theory. Malicki’s critique can be divided into three points. The first one is a critique on Badiou's concept of discernible. According to him, Badiou defines this concept in three ways in Being and Event, of which the second and third definitions are unacceptable, and the first is too narrow. We think the first definition is quite acceptable. The second is a critique on the concept of undecidable and of evental site; he argues that accepting evental site mathematically requires abandoning either the occurrence of an event in a situation or the creation of a truth(a generic extension). However, this concept is not a mathematical concept, but rather a concept on the border between mathematics and philosophy, and the generic extension in historical circumstances can be explained by the Mostowski Collapsing Theorem. The last critique is about the unnameable: Malicki argues that there should only be one unnameable in a situation, whereas Badiou has two, but the two concepts Malitzki pointed out are in fact different names for the same object.