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Matheme and mathematics. On the main concepts of the philosophy of Alain Badiou

In this paper, I present a critical discussion of mathematical arguments employed in the philosophy of event of Alain Badiou. On the basis of "Being and Event" as well as his other writings, I analyze the main notions of his philosophy such as the indiscernible, the undecidable, and the unnameable. The focus of my analysis is both on their mathematical consistency, and their philosophical consequences. I argue that the mathematical approach developed by Badiou is seriously defective, and, as a result, that it cannot serve as an ontological basis for the concept of event as presented in "Being and Event".