The Problem of the Philosophy of Number in Alain Badiou’s Works: A Critical Perspective of François Laruelle’s Non-Standard Philosophy

In this paper, we consider the project of the philosophy of Number proposed by Alain Badiou. In the first part of the work, we discuss the concept of Numbers proposed by Badiou.We argue that such a construction is limited and cannot cover all the concepts of Number. In our work, we try to show that Badiou’s universal concept of Number is unfeasible. As a theoretical basis, we are using Laruelle’s non-standard program which we shall discuss in the third part. We admit that Laruelle’s criticism lacks analysis of the mathematical content of Badiou’s ontology. For this, we discuss two examples: floating point arithmetic and p-adic numbers. Both are extremely important conceptual number systems, which cannot be accommodated by Badiou’s philosophy.