WHAT HAS PHILOSOPHY GOT TO DO WITH MATHEMATICS?

Abstract

This paper explores the philosopher's interest in mathematics. While it is a statement of fact that T philosophers and mathematicians, for the most part, agree with the thesis that there exists some connection between these disciplines, it remains to show what type of relationship exists between them. The paper argues that while philosophy assumes the second-order function in its relations to mathematics and questions the basic assumptions, axioms, and theorems of mathematics, there is a sense in which philosophy does not tell the mathematician what to do or not. We contend that after exposing the low points of the basic assumptions and axioms of mathematics, the onus lies exclusively on the mathematicians to either make changes to their system or remain sacrosanct. In the final third, the paper appraises the three basic schools in the philosophy of mathematics—logicism, formalism, and intuitionism. The paper finds out that, though these schools are seen as grounding for mathematics, Gödel's incompleteness theorem suggests that none of them is philosophically viable. Thus, we conclude that, regardless of the shortcomings and the inability of the aforementioned schools to successfully provide the foundation for mathematics, these schools have helped raise questions and sustained discourses in the philosophy of mathematics.