Making Sense, Making Science

4On the Philosophy of Mathematics: Reflections on “Making Science”, Based on Cavaillès

4.1. Mathematics, a precondition of rational philosophy

Why is there a need for this discussion on the philosophy of mathematics, in a framework that seeks above all to celebrate the thinking and cultural sciences? At first glance, this may seem at odds with the purpose of this book, which, in the general field of science, is concerned with what falls within the domain of the human sciences.

In fact, it is a question of reflecting on the question of the academic territorialization of knowledge, which in many respects seems to be non-congruent with the cultural and scientific spaces actually occupied, saturated, or only crossed by this knowledge. The mathematical science curriculum is of course not reducible to the postulate of a science that aims at accuracy.

What can the philosophy of mathematics bring to the thematic perspective Making Sense, Making Science? Perhaps first of all the fact that the heuristic orientation of the field of philosophy of mathematics is already the guarantee of a fruitful disciplinary diversity. What does the philosophy of mathematics do? It is an offshoot of the philosophy of science, and it mainly questions the foundation of mathematics, i.e. its efficiency, its necessity, the degree of existence of the entities that constitute mathematics, the nature of mathematical objects and also the truth in it.

For this brief overview of the question, we will start from ...