Pratique mathématique et lectures de Hegel, de Jean Cavaillès à William Lawvere

Abstract

Concepts of both paradigm and thematization, through which Jean Cavaillès describes the dynamics of mathematical activity, in the posthu-mous book Sur la Logique et la théorie de la science, find in the category theory an illustration as well as a formalization, and find too a precedent in the Hegelian dialectic. First, we will examine this assumption and will also make sure to define, as a basis for our later development, the concept of thematization and some basic notions of category theory. In supposing then as Hegelian the notion of ’dialectic’ used by Cavaillès, we will check if the concept of ’thematization’ can claim to describe the Hegelian interpretation’s dialectical process. This kind of interpretation can be found in William Lawvere’s writings. Finally, we will put the interpretation to the test in analyzing the Hegelian dialectic about being and nothingness in the Science of Logic and the Lectures on the History of Philosophy. Consequently we will see how the Hegelian dialectic can, in the same time, describe the mathematical practice and be represented by it.