Décisions métaphysiques de la Science et Critique générale de la Raison Pure : le pluralisme inachevé de La Philosophie de l’algèbre

Abstract

In the Introduction to the first volume of La Philosophie de l’algèbre, Vuillemin first gives a preliminary definition of what he means by pure mathematics and the theory of knowledge and then explains his task. He intends to study the important question of the possibility of pure knowledge and of the method of philosophy. When the histories of mathematics and philosophy are considered comparatively, they show clearly how methodological changes in mathematics always have deep consequences on philosophy. According to Vuillemin, modern mathematics induce a methodological renewal that essentially concerns notions of structure, infinite and logic through a movement that exceeds, prolongs and generalizes the achievements of classical mathematics. The second volume of La Philosophie de l’algèbre was intended to show how to define a new method for theoretical philosophy. We will try to show how the last chapter of the first volume contains inherent difficulties which led to the abandonment of the project and how the idea of pluralism outlined therein requires a complete conceptual renewal that Vuillemin would only provide more than twenty years later.