Philosophical Pragmatism in Poincare

Abstract

At the beginning Poincaré is using the terms ‘intuition’ and ‘analysis’ in order to describe two psychological attitudes invoived in the logic of invention: Riemann and Klein represent the attitude of intuition, Hermite and Weierstrass the attitude of analysis. Later on, but usually without explicit indication, these two terms stand likewise for two theories about the nature of mathematical activity: on the one hand you concentrate on investigations into the conditions governing the construction (intuition) of mathematical objects, on the other hand you try to describe (analyze) domains of already existing objects.

This paper, written originally in French, was delivered as a lecture at the University of Aix-en-Provence in October 1985; it derives from an attempt to improve on chapter II of my book: Entre intuition et analyse. Poincaré et le concept de prédicativité, Paris 1985.