Logic and Intuition

Abstract

Poincaré is often called a ‘pre-intuitionist’ or a’ semi-intuitionist’ because he influenced the foundations of intuitionism in the philosophy of mathematics. Intuitionism is a form of constructivism; and constructivism is the general view that mathematical objects (numbers, domains and so on) are mental constructions. That is, it is the view that mathematical objects have no existence independent of the minds of mathematicians. Poincaré was certainly a constructivist, but whether or not he can be grouped with the intuitionists needs to be made clear. And this leads to the further question: if he cannot be grouped with the intuitionists, is his ‘constructivism’ coherent and defensible?