Poincaré's Conception of the Objectivity of Mathematics†

摘要

There is a basic division in the philosophy of mathematics between realist,‘platonist’theories and anti-realist‘constructivist’theories. Platonism explains how mathematical truth is strongly objective, but it does this at the cost of invoking mind-independent mathematical objects. In contrast, constructivism avoids mind-independent mathematical objects, but the cost tends to be a weakened conception of mathematical truth. Neither alternative seems ideal.The purpose of this paper is to show that in the philosophical writings of Henri Poincaréthere is a coherent argument for an interesting position between the two traditional poles in the philosophy of mathematics. Relying on a semi-Kantian framework, Poincarécombines an epistemological and metaphysical constructivism with a more realist account of the nature of mathemati