Russell and Wittgenstein on Incongruent Counterparts and Incompatible Colours

Abstract

Russell (in Principles of Mathematics) and Wittgenstein (in Tractatus Logico-Philosophicus) largely agree on the twin questions of why pairs of congruent objects cannot always be made to coincide and why surfaces can never be uniformly two colours at once. Both philosophers take space and colour to be mathematically representable, construe the relevant impossibilities as mathematical and hold that mathematical impossibility is at root logical. It is not by chance that Russell says nothing about the phenomena in his Introduction to the Tractatus or surprising that Wittgenstein was unmoved by the objection that his account of colour incompatibility puts paid to his early philosophy.