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.