The Color-Exclusion Problem Revisited

Abstract

It is impossible for two different colors to occur at the same place simultaneously.
Therefore if a simple color-statement that ascribes a color to a spatio-temporal
location is true, then any simple color-statement that ascribes another color to the
same spatiotemporal location cannot be true. But Wittgenstein's Tractatus
logico-philosophicus (TLP) requires that elementary propositions must be logically
independent of each other (I'll call this "Independence Requirement"). Thus the
Independence Requirement seems to conflict with the impossibility of simultaneous
presence of different colors at the same place. This color-exclusion problem has been
thought to be one of the main reasons why such a simple color-statement cannot be
elementary proposition of TLP.

In this paper I shall show that such a simple color-statement can be
analyzed into a truth-function of elementary propositions that are logically
independent of each other. This means that we can construct a system of
color-descriptions which satisfies the Independence Requirement, and it will turn out
that our system of color-descriptions given below reflects "the logical structure of
color" (TLP 6.3751) fairly well.