Zeno’s Paradox for Colours

Abstract

Imagine that we proceed along a line through the middle of a disk that is divided into two precisely symmetrical segments, one of which is red, the other green. What happens as we pass the boundary between the two? The paper considers alternative answers to this question, drawing on Franz Brentano's "Philosophical Investigations of Space, Time and the Continuum". The latter provides a theory of boundaries and of related topological notions that is founded not on set theory but on mereology. Brentano's mereotopology is shown to have advantages over standard set-theoretical treatments of the continuum, above all in the representation of perceived qualities and related phenomena.