Abstract

The perception of spatial bodies is at least in part a perception of bodily boundaries or surfaces. The usual mathematical conception of boundaries as abstract constructions is, however, of little use for cognitive science purposes. The essay therefore seeks a more adequate conception of the ontology of boundaries building on ideas in Aristotle and Brentano on what we may call the coincidence of boundaries. It presents a formal theory of boundaries and of the continua to which they belong, of a sort which allows a resolution of certain Zeno-style paradoxes. The theory proves to be applicable not only in the cognitive science field but also in regard to problems relating to the ontology of geographical and geopolitical boundaries.