On the Paradoxical Nature of Surfaces: Ontology at the Physics/Geometry Interface

Antony Galton

In The Monist, special issue on Lesser Kinds (ed. Roberto Casati and Achille Varzi), Volume 90, Number 3 (July 2007), pages 380-390.

Abstract

Surfaces are paradoxical because, on the one hand, they appear to be material objects (as when we speak of a surface as being rough, shiny, soft, or wooden) but on the other hand they do not appear to occupy any volume. It is proposed that, first, we must distinguish between the surface qua object (a physical surface) from the surface qua location (a mathematical surface), and second, that the former is related to the latter by a type of location relation, called 'anchoring', which, unlike strict location, can be applied to objects whose boundaries are partly or wholly indeterminate.

Antony Galton

Last modified: Tue Jun 17 13:38:47 BST 2008