Topological aspects of combinatorial possibility

Abstract

The aim of this paper is to show that topology has a bearing on combinatorial theories of possibility. The approach developed in this article is “mapping account” considering combinatorial worlds as mappings from individuals to properties. Topological structures are used to define constraints on themappings thereby characterizing the “really possible” combinations. The mapping approach avoids the well-known incompatibility problems. More- over, it is compatible with atomistic as well as with non-atomistic ontologies. It helps to elucidate the positions of logical atomism and monism with the aid of topological separation axioms.