The Ontological Triangle
by
Ingrid M Rewitzky
Department of Mathematics and Applied Mathematics, University of Cape Town, South Africa
Coauthors: Chris Brink (University of Wollongong, Australia)

Like many other topics in philosophy and logic, ontology has made its way into new domains of discourse, pulled along by the demands of computing science and information technology. In this paper we address the relationship between an ontology of individuals (nominalism), an ontology of properties (realism), and an ontology of facts (factualism). We demonstrate that in at least one mathematical context, these three ontologies are dual to each other, meaning that each ontology can be translated into, and recaptured from, each of the others. The technicalities are based on a well-established topological paradigm of inter-translatability between logic, algebra and semantics. Suitably adapted and re-interpreted, this leads us to posit an ontological triangle of factualism, realism and nominalism, each of which is essentially equivalent to the others, and none of which has any ontological priority.

Date received: May 16, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagw-56.