Finitist set theory in ontological modeling

Article type: Research Article

Authors: Styrman, Avril^{a; b; *} | Halko, Aapo^c

Affiliations: [a] The Finnish Society for Natural Philosophy, Helsinki, Finland | [b] Physics Foundations Society, Espoo, Finland | [c] Department of Mathematics and Statistics, University of Helsinki, Finland

Correspondence: [*] Corresponding author. E-mail: [email protected]; Tel.: +358407000589.

Note: [] Accepted by: Michael Gruninger

Abstract: This article introduces finitist set theory (FST) and shows how it can be applied in modeling finite nested structures. Mereology is a straightforward foundation for transitive chains of part-whole relations between individuals but is incapable of modeling antitransitive chains. Traditional set theories are capable of modeling transitive and antitransitive chains of relations, but due to their function as foundations of mathematics they come with features that make them unnecessarily difficult in modeling finite structures. FST has been designed to function as a practical tool in modeling transitive and antitransitive chains of relations without suffering from difficulties of traditional set theories, and a major portion of the functionality of discrete mereology can be incorporated in FST. This makes FST a viable collection theory in ontological modeling.

Keywords: Transitivity, intransitivity, non-transitivity, antitransitivity, mereology, finitist set theory, levels, ur-elements, aggregates, sets, computability, collection theory, layer-cake interpretation, vertical-horizontal composition, nested structures

DOI: 10.3233/AO-180196

Journal: Applied Ontology, vol. 13, no. 2, pp. 107-133, 2018