On the Definability of Leśniewski’s Copula ‘is’ in Some Ontology-Like Theories

Marcin Łyczak; Andrzej Pietruszczak

doi:10.18778/0138-0680.47.4.02

Authors

Marcin Łyczak Cardinal Stefan Wyszyński University, Institute of Philosophy, Department of Logic
Andrzej Pietruszczak Nicolaus Copernicus University in Toru´n, Department of Logic

DOI:

https://doi.org/10.18778/0138-0680.47.4.02

Keywords:

elementary ontology, quantifier-free fragment of ontology, ontology-like theories, copula ‘is’, calculus of names, Leśniewski's ontology, subtheories of Leśniewski’s ontology

Abstract

We formulate a certain subtheory of Ishimoto’s [1] quantifier-free fragment of Leśniewski’s ontology, and show that Ishimoto’s theory can be reconstructed in it. Using an epimorphism theorem we prove that our theory is complete with respect to a suitable set-theoretic interpretation. Furthermore, we introduce the name constant 1 (which corresponds to the universal name ‘object’) and we prove its adequacy with respect to the set-theoretic interpretation (again using an epimorphism theorem). Ishimoto’s theory enriched by the constant 1 is also reconstructed in our formalism with into which 1 has been introduced. Finally we examine for both our theories their quantifier extensions and their connections with Leśniewski’s classical quantified ontology.

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