An Axiomatization of the Thomasic Ontology of Composition

Abstract

This treatise delves into the construction and formalization of a precise theory to encapsulate a pivotal facet of Thomas Aquinas’s ontology. In particular, it focuses on the development of a formal language that is adequate for formulating Aquinas’s understanding of the simultaneous nature of divinity as both an object of subsistence and a universal, individual, and actuating form—a concept evocative of the original Platonic sense of form. The presented axiomatized theory as a medium for expounding the ontological principles enunciated by Thomas Aquinas. A comprehensive set of axioms is systematically justified, exhibiting their congruence with Aquinas’s ontological doctrines. To elucidate this harmony, an extensive series of theorems is deduced, closely aligned with the verbal tenets of Aquinas’s teachings. The inherent consistency of the axiom system is proven by the provision of a geometrico-topological model tailored to support it.