The Logic of the Ontological Square

Abstract

The Ontological Square is a categorial scheme that combines two metaphysical distinctions: that between types (or universals) and tokens (or particulars) on the one hand, and that between characters (or features) and their substrates (or bearers) on the other hand. The resulting four-fold classification of things comprises particular substrates, called substances, universal substrates, called kinds, particular characters, called modes or moments, and universal characters, called attributes. Things are joined together in facts by primitive ontological ties or nexus. This article describes a logic that is meant to capture the basic intuitions behind the Ontological Square. Given a minimal correspondence between atomic logical form and ontological structure, the commitment to nexus as a distinct ontological category entails a rehabilitation of copulae as ties of predication. Thus, the Logic of the Ontological Square is a copula calculus rather than a predicate calculus; its soundness and completeness can be established with respect to a model akin to a so-called first-order semantics for standard second-order logic.