HIGHER-ORDER ESSENCES: LOGIC AND SEMANTICS

Abstract This paper develops a logic of essence ( HLE ) in the framework of higher-order logic. The theory aims to provide a general framework for theorizing about the essences of objects, properties, propositions, and logical operations like conjunction, negation, quantification, etc. The first part of the paper presents the formal language and axiom system of HLE . After that, some theorems of the system are proved and it is shown how the logic of metaphysical necessity can be developed within the framework of HLE . The second part of the paper develops a possible worlds semantics for HLE , gives a proof of soundness, and provides examples of models that demonstrate the consistency of some simple essentialist theories.