Essence as a Modality: A Proof-Theoretic and Nominalist Analysis

Abstract

Inquiry into the metaphysics of essence tends to be pursued in a realist and model-theoretic spirit, in the sense that metaphysical vocabulary is used in a metalanguage to model truth conditions for the object-language use of essentialist vocabulary. This essay adapts recent developments in proof-theoretic semantics to provide a nominalist analysis for a variety of essentialist vocabularies. A metalanguage employing explanatory inferences is used to individuate introduction and elimination rules for atomic sentences. The object-language assertion of sentences concerning essences are then interpreted as devices for marking off structural features of the explanatory inferences that, under a given interpretation, constitute the contents of the atoms of the language. On this proposal object-language essentialist vocabulary is mentioned in a proof-theoretic metalanguage that uses a vocabulary of explanation. The result is a nominalist interpretation of essence as a modality, understood in the grammatical sense as a modification of the copula, and a view of metaphysical inquiry that is closely connected to the explanatory commitments present in first-order inquiry into things like sets, chemicals, and organisms.