forthcoming, in G.S. Ciola, M. Crimi, and C. Normore (eds.), Existence and Nonexistence in the History of Logic, Open Philosophy, 8(1), Berlin: de Gruyter.
In this paper, I show how two modes of predication and quantification in a modal context allow one to (a) define what it is for an individual or relation to exist, (b) define identity conditions for properties and relations conceived hyperintensionally, (c) define identity conditions for individuals and prove the necessity of identity for both individuals and relations, (d) derive the central definition of free logic as a theorem, (e) define the essential properties of abstract objects and provide a framework for defining the essential properties of ordinary objects, and (f) derive a theory of truth. I also describe my indebtedness to the work of Terence Parsons, and take the opportunity to advance the discussion in connection with an objection raised to the theory of essential properties.