Singular Terms, Quantification, and Ontology I

Abstract

A central working assumption of the present essay is that at least most of us embrace actualism -the view that there neither are nor could have been objects that do not actually exist.1 Relative to this assumption, my aim is to determine what sort of quantification theory should accompany the actualist ontological stance. To facilitate matters, I shall confine the discussion to just three principal approaches to quantificational logic: Substitutional Quantification. By this view, a universal generalization (VX)B is true if and only if all of its substitution-instances are true, and an existential generalization (3X)B is true just in case at least one of its substitution-instances is true. In addition, the variables of substitutional quantification will have substituends but perhaps no values; that is, B(T/X) may be true and a genuine substitution-instance of (VX)B and (3X)B even though T is nonrefer-