Properties, Predication, and Arbitrary Sets

Abstract

Shapiro and Hale disagree over the appropriate domain of quantification for second-order logic: Shapiro allows property variables to range over the full power set of the first-order domain, whereas Hale restricts the domain to only subsets which can be defined. Hale defends his view, via a discussion of Shapiro’s view that objects in a domain of quantification need not be able to be objects of singular reference (for example, geometrical points and electrons). Shapiro’s view is clearly at odds with Hale’s favoured broadly Fregean approach to ontology, according to which objects are simply those things to which reference may be made by means of actual or possible singular terms.