The Proper Treatment of Predication in Fine-Grained Intensional Logic

Abstract

1 PRPs and Possible Worlds In the not-too-distant past, intensional entities -properties, relations, and propositions (PRPs)-were generally regarded as, at best, obscure. At worst they were shunned as creatures of darkness [12, p. 186], disreputable, shadowy entities against which the clear-headed philosopher maintained a vigilant watch, lest they steal unobserved into some unlit corner of his ontology. Times have changed. While their acceptance is hardly universal, PRPs are now standard fare in the philosophical marketplace. There are at least two good reasons for this. First, those who rejected intensional entities found themselves unable to provide theoretically adequate, let alone intuitively appealing, accounts of the logic and semantics of certain pervasive constructions of natural language. Most notable among these, of course, are intensional contexts, i.e., those linguistic contexts in which extensionally valid forms of inference appear to fail. By contrast, admitting intensional entities into one's ontology readily allowed far simpler and more intuitive explanations of these phenomena. Second, and more important, was the development of possible world semantics. This development had a twofold impact. First, the apparatus of possible world semantics -in particular, its rendering of PRPs -provided a rigorous formal foundation for an intensional logic replete with PRPs that bucked the charge of obscurity leveled by the extensionalists. Second, metaphysics itself was rejuvenated. The credibility won by the sheer power of the theory moved philosophers and logicians to confront and refurbish a host of issues that had been consigned to the philosophical scrap heap: possible worlds, possibilia, essence and accident, necessary truth, and so on. In this rich metaphysical milieu, the extensionalist prejudice against the intensional realm lost its influence.