Intentional Paradoxes and an Inductive Theory of Propositional Quantification

Quantification over propositions is a necessary component of any theory of attitudes capable of providing a semantics of attitude ascriptions and a sophisticated system of reasoning about attitudes. There appear to be two general approaches to propositional quantification. One is developed within a first order quantificational language, the other in the language of higher order logic. The first order theory is described in Asher & Kamp (1986), Asher (1988), Asher and Kamp (1989). This paper concentrates on propositional quantification in a higher order framework, the simple theory of types. I propose a method of resolving difficulties noticed by Prior and Thomason with propositional quantification. The method borrows from Kripke's (1975) defintition of truth and results in a partial logic, which I call the simple theory ofpartial types (SPT). SPT offers a tractable, complete logic (with respect to general models) that includes propositional quantification, accomodates a semantics of the attitudes that avoids logical omniscience, and allows for some self-reference.