Transparent quantification into hyperpropositional contexts de re

Abstract

This paper is the twin of (Duzí and Jespersen, in submission), which provides a logical rule for transparent quantification into hyperpropositional contexts de dicto, as in: Mary believes that the Evening Star is a planet; therefore, there is a concept c such that Mary believes that what c conceptualizes is a planet. Here we provide two logical rules for transparent quantification into hyperpropositional contexts de re. (As a by-product, we also offer rules for possible-world propositional contexts.) One rule validates this inference: Mary believes of the Evening Star that it is a planet; therefore, there is an x such that Mary believes of x that it is a planet. The other rule validates this inference: the Evening Star is such that it is believed by Mary to be a planet; therefore, there is an x such that x is believed by Mary to be a planet. Issues unique to the de re variant include partiality and existential presupposition, substitutivity of co-referential (as opposed to co-denoting or synonymous) terms, anaphora, and active vs. passive voice. The validity of quantifying-in presupposes an extensional logic of hyperintensions preserving transparency and compositionality in hyperintensional contexts. This requires raising the bar for what qualifies as co-denotation or equivalence in extensional contexts. Our logic is Tichy’s Transparent Intensional Logic. The syntax of TIL is the typed lambda calculus; its highly expressive semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The two non-standard features we need are a hyperintension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hyperintensions.