Extensional Logic of Hyperintensions

Abstract

AbstractIn this paper I describe an extensional logic of hyperintensions, viz. Tichý’s Transparent Intensional Logic (TIL). TIL preserves transparency and compositionality in all kinds of context, and validates quantifying into all contexts, including intensional and hyperintensional ones. The availability of an extensional logic of hyperintensions defies the received view that an intensional (let alone hyperintensional) logic is one that fails to validate transparency, compositionality, and quantifying-in. The main features of our logic are that the senses and denotations of (non-indexical) terms and expressions remain invariant across contexts and that our ramified type theory enables quantification over any logical objects of any order. The syntax of TIL is the typed lambda calculus; its semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The only two non-standard features are a hyperintension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hyperintensions.KeywordsQuantifying-inextensional/intensional/hyperintensional contexttransparencyramified type theorytransparent intensional logicextensional logic of hyperintensions