Towards an extensional calculus of hyperintensions

Abstract

In 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 received view is that an intensional (let alone hyperintensional) context is one that fails to validate transparency, compositionality, and quantifying-in; and vice versa, if a context fails to validate these extensional principles, then the context is 'opaque', that is non-extensional. We steer clear of this circle by defining extensionality for hyperintensions presenting functions, functions (including possible-world intensions), and functional values. The main features of our logic are that the senses of expressions remain invariant across contexts and that our ramified type theory enables quantification over any logical objects of any order into any context. 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 of our logic are a hyperintension called Trivialization and a fourplace substitution function (called Sub) defined over hyperintensions. Using this logical machinery I propose rules of existential generalization and substitution of identicals into the three kinds of context.