Organon F 19 (2012), 20-45 © 2012 The Author. Journal compilation © 2012 Institute of Philosophy SAS Towards an Extensional Calculus of Hyperintensions Marie Duží VSB-Technical University, Ostrava Abstract: In this paper I describe an extensional logic of hyperinten- sions, 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 hyperintension- al ones. The received view is that an intensional (let alone hyperinten- sional) context is one that fails to validate transparency, compositional- ity, and quantifying-in; and vice versa, if a context fails to validate these extensional principles, then the context is ‘opaque’, that is non-exten- sional. We steer clear of this circle by defning extensionality for hy- perintensions 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 ramifed type theory enables quantifcation 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 redefnition of, inter alia, functional abstraction and application. The only two non-standard fea- tures of our logic are a hyperintension called Trivialization and a four- place substitution function (called Sub) defned over hyperintensions. Using this logical machinery I propose rules of existential generaliza- tion and substitution of identicals into the three kinds of context. Keywords. Quantifying-in, extensional/intensional/hyperintensional context, transparency, ramifed type theory, transparent intensional logic, extensional rules for three kinds of context. 1 Introduction In this paper I introduce basic fundamentals of an extensional logic of hyperintensions developed within procedural semantics of Transpar- ent Intensional Logic (TIL). Only an extensional logic will validate ex- DSpace VŠB-TUO http://hdl.handle.net/10084/96059 21/1/2014