In slogan form, the view that I will try to explain and defend in this talk is that "the meaning of a term is an algorithm which computes its denotation"; somewhat less flippantly, it is claimed that the meaning of a grammatically correct linguistic expression A can be faithfully modeled by its "referential intension", a (possibly infinitary, not necessarily implementable) process which computes the denotation of A. This is a structural, compositional, and basically Fregean view of meanings, although not necessarily an accurate explication of Frege's views.
Referential Intensions are set-theoretic objects, precisely defined for fragments of language which can be suitably formalized. The basic, technical tool for their study is a "Reduction Calculus of Meanings" which is formalized in the Typed lambda-Calculus with Acyclic Recursion, an extension of Montague's Language of Intensional Logic; this calculus provides a rigorous definition of logical form and the synonymy relation for formalized fragments of language, which can be tested against our intuitions and which supplies evidence for (and against) the basic view.
My aim in the talk is to present the basics of Referential Intension Theory and the Reduction Calculus, and to discuss how they "resolve" some of the classical paradoxes in the Philosophy of Language.
This will be primarily a philosophical logic talk---on what we might call "the logic of meanings".
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