Language and Logic foundational course:
The Logic of Sense and Reference.

Teacher Abstract:

Most of our logics identify semantic values that should not be identified. As a result they come with problems such as prediction of logical omniscience. These can be evaded by distinguishing between an expression's sense and its reference, in Frege's way. This course studies logics in which such a distinction is made and in which even logically equivalent sentences can be kept apart and be assigned different meanings. It will also consider applications of such logics. Church's Logic of Sense and Denotation is a prime example of the kind of logic intended here, but there are now many more. After an overview of some of the proposals that have been made, the course will focus upon the classical theory of types and it will be explained how a natural generalization of Henkin's general models for this logic leads to structures with the desired characteristic: senses as well as referents being available as semantic values. It will turn out that the system thus obtained has many nice logical properties, completeness with respect to a very straightforward Gentzen calculus being one of them. It will also be shown how in a set-up where expressions come with senses the usual ingredients of possible worlds semantics can be constructed. The course will emphasize ideas rather than logical technique and should be accessible to natural language semanticists who are interested in getting rid of a foundational difficulty of their discipline.