Intensional logics

Intensional logics are systems that distinguish an expression’s intension (roughly, its sense or meaning) from its extension (reference, denotation). The purpose of bringing intensions into logic is to explain the logical behaviour of so-called intensional expressions. Intensional expressions create contexts which violate a cluster of standard principles of logic, the most notable of which is the law of substitution of identities – the law that from a = b and P(a) it follows that P(b). For example, ‘obviously’ is intensional because the following instance of the law of substitution is invalid (at least on one reading): Scott = the author of Waverley; obviously Scott = Scott; so, obviously Scott = the author of Waverley. By providing an analysis of meaning, intensional logics attempt to explain the logical behaviour of expressions such as ‘obviously’. On the assumption that it is intensions and not extensions which matter in intensional contexts, the failure of substitution and related anomalies can be understood. Alonzo Church pioneered intensional logic, basing it on his theory of types. However, the widespread application of intensional logic to linguistics and philosophy began with the work of Richard Montague, who crafted a number of systems designed to capture the expressive power of natural languages. One important feature of Montague’s work was the application of possible worlds semantics to the analysis of intensional logic. The most difficult problems concerning intensional logic concern the treatment of propositional attitude verbs, such as ‘believes’, ‘desires’ and ‘knows’. Such expressions pose difficulties for the possible worlds treatment, and have thus spawned alternative approaches.