LIRa Session: Dag Westerstahl

Speaker: Dag Westerstahl

Date and Time: Monday, January 28th 2019, 16:30-18:00

Venue: ILLC Seminar Room F1.15, Science Park 107.

Title: Logicality revisited: constants vs. consequence.

Abstract. There is an abstract Galois duality between (sets of) constants and consequence relations that I will explore, and argue that it gives some insight into both notions, and in particular into the notion of a logical constant. This leads in a natural way to a question posed already by Carnap in 1943, but rather neglected since: To what extent do the properties of a logical consequence relation fix the meaning of the logical constants in the language? Carnap asked this about classical propositional logic, but the question makes sense for any logic. It has a precise and satisfactory answer for propositional and first-order logic, which I will state, and then go on to ask Carnap’s question for modal logic. The situation there is similar to, but also interestingly different from, that in first-order logic, and some new conceptual issues, and some mildly interesting facts, arise. In particular, we get a new perspective on neighborhood semantics for modal logic. This is joint work with Denis Bonnay.