Fri Oct 7, 2016
60 Evans Hall, 4–6 PM
Dag Westerståhl (Stockholm University)
A Carnapian approach to the meaning of logical constants: the case of modal logic
Does a consequence relation in a language L, as a syntactic relation between sets of L-sentences and L-sentences, fix the meaning of the logical constants in L? In his 1943 book The Formalization of Logic, Carnap worried that this seems to fail even for classical propositional logic CL. However, by applying the viewpoint of modern formal semantics, which in particular requires meaning assignment to be compositional, Carnap’s worries about CL can be allayed. More importantly, it provides a precise framework for asking Carnap’s question about any logic. (To what extent) does classical first-order consequence determine the meaning of ∀? What about other (generalized) quantifiers? What about the intuitionistic meaning of the connectives? Or  in (classical) modal logic?  answers the first of these questions. In this talk I focus on the last one. Despite obvious similarities between ∀ and , there are important differences. Roughly, while there is essentially just one first-order logic, there are innumerable modal logics. That makes answers to Carnap style questions about the meaning of  more intricate, and more interesting, than in the case of ∀. Although we in a sense cover extremely familiar ground, the perspective one gets, in particular of neighborhood semantics for modal logic, seems novel. This is joint work with Denis Bonnay.
 D. Bonnay and D. Westerståhl, ‘Compositionality solves Carnap’s Problem’, Erkenntnis 81 (4), 2016 (721–739).