LanCog Logic Seminar Series: Pedro Del Valle-Inclan

Friday, June 2, 11:00—13:00 (Lisbon time)

Centre of Philosophy of the University of Lisbon

The University of Lisbon

Location: Matos Romão Room

 

Speaker: Pedro Del Valle-Inclan

(Scuola Normal Superiore, Pisa)

 

Title: Carnap’s Problem, Definability and Compositionality

Abstract: In his Formalization of Logic (1943), Carnap pointed out that there are non-normal interpretations of classical logic: non-standard interpretations of the connectives and quantifiers that are nevertheless consistent with the classical consequence relation of the appropriate language. Several solutions to the problem have been proposed. In a recent paper, Bonnay and Westerst ̊ahl (2016) argue that we should limit the space of pos- sible interpretations by ‘universal semantic constraints’. According to Bonnay and Westerst ̊ahl, if we restrict attention to interpretations that are (a) compo- sitional, (b) non-trivial and (c) in the case of the quantifiers, invariant under permutations of the domain, Carnap’s Problem is avoided. In this talk I will show that Bonnay and Westerst ̊ahl’s solution fails. Their main result, a characterisation of the interpretations of the quantifiers that are consistent with the classical consequence relation, only holds for second-order languages, for which categoricity is easier to achieve. Ultimately, the failure of their proposal (in the first-order case) can be traced back to the issues of compositionality and definability. Bonnay and Westerst ̊ahl’s use of second-order languages is somewhat anal- ogous to the appeal to ‘open-endedness’ in other attempts at solving Carnap’s Problem (e.g. McGee 2000, Murzi and Topey 2021). In the final part of the talk, I will discuss how their results relate to those approaches, and explore a way to ammend their proposal.