16 February 2023, The Utrecht Logic in Progress Series (TULIPS), Giorgio Lenta

Abstract: David Kaplan famously argued that mainstream semantics for modal logic, which identifies propositions with sets of possible worlds, is affected by a cardinality paradox. A new version of the paradox arises for every logical framework that validates an intuitive principle, when the semantics is extended with impossible worlds to deliver a hyperintensional account of propositions. I discuss two general approaches to a solution: giving up on sets and giving up on worlds, either in the semantics or in the corresponding picture of propositions. I argue that a truthmaker-based approach offers the most promising way to account for hyperintensional propositions, without facing the paradoxical outcome.