(Joint with LIRa)

On standard theories, the basic units of modal discourse are possible worlds, construed as maximal consistent states of affairs. I argue that we should switch to a semantics on which the basic modal entities are possibilities, in the sense of possibility developed by Humberstone and Holliday. Possibilities are analogous to worlds, but may be incomplete: they may leave some propositions unsettled. Using possibilities allows us to model a breed of indeterminacy that affects specifically modal claims, thus solving a number of open puzzles. In particular, I show that Ninan's past-future asymmetry, the problem of counterfactual skepticism, and puzzling phenomena related to the assertion of will-claims can all be explained in a natural way in a possibility framework. The key feature of the new system is that two sentences may be equivalent in the sense that they are true throughout the same region of logical space, but still differ semantically in that they divide up that region in different ways.