Dialetheic conditional modal logic

Abstract

© Springer Nature Switzerland AG 2019. Standard modal logic for alethic modalities analyses modalities as ranging over all possible worlds (the Leibnizian universe). This leaves very little room in the space of worlds to entertain impossible things. My proposal is to liberate the Leibnizian universe and reinforce the relative aspect of possibility; worlds are possible with respect to some worlds, and impossible for others. The central idea is to isolate relative possibility (Kripke) from conditionality (Lewis/Stalnaker). To accommodate counterpossibles, I provide a dialetheic conditional modal logic, a theory that is dialetheic at every level, in the logic as well as in the set theory behind it.