Modal Catapults and the Limits of Modal Logic

Abstract

I explore modal “catapults,” a variety of closure principles for modal operators. Consider a proposition p that logically implies, entails, strictly implies, modally implies, materially implies, …, a proposition q. According to the appropriate catapult for a modal operator M, if Mp, then also Mq. Modal catapults play a crucial role in the logical analysis of traditional philosophical arguments, such as fatalism and incompatibilism. Additionally, standard deontic paradoxes and moral dilemmas involve a deontic modal catapult in some form. In the realm of deontic logic, I advocate for a solution grounded in actualism and counterfactuals (Jackson, Goble). In considering whether it ought to be that A we should look particularly at what would be the case, were A the case. This approach explains the failures of closure while still acknowledging its central role in modal reasoning. Modal catapults are indispensable to the logic of modalities, but they also delineate the boundaries of this approach.