Philosophy Compass 11 (11): 702-715 Modal Semantics without Worlds ⇤ Craig Warmke Abstract Over the last half century, possible worlds have bled into almost every area of philosophy. In the metaphysics of modality, for example, philoso- phers have used possible worlds almost exclusively to illuminate discourse about metaphysical necessity and possibility. But recently some have grown dissatisfied with possible worlds. Why are horses necessarily mammals? Because the property of being a horse bears a special relationship to the property of being a mammal, they say. Not because every horse is a mam- mal in every possible world. Some have recently begun to use properties to develop rivals to possible worlds semantics which may someday com- pare in formal power and capture the different systems of modal logic. In this paper, I do two things. I first offer a quick primer on possible worlds semantics. Then I discuss three rivals and the work they have left to do. 1 Introduction Over the last half century, possible worlds have bled into almost every area of philosophy. In the metaphysics of modality, for example, philosophers have used possible worlds almost exclusively to illuminate discourse about metaphysical necessity and possibility. For this monopoly on matters modal, we have to thank the unrivaled formal power of possible world semantics. Philosophers often formalize their discourse about metaphysical necessity and possibility within the language of modal logic. And possible worlds semantics best captures the differ- ent systems of modal logic. So philosophers naturally appeal to possible worlds when they discuss matters in modal metaphysics. These discussions are often channeled through the heart of possible worlds semantics, the characterization of necessary truth as truth in all possible worlds. We can use a modal semantics as a purely formal tool to prove results about systems of modal logic. As a purely formal tool, a modal semantics doesn’t treat the language of modal logic as being about modal reality, about what’s metaphysically necessary or possible. Or we can use a modal semantics not only as a formal tool, but also as a way to link the language of modal logic to modal reality, as a way to model expressions in the language which we interpret as saying something about modal reality. Given certain purposes, possible worlds semantics may not be the best way to link modal logic to modal reality. For example, some philosophers have recently grown dissatisfied with possible * I am indebted to Barbara Vetter for thorough and thoroughly helpful comments, Carl Gillett for stimulating conversation, and the graduate students in my Fall 2016 Modal Metaphysics seminar at Northern Illinois for helping me think through these topics. 1