Affiliation: College of Arts and Sciences, Department of Philosophy
The traditional approach to modality analyzes necessity and possibility in terms of possible worlds. According to this approach, what is necessarily true is true in (or at) all possible worlds. In the first half of this paper, I argue that there is a genuine alternative approach to modality. The alternative approach does not appeal to possible worlds but properties that bear various relations of inclusion and exclusion to one another. In the second half of this paper, I flesh out the formal details of this approach with respect to the modal propositional calculi. The result is a completely un-Kripkean formal semantics. Along the way, I provide a novel property mereology.