Abstract

Possible worlds talk is, in my view, a metaphor, and what makes it a good metaphor is its capacity to be extended and elaborated in fruitful ways. The essays in this dissertation all concern ways of adding structure to the basic apparatus of possible worlds semantics--the Kripke frame--so as to make it bear more fruit. ;One way of adding structure is to think of possible worlds as histories. In "A Theory of Conditionals in the Context of Branching Time" Richmond Thomason and Anil Gupta use this approach to place Stalnaker's theory of the conditional into a temporal context. They formulate two principles about the relation between historical necessity and the conditional--Past Predominance and the Edelberg Inference--and investigate how these principles place constraints on branching time models of conditional tense logic. In the second chapter of this dissertation I show that Past Predominance can be articulated using Kripke frames, and I prove a completeness theorem for such structures. ;Another way of elaborating the possible worlds metaphor is to introduce apparatus for describing relationships between or among possible worlds. Using this strategy Robert Stalnaker devised a semantic theory of conditional logic that involves a selection function, and in the third and fourth chapters of this dissertation I show how to use selection functions to organize intuitions about causation and ability, respectively. ;A third way of elaborating the possible worlds metaphor is to generalize the notion of a Kripke frame. Bas van Fraassen has shown that the most rational way of characterizing semantic entailment in probabilistic semantics involves replacing individual Popper functions with well-behaved sets of them: probabilistic model sets. The upshot of this is that Popper functions in probabilistic model sets are analogous to possible worlds in Kripke frames, and probabilistic model sets are themselves analogous to Kripke frames. In the final chapter of my dissertation I carry the analogy further by giving a probabilistic semantics for modal logic in which modal operators function as quantifiers over Popper functions in probabilistic model sets, thereby generalizing Kripke's semantics for modal logic along the lines van Fraassen sets out