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The notion of a possible world is familiar from Leibniz's philosophy, especially the idea-parodied by Voltaire inCandide-that the world we inhabit, theactual world, is the best of all possible worlds. But it was primarily in the latter half of the twentieth century that possible worlds became a mainstay of philosophical theorizing. In areas as diverse as philosophy of language, philosophy of science, epistemology, logic, ethics and, of course, metaphysics itself, philosophers helped themselves to possible worlds in order to provide analyses of key concepts from their respective domains. David Lewis contributed analyses in all of these fields, most famously, perhaps, his possible worlds analysis of counterfactual conditionals (Lewis 1973). But these analyses invoking possible worlds cry out for a foundation: how is all this talk about possible worlds to be construed? Do possible worlds exist? If so, what is their nature? David …