Impossibility and impossible worlds

Abstract

Possible worlds have found many applications in contemporary philosophy: from theories of possibility and necessity, to accounts of conditionals, to theories of mental and linguistic content, to understanding supervenience relationships, to theories of properties and propositions, among many other applications. Almost as soon as possible worlds started to be used in formal theories in logic, philosophy of language, philosophy of mind, metaphysics, and elsewhere, theorists started to wonder whether impossible worlds should be postulated as well. To take just one example, possible-worlds theories of mental content associate sets of worlds with beliefs (or perhaps entire belief systems): the content of a belief is (or is represented by) the set of possible worlds where that belief is true. But what should we say about beliefs that cannot possibly be true: false logical or mathematical beliefs, for example, or beliefs in metaphysical impossibilities? It would be natural to represent these beliefs with sets of impossible worlds. If James thinks that 87 is a prime number, the set of worlds associated with his beliefs includes worlds where 87 is prime, for example. If Jane is undecided about the principle of excluded middle, her belief worlds should include some at which the principle is correct and some where it is incorrect. And so on.