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Possible worlds, syntax, and opacity

obtain at a world w, if and only if w is a member of (the set) P. PWA provides intuitively compelling accounts of necessity, contingency, and impossibility. Conjunction and disjunction are representable as intersection and union. We can say that P entails Q just when P c Q, thereby explaining why the objects of thought stand in entailment relations; and it turns out that P entails Q just when the material conditional (P :D Q) is a necessary truth. Kripke's [11] account of names as rigid designators fits well with PWA. And following Stalnaker [18], one can embed PWA in a 'pragmatic' account of intentional states: desiring P is being disposed to perform actions that would tend to make P obtain in a world in which one's beliefs, whatever they are, were true; believing P is being disposed to perform actions that would tend to satisfy one's desires, whatever they are, in a world in which P and one's other beliefs were true.' This account has