 In early work on intensional analysis (Carnap 1947, Kaplan 1964), possible worlds had been identified with models of a suitable extensional language. For reasons indicated in section 3.1, Montague (1969, 164) broke with this tradition, appealing to Kripke’s account of modality based on possible worlds as unstructured basic objects. In his essay ‘On the nature of certain philosophical entities’ (Montague 1969), he argued that this seemingly minor technical innovation opens a new perspective in philosophical analysis, by reducing certain ‘dubious’ entities to predicate intensions or properties – functions mapping possible worlds to sets of objects. The idea was that, once the conceptual and techical problems of the semantics of intensional languages had been overcome, they may replace extensional predicate logic as a basis of philosophical argument: