224 The formalization of sentence-meaning

to encourage the belief that any real understanding of the details can be achieved unless one has a considerable facility in math­ematical logic. However, it is not the details that are of interest to us here. My purpose is simply to explain, non-technically, some of the most important features of Montague grammar, in so far as they are relevant to the formalization of sentence-meaning and are currently exploited in linguistic semantics. In doing so, I will concentrate upon such features as may be expected to have an enduring influence, independently of current or future developments in linguistics and logic, and in the philosophy and psychology of language.

Montague semantics - the semantic part, or module, of a Montague grammar - is resolutely truth-conditional. Its applicability is restricted, in principle, to the prepositional con­tent of its sentences. Just how big a restriction this is judged to be will, of course, depend upon one's evaluation of the points made in the preceding chapter. Most of the advocates of Monta­gue semantics have no doubt been committed, until recently at least, to the view that the whole of sentence-meaning is explic­able, ultimately, in terms of prepositional content. It has long been recognized, however, as was noted in the preceding chapter, that non-declarative sentences, on the one hand, and non-indicative sentences, on the other, are problematical from this point of view. Various attempts have been made to handle such sentences within the framework of Montague grammar. But so far none of these has won universal acceptance, and all of them would seem to be vulnerable to the criticisms directed against the truth-conditional analysis of non-declarative and non-indicative sentences in Chapter 6. In what follows we shall be concerned solely with propositional content.

Unlike certain other truth-conditional theories, Montague semantics operates, not with a concept of absolute truth, but with a particular notion of relative truth: truth-under-an-interpretation or, alternatively, in the technical terminology of model theory, truth-in-a-model. (I will say something presently about the sense in which the initially puzzling term 'model' is being employed here.) What model theory does in effect (though it is not usually explained in this way) is to-

7.5 Montague grammar 225

formalize the distinction that is drawn in this book between pro­positions and propositional content. As used by Montague and his followers (who were in turn drawing upon the work of Carnap and others), it does this by drawing upon the distinction between extension and intension and relating this to a particular notion of possible worlds, which originated (as we saw in section 4.4) with Leibniz. Model theory is by no means restricted to the use that is made of it by Montague: it is much more general than that. But for the moment we can limit the discussion to Montague's version of model theory, since this is so far the one most familiar to linguists.

The traditional distinction between extension and intension has been exploited in a variety of ways in modern logic and for­mal semantics, so that the term 'intensional' (not to be confused with its homophone 'intentional') has a quite bewildering range of historically interconnected uses. We shall be concerned only with those uses that are of immediate relevance. We may begin (following Carnap) by identifying Frege's distinction between reference ('Bedeutung') and sense ('Sinn') with the dis­tinction between extension and intension. (We should note that, as was mentioned earlier, Frege's word for reference -which he did not distinguish from denotation, as he did not dis­tinguish sentences from either utterances or propositions - is the ordinary German word for meaning.) It is generally agreed nowadays that sense, rather than reference, is what is encoded in the sentences of natural languages, and this is what the Ger­man word 'Bedeutung' would normally be used for. We can now go on to apply the extension/intension distinction to the analysis of sentence-meaning, saying that the sense, or intension, of a sentence is its propositional content, whereas its reference, or extension, is its truth-value (on particular occasions of utter- ance). Most people at first find it strange that Frege, and follow- ing him many, though not all, formal semanticists, should have taken sentences (or propositions) to refer to truth or falsity, rather than to the situations that they purport to describe. But this view of the matter has certain formal advantages with respect to compositionality.