220 The formalization of sentence-meaning

than a set of sense-components (or semantic markers, in Katz-Fodor terminology), any two sentences containing exactly the same lexemes would be assigned the same semantic representa­tion. For example, not only

5. 'The dog bit the postman' and

6. 'The postman was bitten by the dog', but also (5) and

(9) 'The postman bit the dog'

(and each of indefinitely many pairs of sentences like them), would be assigned the same semantic representation as one another. This is patently incorrect. What is required is some for-malization of semantic representations that will preserve the semantically relevant syntactic distinctions of deep structure.

It is probably fair to say that in the years that have passed since the publication of 'The structure of a semantic theory' by Katz and Fodor little real progress has been made along these lines. The formalization has been complicated by the introduc­tion of a variety of technical devices. But no general solution has been found to the problem of deciding exactly how many projection-rules are needed and how they differ formally one from another. And most linguists who are interested in either generative grammar or formal semantics are now working within a quite different theoretical framework.

One reason why this is so, apart from developments in Chomskyan and post-Chomskyan generative grammar since the mid-1970s, is that the whole concept of semantic representa­tions has been strongly criticized, on two grounds, by logicians and philosophers.

First of all, they have pointed out that Katz-Fodor semantic representations make use of what is in effect a formal language and that the vocabulary-units of this language (conventionally written in small capitals, as in Chapter 4) stand in need of inter­pretation, just as much as do the natural languages whose

7.5 Montague grammar 221

semantic structure the formal language interprets. This objec­tion may be countered, more or less plausibly, by saying that the formal language in question is the allegedly universal language of thought, which we all know by virtue of being human and which therefore does not need to be interpreted by relating its lexemes to entities, properties and relations in the outside world.

The second challenge to the notion of semantic representa­tions comes from those who argue that they are unnecessary; that everything done satisfactorily by means of semantic rep­resentations can be done no less satisfactorily without them -by means of rules of inference operating in conjunction with meaning-postulates. This approach has the advantage that it avoids many of the difficulties, empirical and theoretical, associated with componential analysis.

7.5 Montague grammar

What is commonly referred to as Montague grammar is a parti­cular approach to the analysis of natural languages initiated by the American logician Richard Montague in the late 1960s. During the 1970s, it was adopted by many linguists, who saw it (as did Montague himself) as a semantically more attractive alternative to Chomskyan transformational-generative gram­mar. (Montague himself died when still quite young, in 1971, and did little more than lay the foundations of what linguists inspired by his ideas called 'Montague grammar'.) In this con­text, 'grammar' is to be understood as covering both syntax and semantics.

Some of the differences between Montague grammar and the Katz-Fodor theory are a matter of historical accident. Monta­gue's work is more firmly rooted in logical semantics than the Katz-Fodor theory is and gives proportionately less considera­tion to many topics that have been at the forefront of linguists' attention. In fact, 'grammar' for Montague included only part of what the standard theory of generative grammar sets out to cover. There is nothing in Montague's own work about phonolo­gical representation or inflection. The Katz-Fodor theory, on

222 The formalizatwn of sentence-meaning

the other hand, finds its place (as Figure 7.1 in section 7.3 indi­cates) within a more comprehensive theory of the structure of languages, in which semantics and phonology (and indirectly inflection) are on equal terms. Linguists who have adopted Montague grammar have seen it as being integrated, in one way or another, with an equally comprehensive generative, though not necessarily Chomskyan, theory of the structure of natural languages, covering not only syntax (and morphology), but also phonology. Having said this, however, I must repeat one of the points made in section 7.3: phonology, unlike seman­tics, is only contingently associated with grammar (and, more particularly, syntax) in natural languages. The fact that Montague, like most logical semanticists, showed little interest in phonology (and morphology) is, therefore, neither sur­prising nor reprehensible.

More to the point is the status of transformational rules, on the one hand, and of componential analysis, or lexical decomposi­tion, on the other. Montague himself did not make use of trans­formational rules. There were at least three reasons for this. First, the syntactic rules that he used in what we may think of as the base component of his grammar are more powerful than Chomskyan phrase-structure rules. Second, he was not particu­larly concerned to block the generation of syntactically ill-formed strings of words, as long as they could be characterized as ill-formed by the rules of semantic interpretation. Third, he had a preference for bringing the semantic analysis of sentences into as close a correspondence as possible with what transforma­tionalists would describe as their surface structure. There is therefore no such thing as deep structure in Montague's own sys­tem. But this is not inherent in Montague grammar as such; and, during the 1970s, a number of linguists made proposals for the addition of a transformational component to the system. At the same time, it must also be noted, as we shall see, that the role of transformational rules was successively reduced in Chomskyan transformational-generative grammar in what we now think of as the post-classical period. By the end of the 1970s, if not earlier, the view that Montague took of the relation between syntax and semantics no longer seemed as eccentric

7.5 Montague grammar 223

and as badly motivated to generative grammarians as it may have done initially. And there are now, in any case, many differ­ent, more or less Chomskyan, systems of generative grammar, other than Chomsky's own system (which has been continually modified over the years and is now strikingly different from the standard, or classical, Aspects system). No one of these enjoys supremacy; and no linguist, these days, could sensibly think that formal semanticists have a straight choice between two, and only two, rival systems of linguistic analysis and description, when it comes to the integration of semantics and syntax.

As for componential analysis (or lexical decomposition), much the same remarks can be made here too. Montague gram­mar as such is not incompatible, in principle, with the de­composition, or factorization, of lexical meaning into sense-components. Indeed, some linguists have made proposals for the incorporation of rules for lexical decomposition within the general framework of Montague grammar. But, once again, as I have mentioned in the previous section and in Chapter 4, componential analysis is not as widely accepted by linguists now as it was in the 1960s and early 1970s.

The comparison of Chomskyan generative grammar with Montague grammar is complicated by the fact that, as I have said, some of the differences between them derive from purely historical circumstances. Most earlier presentations of Monta­gue grammar were highly technical and took for granted a considerable degree of mathematical expertise and some back­ground in formal logic. The situation has improved recently in that there are now good textbook presentations that are designed specifically for students of linguistic semantics. As for textbook accounts of Chomskyan generative grammar (of which there are many), most of these, whether technical or non-technical, fail to draw the distinction between what is essen­tial to it and what is contingent and subject to change. They also fail to distinguish between generative grammar, as such, and generativism or what is commonly referred to nowadays as the generative enterprise.

Montague grammar is of its nature a very technical subject (just as Chomskyan generative grammar is). It would be foolish