208 The formalization of sentence-meaning

with a semantic rule which assigns an interpretation to the com­posite expression which is formed by the grammatical rule in question; and (ii) there are no semantically vacuous grammati­cal rules. The problem is that it is not usually as clear as it is in the case of (1) that correspondence between grammatical and semantic structure in natural languages is a matter of theory-neutral and empirically determinable fact. Those scholars who subscribe to the so-called rule-to-rule hypothesis are subscribing to a particularly strong version of the principle of compositionality.

To be compared with the rule-to-rule hypothesis, which can be seen as a methodological principle adopted by certain formal semanticists to guide them in their research, is the traditional methodological principle of saving the appearances — being duly respectful of the phenomena — which I have invoked on several occasions. A classic case of violating the principle of sav­ing the appearances was Russell's (1905) analysis of the preposi­tional content of grammatically simple (one-clause) sentences containing noun-phrases introduced by the definite article, such as (4) 'The King of France is bald',

whose logical form, under Russell's analysis, turned out to be a composite (three-clause) structure, for two of whose (conjoined) component propositional structures (one containing the existen­tial quantifier and the other the operator of identity) there is no syntactic support. One of the things about Montague's work that attracted linguists was that it brought the logical form of (the propositional content of) many such sentences of English and other natural languages into closer correspondence with their apparent syntactic structure.

In the account of formal linguistic semantics that is given in this chapter, I will begin by considering two of the best-known approaches to the problem of determining the compositional function (whatever it is) which assigns sense to the lexically com­posite expressions of natural languages. I will do so at a very gen- . eral level, and I will restrict my treatment to what is uncontroversially a matter of propositional content. The two

7.3 Deep structure and semantic representations 209

approaches to be considered in the following sections of this chapter are the Katz-Fodor approach and what might be described as classical Montague grammar. I have added a sec­tion on possible worlds. The purpose of this is twofold. In the context in which it occurs, it is intended primarily to provide rather more background, philosophical and linguistic, than is usually given in textbook treatments of formal semantics for the particular notion of intensionality that has been developed by Montague and his followers. But it will also serve the more gen­eral purpose of raising two questions which have been much dis­cussed (and left unresolved) in the past and have been begged, rather than answered, in much recent work in linguistic seman­tics, both formal and non-formal: (1) Do all natural languages have the same semantic structure? (2) Do all natural languages have the same descriptive and expressive power? Formal seman­tics may not be able to provide an answer to either of these two questions, but it has clarified some of the issues.

7.3 DEEP STRUCTURE AND SEMANTIC REPR ESEN TATIONS

What I will refer to as the Katz-Fodor theory of sentence-meaning is not generally described as a theory of formal semantics, but I will treat it as such. It originated with a paper by J.J. Katz and J. A. Fodor, 'The structure of a seman­tic theory', first published in 1963. The theory itself was subse­quently modified in various ways, notably by Katz, and has given rise to a number of alternatives, which I will not deal with here. Indeed, I will not even attempt to give a full account of the Katz-Fodor theory in any of its versions. I will concentrate upon the following four notions, which have been of historical importance, and are of continuing relevance: deep structure, semantic representations, projection-rules and selection-restrictions. In this section we shall be concerned with the first two of these four notions, which are of more general import than the other two and, though they may now be obsolete in their original form, have their correlates in several present-day theories of formal semantics.