Chapter 7

The formalization of sentence-meaning

7.0 Introduction

This chapter follows on from the preceding one and looks at two historically important and highly influential theories of sen­tence-meaning which, since the mid-1960s, have been associated with the attempt to formalize the semantic structure of languages within the framework of Chomskyan and non-Chomskyan generative grammar.

The first is the Katz-Fodor theory of meaning, which origi­nated in association with what we may now think of as the classi­cal version of Chomsky's theory of transformational-generative grammar. The second theory is a particular version of possible-worlds semantics, initiated also in the late 1960s by Richard Montague, and, having been further developed by his followers, is now widely recognized as one of the most promising approaches to the truly formidable task of accounting for the propositional content of sentences in a mathematically precise and elegant manner.

The treatment of both theories is very selective and almost completely non-technical. I have been more concerned to explain some of the basic concepts than to introduce any of the formalism. At the same time, it must be emphasized that modern formal semantics is a technical subject, which cannot be under­stood without also understanding the mathematical concepts and notation that are a part of it. This chapter should definitely be read in conjunction with the more specialized introductions to formal semantics mentioned in the 'Suggestions for further reading'. Students who have mastered the concepts that are

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explained below should be able to tackle these other works and, equally important, to contextualize them within the framework of a broader approach to linguistic semantics than is customarily adopted by formal semanticists.

There is a sense in which the Katz-Fodor theory is now out­dated, as also in much of its detail is the so-called standard theory of transformational grammar. But, as I explain below, taken together, both theories are historically important, in that they introduced linguists to the principle of compositionality, as this is understood in formal semantics. Each of them is widely referred to in textbooks and is still taught in linguistics courses (if only as a foundation upon which to build). In my view, a good knowledge of each is indispensable for anyone who wishes to understand the more recent developments in linguistic seman­tics. They can also be used, as I use them here, with the more spe­cific purpose of introducing students of linguistics to formal semantics.

In the last twenty years or so considerable progress has been made in the formalization of the semantic structure of natural languages. However, as we shall see in the later sections of this chapter, it is so far only a relatively small part of linguistic mean- ing that has been brought within the scope of formal semantics.

We begin the chapter by considering the relation between for­mal semantics and linguistic semantics, as the latter has been defined in Chapter 1; and we end with a (non-technical) discus­sion of some of the underlying philosophical concepts upon which formal semantics is based. These are generally taken for granted, rather than explained, in more technical works.

7.1 FORMAL SEMANTICS AND LINGUISTIC SEMANTICS

The term 'formal semantics' can be given several different inter­pretations. Originally, it meant "the semantic analysis of formal systems (or formal languages)" - a formal system, or formal language, being one that has been deliberately constructed by logicians, computer scientists, etc. for philosophical or practical purposes. More recently, the term has been applied to the analy-

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sis of meaning in natural languages, but usually with a number of restrictions, tacit or explicit, which derive from its philosophi­cal and logical origins.

In this book, we are not concerned with formal semantics for its own sake, but only in so far as it is actually or potentially applicable to the analysis of natural languages. I will now intro­duce the term 'formal linguistic semantics' to refer to that part, or branch, of linguistic semantics which draws upon the methods and concepts of formal semantics for the analysis of the semantic structure of natural languages. In doing so, I am deliberately avoiding commitment, one way or the other, on the question whether natural languages are fundamentally different, seman-tically, from non-natural (i.e., artificial or constructed) languages. Some twenty years ago, Richard Montague, whose own theory of formal semantics we shall be looking at in a later section, gave it as his opinion that there is "no important theoretical difference between natural languages and the artificial languages of logicians" and that it is "possible to comprehend the syntax and semantics of both kinds of languages within a single natural and mathematically precise theory". Whether Montague was right or wrong about this is still unclear. Indeed, given his failure to say exactly what he meant by 'important theoretical difference', it is not obvious that he was making, or intended to make, any kind of empiri­cally confirmable claim about the semantic (and syntactic) structure of natural languages. He was declaring an attitude and, as it turned out, initiating a highly productive, but delib­erately restricted, programme of research.

Formal linguistic semantics is generally associated with a restricted view of sentence-meaning: the view that sentence-meaning is exhausted by prepositional content and is truth-conditionally explicable. As we have seen in Chapter 6, there are - or would appear to be - various kinds of meaning encoded in the lexical or grammatical structure of sentences which are not readily accounted for in terms of their preposi­tional content. Two reactions are open to theorists and practi­tioners of formal linguistic semantics in the face of this difficulty, if they accept, as most of them do, that it is a genuine