CHAPTERS6 1 страница

Sentence-meaning and propositional content

6.0 INTRODUCTION

This chapter is pivotal in the structure of the book. It is also one of the longest, and there is a distinct change of gear. We shall be making full use of logical notions and discussing in greater detail than we have done so far the basic concepts of modern formal, truth-conditional, semantics, which, as we saw in the preceding chapter, were first developed within logic and the philosophy of language and were subsequently extended to linguistics.

There is nothing new or revolutionary about the influence of logic on linguistics (and vice versa). Grammatical theory and logic have been closely associated for centuries. Indeed, much of the terminology of traditional grammar - 'subject', 'predi­cate', 'mood', etc. - is also part of the logician's stock in trade. But does this use of the same terminology reflect any more than a purely historical, and accidental, association between the two disciplines? Does the grammatical structure of a sentence corre­spond directly to the logical form of the proposition it expresses? More generally, is there nothing more to the meaning of a sen­tence than its propositional content? These are the principal questions that we shall be addressing in the present chapter.

Our general conclusion will be that there are certain aspects of sentence-meaning that cannot be adequately represented by standard propositional logic. In coming to this conclusion, how­ever, we shall also see that our understanding of the way mean­ing is encoded in sentences has been greatly increased in recent years by the attempt to describe precisely the interaction

154 Sentence-meaning and prepositional content

between the logical form of propositions and the grammatical structure of sentences (and clauses).

Some parts of this chapter may seem somewhat technical to those who are not acquainted with modern formal logic. But none of the concepts that we shall be invoking is inherently diffi­cult to understand. And it is only by looking at some of the points where prepositional logic fails to give a full account of sentence-meaning that we can begin to appreciate both the achievements and the limitations of modern truth-conditional semantics.

6.1 THEMATIC MEANING

 

Sentences have the same prepositional content if and only if they have the same truth-conditions. This is the principle which was established in the preceding chapter; and we shall stick to it throughout. We shall also continue to identify the prepositional content of a sentence with its sense and, for present purposes, with its descriptive meaning.

One part of the meaning of sentences - as sentences are com­monly defined - that is definitely not part of their prepositional content is thematic meaning. For example, the following sen­tences, which differ in thematic meaning, all have the same truth-conditions, and therefore the same propositional content:

'I have not read this book',

'This book I have not read',

'It is this book (that) I have not read',

'This book has not been read by me'.

So too do the following:

'A man is standing under the apple-tree',

'There is a man standing under the apple-tree'.

This kind of meaning is called thematic because it is determined by the way speakers present what they are talking about (the theme of their utterance) in relation to particular contextual presuppositions. (This is the only sense in which the terms 'theme' and 'thematic' are employed in this book. Regrettably, there are other, less traditional, conflicting senses now current

6.1 Thematic meaning 155

in the literature, which can lead to confusion.) Frequently, but not always, what the speaker presents as thematic is also given elsewhere in the context and can be taken for granted as being known to the addressees or readily identifiable by them.

Actually, it is by no means clear that (1)-(4), on the one hand, or (5)-(6), on the other, are different sentences. An alternative view would be that some or all of the following,

(la) I have not read this book,

(2a) This book I have not read,

(3a) It is this book (that) I have not read,

(4a) This book has not been read by me,

are different forms of the same sentence, whose citation-form -the stylistically and contextually unmarked, or, neutral, form -is (la). That (2a) and (4a), if not (2a) and (la), are traditionally regarded as forms of different sentences is perhaps no rnore than a consequence of the fact that Greek and Latin, much more clearly than English, had inflectionally distinct active and pas­sive forms of the verb. As for (3a), this too would be traditionally regarded as a form of a distinct sentence, because, superficially at least, it is composed of two clauses. Similarly for

(5a) A man is standing under the apple-tree,

by comparison with

(6a) There is a man standing under the apple-tree:

(6a) is composed, at least superficially, of two clauses and is therefore composite, rather than simple. The distinction between simple and composite sentences is something we shall look at in the following section.

For our purposes, the most important point to be noted here is that the question whether (la)-(4a) are forms of the same sen­tence or of two or more different sentences is not a matter of fact to be settled by observation or intuition, but a matter of theoretical decision. There are perhaps good reasons for saying that (la) and (2a) are forms of different sentences (although a traditionally minded grammarian might take the contrary view): word-order plays a crucial structural role in the grammar

1.56 Sentence-meaning and propositional content

of English. There are other language's, however, in which it does not. Much current syntactic theory, for reasons that we need not go into here, is typologically biased in that it makes it axiomatic that no two utterances that differ at all in word-order (more pre­cisely, in the sequential order of their constituent forms, simple or composite) can be forms of the same sentence. This axiom is often built into the formalization of generative grammars (as it was in Chomsky's original formalization of transformational-generative grammar) by defining the sentence as a string of forms. From time to time, in this chapter and elsewhere in the present book, this point will be of importance. Obviously, if one took the view that (1 a)-(4a) are all forms of the same sentence, whose citation-form is (la), one would say that thematic meaning (in this case at least) is not a part of sentence-meaning. This view is not to be rejected out of hand.

It might be argued, then, that the difference between, say, (la) and (2a) has nothing to do with the grammatical or seman­tic structure of the sentence of which they are alternative forms, but rather with the utterance of the same sentence in one contex-tually determined word-order or another. Issues of this kind will occupy us in Part 4, when we look more closely at what is involved in the utterance of a sentence. For the moment, it suf­fices to note that the kind of question with which we have been concerned in this section is usually begged, rather than properly addressed, in current works in linguistic semantics. Thematic meaning is primarily, if not wholly, a matter of utterance-meaning. Just how much, if any, is also to be regarded as a part of sentence-meaning is debatable. But it cannot be properly debated unless and until those involved in the debate say exactly what their criteria are for sentence-identity.

It should also be noted that, as we have seen earlier (1.3), it is somewhat unrealistic to discuss what we are now calling the­matic meaning without mentioning stress and intonation! Much the same communicative effect can be achieved by put­ting heavy stress on this book in (la) as can be achieved by utter­ing (2a). Moreover, when (2a) is uttered, it will not only have a non-neutral word-order, in contrast with (la), but also a non-neutral intonation-contour. There is no general consensus

6.2 Simple and composite sentences 157

among linguists as to how much of this thematically significant variation in the prosodic structure of utterances is to be accounted for in terms of sentence-structure.

One point, however, is clear. It is part of one's linguistic com­petence to be able to control and interpret variations of word-order and grammatical structure of the kind that are exempli­fied in the sentences cited above. It is also part of one's linguistic competence to be able to control and interpret differences of stress and intonation that are functionally comparable with such variations of word-order and grammatical structure. We cannot, therefore, hold simultaneously to the following two prin­ciples:

(i) linguistic competence is restricted to the knowledge of sen­tence-structure; (ii) all aspects of sentence-meaning are truth-conditional.

If we want to maintain (i), we must accept a much broader con­ception of sentence-structure than is traditional and, in doing so, abandon (ii). Alternatively, if we wish to defend (ii), we must either accept a much narrower conception of sentence-structure than is traditional or define thematic meaning to be something other than meaning. The view taken in this book is that there is no good reason to subscribe to either of the two prin­ciples.

6.2 SIMPLE AND COMPOSITE SENTENCES

A simple sentence, in traditional grammar, is a sentence that contains only one clause. What I am calling composite sen­tences - there is no generally accepted term for non-simple sen­tences - fall into two classes: compound and complex. The former may be analysed, at their highest level of structure, into two or more co-ordinate clauses; the latter into a main clause (which may be simple or composite) and at least one subordi­nate clause. Although these, traditional distinctions are not with­out their problems, we can use them satisfactorily enough in our general discussion of the propositional content df sentences.

158 Sentence-meaning and prepositional content

Roughly comparable with the distinction between simple and what I will call composite sentences is the distinction drawn in logic between simple and composite propositions. (What I am calling composite propositions are usually referred to as com­plex, and occasionally as compound. However, it seems prefer­able in the present context to standardize the grammatical and the logical terminology as far as possible. 'Composite' has the further advantage that it is transparently related both to 'com­positional' and to 'component'.) But no distinction can be drawn (in standard first-order prepositional logic) among dif­ferent kinds of composite propositions that matches, in any sig­nificant way, the grammatical distinction between compound and complex sentences. For example,

'If he passed his driving test, I am a Dutchman'
is complex, whereas

'Either he did not pass his driving test or I am a Dutchman'

is compound.

The propositions expressed by the above two sentences are normally formalized in the prepositional calculus by means of implication and disjunction, respectively:

(9) " p implies q ",

 

on the one hand, and

 

(10) "either not - p or q ",

on the other. At first sight, these two composite propositions (9) and (10) look as if they might differ semantically, but, as they are standardly interpreted by logicians, they do not. They have exactly the same truth-conditions. Granted that "p implies q " and "either not - p or q" correctly formalize the range of proposi­tions that can be asserted by uttering our sample complex and compound sentences, (7) and (8), it follows that the sentences in question must have the same prepositional content. And yet one might hesitate to say that, as sentences, they have the same meaning.

Even more striking are such examples as the following:

6.2 Simple and composite sentences 159

'He was poor and he was honest'

'He was poor but he was honest'

'Although he was poor, he was honest'.

Most people would probably say that all three sentences differ in meaning, but that the second, which is compound, is closer in meaning to the third, a complex sentence, than it is to the, first, which is another compound sentence. Once again, however, the composite propositions expressed by these sentences are nor­mally held to be semantically equivalent. If there is any differ­ence of sentence-meaning in (11)-(13), then (on the standard view of prepositional content), it is not a matter of prepositional content. (The question why logicians normally treat the compo­site propositions expressed by (11)—(13) as equivalent will be taken up in section 6.3.)

There is much more that would need to be said in a fuller dis­cussion of the relation between the grammatical structure of composite sentences and the logical form of composite proposi­tions. For example, one would need to consider more generally the relevance to the prepositional content of sentences of the tra­ditional grammatical distinction between co-ordination and subordination (upon which the more particular distinction between compound and complex sentences is based). Rightly or wrongly, standard analyses of the logical form of the compo­site propositions expressed by uttering natural-language sen­tences take no account of this. Similarly, one would need to consider whether, and if so how, the traditional classification of subordinate clauses as nominal, adjectival, adverbial, etc., should be reflected in the formalization of the propositional con­tent of complex sentences. This too is something that is not taken into account, except partially and indirectly, in standard formal-semantic analyses of natural-language sentences.

What is commonly referred to in the literature of linguistic formal semantics as the rule-to-rule hypothesis rests on the assumption that, generally speaking, there is congruence between grammatical structure and logical form (see 7.2). If this assumption is valid, it is to be anticipated that further devel­opments in the application of the notions of formal semantics to

160 Sentence-meaning and prepositional content

the analysis of the prepositional content of the sentences of nat­ural languages will exploit some of these traditional notions about the grammatical structure of composite sentences. Some of them appear to be relevant, at least intuitively, to the seman­tic analysis of sentences. However, there is as yet no consensus among linguists whether, and if so how, they should be rep­resented formally in purely syntactic terms.

As we shall see, in connexion with the principle of composi-tionality in Chapter 7, formal semantics always presupposes and operates in conjunction with a particular syntactic model. We shall be looking at two historically important approaches to the formalization of sentence-meaning which sought to give effect to this principle in quite different ways. One of them, the Katz-Fodor theory, originated in linguistics and used the Chomskyan model of transformational-generative grammar (in its so-called standard version); the other, Montague semantics, originated in formal logic and used a very different, less power­ful, but logically (and in certain respects semantically) more elegant and more perspicuous, model of syntactic analysis (cat-egorial grammar). In the last twenty-five years or so, these two different models of syntactic analysis have been further refined and modified, and other models have been developed which seek to combine the theoretical and descriptive strengths of both (without, ideally, the weaknesses of either). These develop­ments have been motivated by both empirical and theoretical considerations. Not only has a much wider range of relevant data been investigated, but there has also been a conscious attempt by linguists, as there was not in an earlier period, to get the best fit - to achieve the highest degree of congruence -between grammatical and semantic structure in their descrip­tions of natural languages.

Throughout this book I have deliberately adopted the con­ceptual framework and, as far as possible, the terminology of tra­ditional grammar. Students who are familiar with modern syntactic theory should have no difficulty in making the neces­sary terminological adjustments and, if they have some knowl­edge of the more recent developments to which I have just been referring, they will see the force of the comments about syntactic

6.2 Simple and composite sentences 161

and semantic congruence. Students who do not have this famil­iarity with modern syntactic theory, however, are in no way dis-advantaged. Everything that follows in Chapter 6 is intended to be comprehensible (and has at times been deliberately simpli­fied for the purpose) on the basis of a fairly non-technical knowl­edge of traditional grammatical concepts. One or two of the relevant concepts drawn from modern generative grammar will be introduced and explained in Chapter 7, where something more will also be said about compositionality, grammatical and semantic congruence, and the rule-to-rule hypothesis.

In this section, we have been considering the relation between the grammatical structure of composite (i.e., compound and complex) sentences and the logical form of composite proposi­tions. In doing so, we have adopted the traditional view of the distinction between clauses and sentences, according to which a composite sentence is composed of more than one clause and a simple sentence is composed of, and may be identified with, a single clause. We have also tacitly taken the view, for which there is some support both in traditional grammar and modern linguistic theory, that sentences are more basic than clauses, in that (i) there is no distinction to be drawn between clauses and sentences as far as simple sentences are concerned and (ii) the clauses of composite sentences can be derived from simple sen­tences by embedding them (or some transform of them) in complex sentences or conjoining them (or some transform of them) in compound sentences. (The terms 'embedding', 'con­joining' and 'transform' are drawn from the terminology of Chomskyan transformational-generative grammar, which will be referred to again in Chapter 7, but the concepts with which they are associated are traditional enough and have their place in many different models of grammatical structure.) According to an alternative view of the relation between sentences and clauses (as we shall see in section 6.6), it is the clause, rather than the sentence, that is the more basic structural unit and the one that corresponds most closely to the proposition. Everything that has been said in this section and in the following sections could be reformulated in terms of this alternative view; and, from time to time, I will remind readers that this is so by using

162 Sentence-meaning and propositiqnal content

the phrase 'sentence (or clause)' in place of 'sentence' and, when we come to section 6.6, 'sentence-type (or clause-type)' in place of 'sentence-type'.

In conclusion, it may also be useful to make explicit the fact that, in this section and throughout this book, the term 'logical form' is being used with reference solely to the structure of prop­ositions (and prepositional content): the term 'form', in this con­text, is in fact synonymous with 'structure'. The reason for making this point is that the term 'logical form' is used in certain modern theories of syntax for an underlying level of grammati­cal structure (roughly comparable with what was called the deep structure of sentences in the so-called standard model of transformational grammar: see 7.3). The two senses of the term are of course connected; but they must not be confused.

6.3 TRUTH-FUNCTIONALITY (1): CONJUNCTION AND DISJUNCTION

As we saw in the prteceding section, under standard logical assumptions the composite, propositions expressed by sentences such as (11)-(12) are held to be semantically equivalent. This is because the operations whereby composite propositions are formed out of simple propositions are, by definition, truth-functional.

What this means is that the truth-value of a composite prop­osition is fully determined by - is a function of (in the special­ized mathematical sense of 'function' explained in Chapter 4) - the truth-values of its component propositions and the specified effect of each operation. The four operations that are of concern to us are conjunction, disjunction, negation and implication.

Conjunction (&) creates a composite proposition (p & q: " p -and- q "), which is true if, and only if, both p and q are true. Dis­junction (V), mentioned earlier, creates a composite proposi­tion (p V q: "either- p -or- q ") which is true, if, and only if, either p is true or q is true (or both are true). Negation (~) creates a composite proposition (~ p)) out of a simple proposition (p); and ~ p is defined to be true when p is false and false when p is true.

6.3 Truth-functionality (1): conjunction and disjunction 163

Implication (—>) creates a composite proposition (p —> q: " p -implies- q ") which is true if, and only if; (i) both p and q are true, (ii) both p and q are false, or (iii) p is false and q is true.

The question which we now have to address is whether the operations associated with the formation of composite sentences in natural languages are similarly truth-functional. In this sec­tion we shall restrict our attention to compound sentences formed by means of the operation of conjunctive and disjunctive co-ordination. Sentences which are commonly held to exemplify implication and negation will be dealt with in subsequent sec­tions.

At first sight, the logical definition of conjunction and its application to the semantic analysis of compound sentences in natural languages might seem to be straightforward enough. We have already noted, however, that there seems to be a differ­ence of meaning between such sentences as (11) and (12) - a dif­ference which can be associated with the English forms and and but (and with grammatically and semantically comparable forms in other languages). Let us n9w look more closely at what I will call clausal and -co-ordination: the co-ordination of clauses by means of and. This is the most neutral kind of conjunctive co­ordination in English; and its closest equivalent in the preposi­tional calculus is undoubtedly logical conjunction (&). Even and -co-ordination, however, is problematical from the point of view of truth-functionality.

Very often there is felt to be some kind of temporal or causal link between the situations described by the component proposi­tions, such that the ordering of the clauses expressing these prop­ositions is semantically significant. For example

'John arrived late and missed the train'
and

'John missed the train and arrived late'

would normally be used in different circumstances. To make the point briefly, but loosely: and here appears to mean "and then" or "and therefore". Obviously, if and does have this meaning, it is not equivalent to the connective for prepositional conjunction, &. For p & q has the same truth-values as q & p.

164 Sentence-meaning and prepositional content

But does and - more precisely, the ca-ordination of clauses in sequence by means of and - actually have the meaning "and then" or "and therefore"? An alternative view is that "then" or "therefore" is not part of the prepositional content, but some­thing that is merely implied (in a broad sense of 'implied') by our general tendency to adhere to the communicative norms of relevance and orderliness. Those who hold this view would argue that, in normal circumstances and in default of contextual information to the contrary, we can reasonably infer from the utterance of the sentence 'John arrived late and missed the train' that John's late arrival was the cause of his missing the train even though there is nothing in the actual meaning of the sentence that gives us this information - because we can assume that the speaker is not misleading us by deliberately and gratui­tously flouting the ground-rules, or maxims, of normal commu­nicative behaviour.

It is, of course, possible to think of circumstances in which (14) and (15) could be uttered to assert two otherwise unconnected facts. But these circumstances must be rather special and will generally be clear from the context of utterance. Let us grant, therefore, that in what we may think of as more normal or more usual contexts of utterance anyone uttering either (14) or (15) would be implying, if not actually expressing, the fact that there was some kind of causal connexion between John's late arrival and his missing the train.

This argument has been used by adherents of truth-conditional semantics. We shall come back to this in Chapter 9 in our discussion of Grice's notion of conversational implica-ture. At this point, however, it is worth noting that, however per­suasive the arguments might be in the case of the English form and, they cannot be assumed to hold for all natural languages. It so happens that English has compound, as well as complex, sen­tences and what can be plausibly seen as a neutral co-ordinating conjunction. Many familiar European languages are like English in this respect, but not all languages are.

The arguments in favour of a truth-functional analysis of com­posite sentences in English are rather less persuasive when they are used in support of the thesis that sentences containing but or

6.3 Truth-functionality (1): conjunction and disjunction 165

although have the same meaning as sentences containing and, as in (12) and (13) mentioned earlier. If we concede the truth-functionality of what I have called the most neutral kind of con­junctive co-ordination involving the use of and, we must also allow that speakers may utter sentences such as (11) in several prosodically different forms which also differ in meaning. For example, they may superimpose upon their utterance of what is in itself a grammatically and lexically neutral compound sen­tence such as (11) a prosodic contour (comprising stress and into­nation) which indicates their own feelings about the propositions expressed and the connexion between them. That is to say, it is possible to say (11a) He was poor and he was honest, (11a) being one of the forms — an utterance-inscription — which results from the utterance of (11), in such a way that, in asserting the conjunction of the two propositions, p & q, speakers simul­taneously reveal their surprise that both p & q should be true. In such circumstances, they might equally well have uttered, not a form of (11), but of (12) or even of (13), each with the appropriate prosodic contour. There would be no difference in the composite proposition which they assert, and no readily identifiable differ­ence in the degree or nature of the feeling that they indicate. Nevertheless, the two sentences differ in meaning, since but, unlike and, is never a purely neutral marker of the conjunction of propositional content.

Similar problems arise, in certain languages, in connexion with disjunction. For example, in Latin there are two ways of translating English either-or sentences. One can use the particles... vel... vel... or alternatively the particles ...aut...aut.... It has been suggested, at times, that the difference between these two alternatives is that the vel -construction is used for inclusive dis­junction and the aut -construction for exclusive disjunction.

An inclusive disjunction, p Ú q, is true, not only if either p or q is true and the other is false, but also if both p and q are true. An exclusive disjunction, on the other hand, is true only if either p is true and q false or q is true and p false: it excludes the possibility of both p and q being true. For example, the following regulation might, in principle, be interpreted either inclusively or exclu­sively:

166 Sentence-meaning and prepositional content

(16) Students who do not arrive in time or have not completed all their
assignments will be refused admission to the examination.