CHAPTER 4 2 страница

John and Jane are children

(in the relevant, non-relational, sense of 'child'). And there is no point in arguing that this is a matter of the use, rather than the meaning, of 'child', or alternatively of the non-literal meaning or of some aspect of meaning other than sense. The English expressions 'male child' and 'female child' are not descriptively synonymous with 'boy' and 'girl'. At the very least, therefore, something must be added to the analysis to capture this fact. And what about the analysis of the sense of 'boy' and 'girl' in relation to that of'man' and 'woman? Even here not-ADULT cre­ates difficulty. First of all, neither the proposition "That boy is now an adult" nor "That girl is now an adult" (unlike "That child is now an adult") appear to be in any way anomalous. How then, in this case, does the hypothetical universal sense-component adult relate to "adult" (the sense of the English word 'adult')? This question needs to be answered.

Second, there is the fact that, in most contexts, 'girl' and 'woman' are not used as contradictories, whereas 'boy' and 'man', though they may not be contradictories in the strict sense, are certainly more sharply opposed to one another seman-tically than 'girl' and 'woman' are. Finally, none of the more obvious and relatively objective biological or cultural criteria of adulthood - sexual maturity, legal majority, economic and social independence, etc. - is relevant, except in certain con­texts, to the use, descriptively, of 'man' rather than 'boy' or of 'woman' rather than 'girl'. Needless to say, these difficulties are compounded when we start comparing the analysis of 'child' with that of'lamb' or 'foal' - not to mention that of'boy' and 'girl' with that of 'colt' and 'filly'.

116 The structural approach

Similarly, it can be argued that, although human is an essen­tial component of ''man" and "woman'', it is not an essential component of "boy", and possibly not of "girl". The male off­spring of the gods (e.g.. Cupid) are regularly described as boys 'and their female offspring, in the appropriate circumstances.) as maidensj; but they do not grow up to be men, and they are not said to be human. And, once again, it is unreasonable to say that, in cases like this, 'boy' or 'girl' is being used non-literally. We must be careful not to import our own metaphysical preju­dices into the analysis of the vocabularies of natural languages. And we must not make the distinction, between literal and non-literal meaning dependent upon them.

If componential analysis is defective both theoretically and empirically, why have I devoted so much space to it? Partly, because it has figured prominently in recent works on semantics and has guided a good deal of undoubtedly valuable research. Partly, also, because there is another way of looking at componential analysis which makes it less obviously defective. This is to take it, not as a technique for the representation of all of the sense (and nothing but the sense) of lexemes, but as a way of formalizing that part of their prototypical,nuclear or focal, sense which they share with other lexemes. For example, there is no doubt that 'boy' is used prototypically of human beings and furthermore that, in so far as we understand it when it is used descriptively of Cupid, we do so because we understand it, first of all. in relation to human beings. So human is criterial for the focal meaning of 'boy' and serves; also, analogically, in non-focal uses. But it is not part of its intension: i.e., of the property which defines the class whose members it denotes. Most of the allegedly universal components that have been proposed are of this kind.

Componential analysis is no longer defended by linguists, on theoretical grounds, as enthusiastically as it was by many a few years ago. Some of the reasons for this change of heart on the part of many, though by no means all, linguists have to do with more general issues pertaining to any allegedly exhaustive and determinate analysis of the sense of lexemes. Others relate speci­fically to componential analysis as such. As I have suggested in

4.4 Entailment and possible worlds 117

the account of componential analysis that has been given here, it is perhaps empirically indefensible in what might be called its standard or classical version, especially if this is coupled with assumptions of universality. At the same time, it has been of con­siderable historical importance and is still quite widely accepted. In the following sections, we shall see that, far from being in con­flict with other approaches to structural semantics, it is, at least in principle, fully compatible with them. In particular, it is com­patible, not only with the, appeal to prototypes, but also, as will be explained presently, with the use of what are called meaning-postulates.

 

4.4 ENTAILMENT AND POSSIBLE WORLDS

Entailment plays an important role in all theories of meaning, and a more central role in some than in others. Take the follow­ing two propositions, which I have labelled p and q (for reasons that will be explained immediately):

"Achilles killed Hector" (p)

"Hector died" (q)

Here the first proposition, p, necessarily implies, or entails,the second proposition, q: if it is the case that Achilles killed Hector, then it is necessarily the case that Hector died. In logical termi­nology, entailment is a relation that holds between p; and q - where p and q are variables standing for propositions - such that; if the truth of q necessarily follows from the truth, of p) (and the falsity of q necessarily follows from the falsity of p), then p entails q. The key term here is 'necessarily'.

It should be noted, first of all, that entailment has been defined as a relation between propositions. This is important. Some authors talk of entailments as holding between sentences. In doing so, they are using the term 'sentence' either loosely or in a very special sense. Others, for reasons that we need not go into here, define entailment as a relation between statements. But this usage, too, rests upon a specialized definition of 'state­ment', which conflicts in several respects with its everyday sense in English and can lead to confusion. I will discuss the relation

 

118 The structural approach

between sentences and propositions in Part 3, and the nature of statements, as well as that of questions, commands etc., in Part 4. At this point, I would simply draw readers' attention to the fact that here (as indeed earlier) I have tacitly extended my use of double quotation-marks to cover propositions. A proposition, as we shall see later, is one part of the meaning of the utterance in which it is expressed.

There is no standard symbolization of the relation of entail-ment. I will use a double-shafted arrow. Thus

(14) p Þ q

will mean " p entails q". The logical relation thus symbolized can be defined, in modal logic, in terms of implication and necessity. We need not go into the formalism. But we do need to discuss the notion of necessity itself. Propositions may.be either necessa­rily or contingently true (or false). A necessarily true (or false) proposition is one that is true (or false) in all possible cir­cumstances: or. as the seventeenth-century German philos­opher, Gottfried Leibniz (1646-1716) put it, in all possible worlds. For example, the propositions

(15) "Snow is white" and (16) "Rabbits are human''

might well be necessarily true and necessarily false, respectively. A contingently true (or false) proposition, on the other hand, is one whose truth-value might have been, or might be, different in other circumstances (in other possible worlds). For example,

(17) "Napoleon was defeated at Waterloo"

is contingent in the required sense. We can envisage a possible, world, or a possible state of the world, of which it is not true. This intuitively comprehensible notion of possible worlds (satirized, incidentally, in its theological development by Leib­niz, in Voltaire's Candide] has been formalized in various ways in modern modal logic. For logical purposes, a possible world may be identified with the set of propositions that truly describe

4.4 Entailment and possible worlds 119

it. It is under this interpretation of 'world' that one talks of prop­ositions being true in, rather than of, a world. It will be noted that I have used both ways of talking about worlds in this para­graph. For the present, I will draw no distinctions between these two ways of talking. It may be helpful, however, if one thinks of the world in which propositions are true (or false) as the inner, mental or cognitive, world and the world of which the propositions are true as the outer (i.e., extramental) world which is represented by the inner world.

This is straightforward enough as far as it goes. Problems emerge as soon as one looks at the notion of necessity more clo­sely. We may begin by considering two kinds of necessary truths recognized by philosophers: analytic and logical. (These are not always clearly distinguished in linguistic semantics.) The notion of analytic truth (in the modern sense of 'analytic') derives from the work of the great eighteenth-century German philosopher Immanuel Kant (1724-1804). According to Kant, a proposition (traditionally represented as the combination of a subject and a predicate) is analytically true if the meaning of the subject is contained in that of the predicate and can be revealed by analysis. For example, granted that "female" (the meaning of 'female') or alternatively female (a universal sense-component which is identical with or includes "female") is included in "girl", the truth of

(18) "All girls are female"

can be demonstrated by the analysis of the subject-expression, 'all girls', and more especially of the lexeme 'girl'. The sense of 'girl' (i.e., "girl") can be analysed, or decomposed, into "human" x "female" X "non-adult": see (4) in section 4.2. So the proposition we are discussing is equivalent to

(19) "All human, female, non-adults are female",

in which the predicate "female" is patently contained in the sub­ject. One can see immediately both the original motivation for the use of the term 'analytic' and the relevance, to this topic, of the technique of componential analysis. Nowadays, it is more common to reformulate the definition of analyticity in more

 

 

120 The structural approach

general terms: an analytically true (or analytic) proposition is one which is necessarily true by virtue of its meaning - one which can be shown to be true by (semantic) analysis. This is the formulation that we shall adopt.

Any proposition that is not analytic is, by definition, syn­thetic. Therefore, all contingent propositions, such as

(20) "Napoleon was defeated at Waterloo",

are synthetic. (And, here again, I take the opportunity of reminding readers that (20) is a proposition only if the referring expressions in it, notably 'Napoleon' and 'Waterloo', are fixed in their reference.) It does not follow, however, that all synthetic propositions are contingent. This point is important and has been much discussed by philosophers. We shall not need to deal with it here. It suffices that, as' linguists, we are aware that a case can be made for the (rationalist) view (rejected by many empiricist philosophers) that there are some synthetic necessary truths which are known to be true a priori: i.e., prior to, or independently of, experience.

We come now to the question of logical truth. A logically true for false) proposition is one whose truth-value is determined solely by the logical form of the proposition: e.g.,

(21) "Every person who is female is female".

What is meant by 'logical form' is, in part, controversial. Even more controversial is the relation between the logical form of propositions and the structure of natural-language sentences. But for present purposes it may be assumed that 'logical form' is satisfactorily defined in standard systems of logic and that, in straightforward rases at least, we have an intuitive understand­ing of it. It may be assumed, for example, that

"All female persons are female",

"All red books are red",

etc. are recognized intuitively as logical truths. They would cer­tainly be so classified, by virtue of their form (i.e., their struc­ture), in all standard systems of logic. As I have said earlier, logical truths constitute one of two kinds of necessary truths.

4.4 Entailment and possible worlds 121

Moreover, if logical form is held to be a part of the meaning of propositions, logical truths are a subclass of analytic truths. All this follows by definition. It has been argued that all analytic truths are also logical truths; but this is highly controversial and cannot be taken for granted. It has also been argued, or simply assumed without argument, that the only necessary truths are logical truths. In my view, there are very good reasons for recog­nizing different kinds, not only of non-logical necessity, but also of non-analytic necessity.

Linguists have often used the term 'necessarily', and even 'entailment', rather loosely. In so far as they are concerned with the semantic structure of natural languages, it is not neces­sarily true propositions as such that should be of interest to them, but analytically true propositions (including logical truths). Similarly, if entailment is defined as above, it is not entailment in its entirety that is, or should be, of central concern, but rather what might be called semantic, or analytic, entail­ment. Generally speaking, this is what linguists; have in mind when they invoke the notion of entailment. Henceforth I will use the term 'entailment' in this narrower sense. It is of course possible to argue that all necessary truths are analytic, as I indi­cated earlier. On the face of it, however, this docs not seem to be so.

First of all, there are propositions which, if true, are true by virtue of natural, or physical, necessity: i.e., by virtue of the laws of nature. The qualification, "if true", is important. We must never confuse the epistemological status of a proposi­tion with its truth-value. There is a difference between a prop­osition's being true (or false) and a proposition's being held to be true. Propositions do not change their truth-value; their epis­temological status, on the other hand, is subject to revision in the light of new information, changes in the scientific or cultural frame of reference which determines a society's generally accepted ontological assumptions, etc. (We have already noted the importance of allowing for such changes in our discussion of the Putnam-Kripke view of natural-kind expressions: see 3.3.) A proposition which is true by virtue of natural necessity might be:

122 The structural approach

(24) "All human beings are mortal".

Arguably this proposition, if true, is true by virtue of biological necessity (which, according to current conceptions, is a particu­lar kind of natural necessity). And yet it is surely not analytic. The meaning of 'human' would not suddenly change (nor would the meaning of 'mortal') if it were discovered, contrary to popular belief and so far well-established scientific hypoth­eses, that some human beings are immortal or could be made so by regular and repeated surgical intervention.

Once we have seen the distinction between natural necessity and necessity by virtue of meaning in a fairly obvious case such as the one just mentioned, it is easier to appreciate that many examples of entailment which figure in the recent literature are dubious, to say the least. What about (25), for instance?

(25) "Jackie is pregnant" => "Jackie is female".

At first sight, one might be inclined to say that (25) is true by vir­tue of the meaning of 'pregnant' and 'female'. A moment's reflection, however, will show that we are not dealing with a valid example of semantic entailment. Let us suppose that advances in surgical and immunological techniques made it pos­sible to transplant into a man a foetus-bearing womb (and to do everything else that the hypothesis requires) and then to de­liver the child by Caesarean section. One can think of several variations on this theme, all of which, simply by being concep­tually coherent, cast doubt upon the view that "female" is part of the meaning of 'pregnant'. But we do not have to speculate about the details. It suffices that we are able to discuss rationally the possibility of a man being pregnant and argue about (he per­sonal and social consequences. If we impose upon 'possible world' the same restrictions as we have imposed upon 'entail­ment'. we can say that there are possible worlds in which "x is pregnant" does not entail " x is female" (where "a" is a variable which stands for any appropriate expression). After all, as Leibniz might have said, things could have been different in some world other than the best of all possible worlds, which God, in his wisdom, has actualized (and which, in ways yet to

4.4 Entailment and possible worlds 123

be revealed to theologians and scientists, he may change, for example by making it possible for men and women to share the onerous responsibility of child-bearing).

As we have recognized cultural kinds, in addition to natural kinds, so we might recognize cultural necessity, in addition to natural necessity. For example, it is arguably a matter of cul­tural necessity (in our culture), that marriage should be viewed as a symmetrical relation between two persons of different sex. This being so, provided that we are using English to talk about a culture in which the same conditions hold true (in relation to cohabitation, social and economic roles, etc.), we could say that "x is married to f necessarily implies "y is married to ac"; that the conjunction of "x is male" and "x is married to f necessarily implies "y is female", etc. This is obviously different from nat­ural necessity. Furthermore, it is easy to envisage other cultures (or subcultures in our own culture) in which homosexual unions (involving cohabitation, etc.) come to be, not only accepted, but regulated by law and religion on the same footing as heterosexual unions. One can envisage, without much difficulty, trilateral unions in which each member is correctly described, regardless of his or her biological sex, as the wife of one and the husband of the other. Or again, we can easily imagine amend­ments to our own divorce laws such that it becomes possible for one's partner's marital status to be changed without consequen­tial and reciprocal changes in the status of the other. In such cir­cumstances "x is married to y",would no longer necessarily imply "y is married to x". Would the meaning of 'married' have changed? It is at least arguable that it would not.

The consideration of possibilities such as this makes us realize that semantic entailment is by no means as clear-cut as it is often held to be. We do not have to go all the way with such philos­ophers as Quine (1953) in their criticism of the analytic/synthetic distinction. But we must certainly agree with him when he says that the distinction, as far as natural languages are concerned, is not sharp. I will not press the point further. But I would en­courage the reader to look critically at what are alleged to be entailments in recent works in theoretical semantics. Many of them are certainly not entailments, and others are of doubtful

124 The structural approach

status with respect to analyticity. And many sentences that are cited in textbooks of linguistics as examples of grammatical, but meaningless or semantically ill-formed, sentences, such as

(26) 'My uncle is pregnant again',

are. not only fully meaningful, but usable to assert what might be a true proposition in some possible world. We shall return to this question in the following chapter.

 

4.5 SENSE-RELATIONS AND M E A N I NG - POSTU L ATES

In Chapter 3, a distinction was drawn between denotation and sense, and sense was defined in terms of sense-relations. Some sense-relations were exemplified, but without discussion. None of them, apart from descriptive synonymy, has yet been named or defined. For a more detailed account of various sense-relations, reference may be made to other publications. I will give the briefest possible outline here. My principal concern in the present context is to show how sense-relations of various kinds can be formalized.

Sense-relations are of two kinds: substitutional and com­binatorial (or, in the Saussurean terms more familiar to lin­guists, paradigmatic and syntagmatic). Substitutional relations are those which hold between intersubstitutable members of the same grammatical category; combinatorial relations hold typically, though not necessarily, between expressions of different grammatical categories (e.g., between nouns and adjectives, between verbs and adverbs, etc.), which can be put together in grammatically well-formed combina­tions for constructions). For example, a substitutional relation (of a particular kind) holds between the nouns 'bachelor' and 'spinster', whereas the relation that holds between the adjective 'unmarried' and the nouns 'man' and 'woman' is combinator­ial. The lexically composite expressions 'unmarried man' and 'unmarried woman' are not only grammatically well-formed, but by virtue of what I will call the congruity of the sense of the adjective with the sense of both of the nouns they are also collocationally acceptable: that is, they can occur together

45 Sense-relations and meaning-postulates 125

in the same construction. It is intuitively obvious, on the basis of these and other examples, that a more specific, lexically and grammatically simpler, expression may be more or less descriptively equivalent to a lexically composite expression in which two (or several) more general expressions are combined. For example, 'foal' may be descriptively equivalent to 'baby horse'.

I shall have little to say^: here about combinatorial sense-relations, since they bring us into the area of grammatical meaning and sentence-semantics. It is important to note that certain lexemes are sohighly restricted with respect to collocational acceptability that it is impossible to predict their combinatorial relations on the basis of an independent characterization of their sense. Classic examples from English are the adjectives 'rancid' and 'addled'. It is clearly an important part of knowing their sense to know that 'rancid' combines, or collocates,with 'butter', and 'addled' with 'egg' (and, metaphorically, with 'brain'). The view taken here is that the sense of any lexeme, whether it is highly restricted with respect to collocational acceptability or not, includes both its combinatorial and substitutional relations.

Only two kinds of substitutional relations of sense will be dealt with in detail here: hyponymy and incompatibility. They are both definable in terms of entailment.

The relation of hyponymy is exemplified by such pairs of expressions as 'dog' and 'animal', of which the former is a hypo-nym of the latter: the sense of 'dog' includes that of 'animal'. Entailment, as we saw in the previous section, is a relation that holds between propositions. However, provided that we keep this fact in mind, it is convenient to be able to say, in a kind of shorthand, that one word or phrase entails another, just as it may be convenient to be able to say, also in a kind of shorthand, that one sentence entails another. Adopting this kind of short­hand we can say one expression, f, is a hyponym of another expression, g, if and only if entails g: i.e.,

(27) f => g.

126 The structural approach

For example, 'dog' entails 'animal'. Given a proposition p con­taining "dog", the substitution of "animal" for "dog" in p will yield another proposition q which is entailed by p. Thus:

(28) "I saw a dog" (p) entails

(29) "I saw an animal" (q).

In this case no syntactic adjustments need to be made. We still have to relate propositions to utterances (and prepositional content to sentences). If this can be done, the statement that 'dog' is a hyponym of 'animal' can be given a precise formal interpretation. All this will be of concern to us later. But what is the status of f => g from a formal point of view?

It is best construed as what some logicians, following Carnap (1956), call a meaning-postulate. Generally speaking, the use of meaning-postulates has been seen by linguists as an alter­native to componential analysis. Looked at from this point of view, the advantage of meaning-postulates over classical or stan­dard versions of componential analysis is that they do not pre­suppose the exhaustive decomposition of the sense of a lexeme into an integral number of universal sense-components. They can be defined for lexemes as such, without making any assump­tions about atomic concepts or universality, and they can be used to give a deliberately incomplete account of the sense of a lexeme. From an empirical point of view these are very consider­able advantages. It is, after all, a matter of dispute whether it is possible, even in principle, to give a complete analysis of the sense of all lexemes in the vocabularies of natural languages. As I have emphasized, on several occasions, it is, to say the least, arguable that the sense of some natural-language lexemes is to a greater or less degree fuzzy and indeterminate.

Of course, the validity of any particular meaning-postulate,such as

(30) 'dog' => 'animal'

for English, will depend upon whether the alleged entailment is in fact analytic. In this connexion, it is worth noting the

4.5 Sense-relations and meaning-postulates 127

possibility of ordering the meaning-postulates associated with a particular lexeme hierarchically in terms of their degree of analy-ticity. For example,

(31) 'bachelor' => 'unmarried'

(in the relevant sense of the word 'bachelor') seems to be more highly, or more definitely, analytic than

'bachelor' => 'adult'
and perhaps also than

'bachelor' => 'man'.

Let us suppose, for example, that child-marriages were legalized and became a matter of everyday occurrence in some English-speaking society. One would presumably not hesitate to use the word 'bachelor' of an unmarried child in such circumstances. And, arguably, there would have been no change in the sense of 'bachelor'. It is far more difficult to envisage comparable cir­cumstances in which 'bachelor' => 'unmarried' is invalidated without some other associated change in the sense of either 'bachelor' or 'unmarried'. Regardless of the empirical status of the particular example, it is clear, therefore, that speakers of a language may regard some entailments of a word as more cen­tral or more determinate than other entailments of the same word.

Hierarchically ordered meaning-postulates can be used to capture the indeterminacy of the boundary between the analytic and the synthetic. I have made this point in relation to hypo-nymy, but it holds for all the sense-relations that can be forma­lized in terms of meaning-postulates. Before we continue, it is now worth noting that descriptive synonymy may be defined in terms of symmetrical hyponymy. Although the term 'hypo­nymy' is customarily used for an asymmetrical relation of entail­ment (i.e., where f entails g, but g does not entail f: 'dog' => 'animal' is true, whereas 'animal => 'dog' is false), there is noth-ing in the formal definition of hyponymy which makes this essen­tial. Using a double-headed, double-shafted arrow to symbolize symmetrical entailment, we can say that

128 The structural approach

 

(34) f => g

establishes the descriptive synonymy of/and g (e.g., 'puppy' <=> ' baby dog'). It can be readily proved that the definition of descriptive synonymy in terms of symmetrical entailment is equivalent to the following: two expressions are descriptively synonymous if and only if they have the same entailments.