CHAPTERS6 2 страница

If it is interpreted inclusively (which is clearly the most likely interpretation in a case like this), this would mean that students who fail to fulfil both conditions, in addition to students who fail to fulfil only one of the conditions, will be refused admission; if it were interpreted exclusively, this would mean that students failing to fulfil only one of the conditions would be refused admission, but not necessarily students who fail to fulfil both conditions. In other cases, an exclusive interpretation is more likely:

e.g.,

(17) For the main course you may have meat or fish.

Usually, when logicians 'use the term 'disjunction', without qualification, they mean inclusive disjunction.

To return, then, to the Latin example. In fact, it does not seem to be the case, except perhaps in the specialized usage of logi­cians, that vel is used for inclusive and aut for exclusive disjunc­tion. What is true, however, is that the aut -construction is stronger or more expressive than the vel -construction, in much the same way that but -conjunction is stronger and more expres­sive than and- conjunction in English. It is difficult to be more precise than this without attributing to aut, in contrast with vel, several distinct meanings.

Perhaps the best way of explaining what is meant by 'stronger and more expressive' in this context is to say that the nearest equivalent to the aut -construction in (spoken) English is (either)... or... with heavy stress on the disjunctive particles. Much the same effect is achieved in French by adding bien to the otherwise neutral disjunctive particles (ou)... ou..., and in Russian simi­larly by adding zhe. In some contexts, stronger or more expres­sive disjunction will indeed be understood to be exclusive in the logician's sense; in others, however, it will indicate that, in the speaker's opinion, the alternatives p and q are the only proposi­tions worth considering and will dramatize, or emphasize, the necessity of opting for one or the other. The distinction between inclusive and exclusive disjunction can be accounted for truth-

6.4 Truth-functionality (2): implication 167

functionally; the distinction between neutral and stronger, or more expressive, disjunction cannot.

6.4 TRUTH-FUNCTIONALITY (2): IMPLICATION

Implication (more precisely, what logicians call material implication) is usually rendered into English by means of a conditional sentence: for example,

(18) 'If Ann has passed her driving test, her parents have
bought her a Porsche'.

As was mentioned in section 6.2, the composite proposition p —> q (" p- implies- q ") is true, by definition, not only when both p) and q have the same truth-value (i.e., when both are true or both are false), but also when p is false and q is true. (It follows that p —> q is false only when p is true and q is false.) So the proposition expressed by (18) — if it has the logical form of " p implies q" — is true not only (i) if Ann has passed her driving test and her par­ents have bought her a Porsche (p & q), but also (ii) if she has not passed her driving test and/but her parents have bought her a Porsche (~ p & q), and (iii) Ann has not passed her driving test and her parents have not bought her a Porsche (~ p & ~ p). Most people find (ii), if not (iii), paradoxical. Indeed, the fact that any false proposition (materially) implies every true propo­sition is commonly referred to as one of the paradoxes of implication.

A second point is that (in standard propositional logic) the truth-value of "p implies q", like that of "p and q", is totally independent of any causal connexion between the situations described by each of the component propositions. For example, the proposition expressed by

(19) ' If Lady Godiva had blue eyes, Ann's parents have bought
her a Porsche'

would be true (independently of the colour of Lady Godiva's eyes) if the parents of the person referred to by 'Ann' and 'she' (in the form her), on some occasion of the utterance of the sen­tence, have indeed bought her a Porsche. Once again, most

168 Sentence-meaning and propositioned content

people find this paradoxical. More generally, they find it para­doxical that the truth-functionality of an implication is unaf­fected by the absence of any kind of causal connexion between the situations referred to in the two component propositions, p and q. Of course, it is always possible to devise a more or less plausible connexion for any two clauses in any conditional sen­tence and thereby eliminate the apparent paradox; and the full importance of this fact will emerge in our treatment of the notion of relevance in Chapter 9. For example, the Porsche might have been a prize for knowing or discovering the colour of Lady Godiva's eyes. But what if we do not seek to eliminate the so-called paradoxes of implication in this way?

One of the conditional sentences cited earlier, which is here
repeated,

(7) 'If he passed his driving test, I am a Dutchman',

is interesting (but highly untypical) from this point of view. As it would normally be used (by non-Dutchmen), it depends for its effect upon the known falsity of q ("I am a Dutchman") and the presumed absence of any causal link between the situations described by p (in this case "He passed his driving test") and q. Under these circumstances, we might well be prepared to say that the composite proposition (p — > q) expressed by the sentence as a whole is equivalent to the one expressed by 'Either he did not pass his driving test or I am a Dutchman' (~p V q), and that it is true if both p and q are false. But this is surely because the utterance of this sentence is rhetorically equivalent to the denial of q in a context in which the denial of p is nop-informa-tive. In other words, the speaker can trade on the hearer's knowledge that the speaker is not a Dutchman and the hearer's consequential ability to infer the falsity of p ("He passed his driv­ing test") from the truth of the presumably informative compo­site proposition "p implies q ". The speaker can be all the more certain that the hearer will draw the, correct inference in a case like this because the proposition "I am a Dutchman" has been conventionalized in some English-speaking societies for this very purpose. However, any sufficiently prepo'sterous or self-evidently false proposition 'will serve the same rhetorical

6.5 Truth-functionality (3): negation 169

purpose ("If he has got a degree in linguistics, I am the Queen _of Sheba", etc.). We do indeed make rhetorical, or as many would say these days pragmatic, use of at least a subclass of conditional sentences in the way that I havejust illustrated.

In this section, we have been dealing with what logicians call material implication. There are other kinds of implication recognized in current linguistic semantics (and pragmatics), two of which may be mentioned here: entailment and impli-cature. The former, sometimes called strict implication, was introduced in section 4.4 in association with the notion of poss­ible worlds: as we saw there, a proposition p entails a proposition q if, when p is true, q also is necessarily (and not just contin­gently) true (i.e., it is true in all possible worlds). The notion of entailment plays a major role in formal semantics: it is by no means restricted to the purpose for which it was introduced earlier (for the definition of sense-relations between lexemes). Implicature, by contrast, is a looser kind of implication, closer to what is often meant by 'implication' in everyday,¹ non­technical, usage: a proposition p is said to implicate (rather than to imply) a proposition q if the truth of q can be reasonably inferred from p in the context in which p is asserted or is otherwise known or assumed to be true. The important point to note for the moment is that implicature is context-dependent and therefore, in terms of the theoretical framework adopted in this book, is a matter of utterance-meaning. It will be dealt with in Part 4.

6.5 TRUTH-FUNCTIONALITY (3): NEGATION

As we saw m section 6.2, negation (symbolized by '~') is regarded by logicians as an operation which forms a composite proposition (~ p) out of a simple proposition (p). As far as stan­dard, two-yalued, prepositional logic is concerned, the truth-functional definition of negation is straightforward: whenever p is true, ~p is false and whenever p is false, ~ p is true. It is further allowed that negation should be recursive, so that the negation of ~ p, yields ~ ~ p, which is equivalent to p (two negatives make a positive), the negation of ~ ~p yields ~ ~ ~ p, which is

170 Sentence-meaning and propositional content

equivalent to ~ p, and so on. How does the standard logical account of negation relate to the meaning and use of negative sentences in natural languages? More particularly, how much of the meaning of negative constructions is part of the prop­ositional content of sentences?

There are various ways in which negative sentences are con­structed in natural languages. Only rarely, however, is there any reason to say that a negative sentence is grammatically com­posite by contrast with the corresponding positive, or affirma­tive, sentence. Generally speaking, corresponding sentences of opposite polarity have the same clause-structure, and what we can identify most easily with propositional negation applies within clauses and does not extend to whole sentences. Indeed, in many languages (including Finnish and Irish) the negative polarity of a clause (like its mood or its tense) is marked not by means of a separate particle like the English not, but by special forms of the verb, or predicate. Hence the traditional maxim: negation of the predicate is equivalent to negation of the prop­osition.

But there is one kind of predicate-negation which is clearly not equivalent to the negation of the whole proposition. This may be exemplified by

'John is unfriendly',
which, unlike

'John is not friendly',

expresses a proposition that is not just the contradictory of the proposition expressed by

'22) 'John is friendly',

but its contrary. 'John is unfriendly" is not simply the negation of "John is friendly": it implies "John is hostile". (In standard logical terminology, one proposition is the contradictory of another if it is impossible for both of them to be true and both false. One proposition is the contrary of another if both cannot be true, though they may both be false.) It is quite possible for John to be neither friendly nor unfriendly.

6.5 Truthjunctionality (3): negation 171

i In facti 'John is not friendly' is often used in eyeryday conver-^!sation as if it had the same sense as 'John is unfriendly'. (We are not concerned, in this context, with spoken utterances ol (21) in which the forms not and friendly are, as it were, hyphenated pro-sodically. In such utterances, not friendly is obviously to be inter­preted as the form unfriendly would be.) There are three ways of handling this fact. The first, which is excluded by the formula­tion I have just used, is to say that there are two distinct sen­tences represented in written English by 'John is not friendly' and that they are distinguished, at least optionally, in spoken English by means of rhythm and intonation. But rhythm and the fine differences of intonation that are involved in cases such as this are universally excluded by linguists from what they con­sider to be part of the prosodic structure of sentences. The second way is to say that there is one sentence, and that it is structurally ambiguous. But there are no other, independently motivated, reasons for adopting this view. The third way is to draw upon the distinction between sentence-meaning and utterance-meaning and to say that 'John is not friendly' is a single un­ambiguous sentence which can be uttered in a particular way, and perhaps also in identifiable contexts, with more or less the same communicative effect as the utterance of 'John is unfriendly'. It is the third of the three analyses that is adopted here.

It is also possible to have negated nominal expressions occur­ring as clause-constituents. For example,

(23) 'Non-students pay the full entrance-fee'

expresses a proposition which differs from, and does not entail (though it may, in context, implicate) the proposition expressed by

(24) 'Students do not pay the full entrance-fee'.

Nominal negation of this kind ('non-students'), like predicative negation ('do not pay'), has an effect on the propositional con­tent of the clause in which it occurs and is in principle truth-functional; but it cannot be readily formalized in standard propositional logic.

172 Sentence-meaning and prepositional content

To be contrasted with nominal negation of the kind exempli­fied by 'non-students' above is the use of negative indefinite pro­nouns such as 'no-one' or 'nothing' or the semantically comparable nominals introduced with the ^djectival 'no' (e.g., 'no man': cf. French 'aucun homme', German 'kein Mensch', etc.j. It is obvious, upon reflection, that

(25) 'No-one telephoned'

expresses a proposition which contradicts the proposition expressed by

'Someone telephoned',
whereas

'Someone did not telephone',

which looks as if it is the negative sentence that most directly cor­responds to (26), can be conjoined with (27) to express the non-contradictory composite proposition,

(28) "Someone telephoned and someone did not telephone".

Most logicians and linguists have taken the view, until recently at least, that the propositions expressed by (25), (26) and (27) differ in logical form from the propositions expressed by, say,

(29) 'John telephoned'

 

and

(29a) 'John did not telephone'.

Standard logical analyses of the prepositional content of (25), (26) and (27); all make use of the existential quantifier with or without negation, as the case may be, and handle the seman­tic difference between (25) and (27) in terms of the relative order of the quantifier and the negation operator. The most notable difference between the negative sentences (25) and (29a), from this point of view, is that the latter (when it is used to make a statement) is associated with a particular kind of exis­tential presupposition: that is, it conveys the speaker's pre­supposition that there exists some entity that may be

6.5 Truth-functionality (3): negation 173

appropriately referred to with the expression 'John'. There is no existential presupposition associated with the use of 'nobody', 'nothing', etc. The standard analysis of (25) correctly accounts for its difference, in this respect, from (29a). But it does so at the price of discounting their apparent grammatical parallelism.

Consideration of sentences such as those listed above within a more comprehensive discussion of negation in English and other languages raises further problems. How are positive sentences containing 'some' (or 'someone', 'somewhere', etc.) related grammatically and semantically to corresponding nega­tive sentences containing 'any' (or 'anyone', 'anywhere', etc.)? (What is the relation, for example, between 'He saw someone' and 'He did not see anyone'?) And how are they related to corre­sponding negative sentences containing 'some'? (Does 'He saw no-one' mean exactly the same as 'He did not see anyone'?) Problems like this, involving the complex interaction of nega­tion, the use of determiners, quantifiers and indefinite pronouns (and adjectives), etc., have been extensively treated by linguists in recent years. In some cases, the facts themselves are in dispute, especially when it comes to alleged differences of meaning which cannot be accounted for truth-functionally. But it is very difficult to handle even the undisputed cases of prepositional negation in a theoretically unified framework within which grammatical structure and logical form can be put into corre- spondence simply and systematically.

Negation is an operation that applies to a single expression. But the expression in question can be simple or composite. In ~ p, the expression to which the operator applies - the expres­sion that is in its scope - is simple, whereas in ~ (p & q) it is composite. Everything within the matching left and right brack­ets that immediately follow the negation-operator is in its scope: in default of such brackets the negation-operator is taken to apply to the smallest expression on its right. There is therefore a significant difference between ~ (p &. q) and ~p & q: between, say,

(30) "Mary was not (both) well-and-cheerful" and

174 Sentence-meaning and propositional content

(31) "Mary was (both) not-well and cheerful"

(if I may informally indicate the difference by means of hyphens).

It is easy to see that there are other such differences of scope in respect of propositional negation in natural languages. For example, the English sentences

(32) 'John did not kiss Mary because she was his sister'
can be construed in two ways: as

(33) "It was because she was his sister that John did not kiss
Mary"

or, alternatively, as

(34) "It was not because she was his sister that John kissed
Mary".

Under interpretation (33), the sentence in question is taken to be one in which negation applies only to the propositional content of the main clause ("John kissed Mary"); under interpretation (34), it is a sentence in which negation applies either to the content of the subordinate clause ("because she was his sister") or (and this is perhaps the preferred analysis) to the composite proposition "John kissed Mary because she was his sister". Of course, the difference between (33) and (34) is not correctly formalized in terms of the truth-functional difference between ~ p & q and ~ (p & q). As we have seen, the propositional calculus cannot draw the distinction between conjunction and causal subordination. Nevertheless, it is intuitively clear that the difference between (33) and (34) is, in principle, formalizable in terms of the scope of propositional negation. There are man)- such examples.

The scope of negation is also relevant in modal logic, which extends the propositional calculus by means of the logical operators of necessity (N) and possibility (M). The proposition

(35) "It is not necessary that p " (~ Np). differs truth-functionally from

6.5 Truth-functionality (3): negation 175

"It is necessary that not ~ p " (N~p}.
For example,

"The sky is not necessarily blue"
differs in truth-value from

"Necessarily, the sky is not blue".

As we shall see in Part 4, at least some of what can be identified as modality in natural languages can be ascribed to the prop­ositional content of sentences. In such cases, there is some degree of correspondence between the scope of negation and gram­matical structure. For example, the utterance

(39) He may not come

can be construed, syntactically, in two ways (and thus put into correspondence with two different sentences), according to whether the negative particle not has narrower or wider scope than the modal verb 'may':

"It is possible that he will not come" (M~p),
in contrast with

"It is not possible/allowed that he will come" (~Mp).

What cannot be formalized, even in modal logic, is the differ­ence between the assertion of a negative proposition ("I say that it is not raining") and the denial of a positive proposition ("I deny that it is raining"); or again, the difference between the assertion of a positive proposition ("I say that it is raining") and the denial of a negative proposition ("I deny that it is not raining"). Here, too, we have differences that can be accounted for in terms of the scope of negation. Moreover, they are differ­ences that are reflected, at least partly, in the syntactic and pro-sodic structure of sentences in many languages. But assertion and denial are not, and cannot be, constituents of propositions or propositional content; they are different kinds of communica­tive acts. In so far as the difference between assertion and denial, and between other kinds of communicative acts, is

176 Sentence-meaning and prepositional content

systematically encoded in what was earlier referred to as the face-value of sentences, it is yet another part of the meaning of sentences that is not part of their prepositional content.

6.6 S E X T E N C E - T Y P E, C L A U S E - T Y P E A N D MOOD

It is by now common enough for linguists to draw a terminologi­cal distinction between declarative sentences and statements, between interrogative sentences and questions, between impera­tive sentences and commands, between optative sentences and wishes,' between exclamative sentences and exclamations. It is far less common for them to point out that, in traditional usage, there is a crucial difference between 'declarative', 'interrogative' and 'exclamative', on the one hand, and 'imperative' or 'opta­tive', on the other. The formed set of terms subclassify sentences according to what is often failed sentencfe-type. (This is a quite different sense of the term 'type' from the sense in which 'type' is opposed to 'token'. As we shall see in Part 4, within the conceptual and terminological framework adopted in this book, the type/token distinction does not apply to sentences, since, unlike utterances, they are hot forms.) The terms 'impera­tive' and 'optative', however, go traditionally with 'indicative', 'subjunctive', 'dubitative', 'evidential', etc., and subclassify sen­tences (or clauses) according to mood. Some terms, notably 'conditional', are used traditionally both of sentence-type and mood: this point, in respect of the term 'conditional', will be picked up presently, since conditional propositions have long been of particular concern in logical semantics.

At this point, I should remind the reader that, although we are operating throughout this book with two fundamental dis­tinctions, the distinction between lexical meaning (or word-meaning) and sentence-meaning, on the one hand, and the dis­tinction between sentence-meaning and utterance-meaning, on the other, it is arguable that it is clauses, rather than sentences, that correspond most closely to propositions and also that they are more basic grammatically (cf. 6.2). In what follows, I will, for simplicity, use the terms 'sentence' and 'sentence-type', where some grammarians might prefer to use 'clause' and

6.6. Sentence-type, clause-type and mood 177

'clause-type'. My principal reason for continuing to operate, pri­marily, with 'sentence' and 'sentence-type' is that these are the terms that are most commonly used in formal semantics (where, furthermore, a clear distinction is not always drawn between sentences and propositions). Nothing of substance is affected by this purely terminological decision, since everything that is said in Parts 3 and 4 of this book could be reformulated without difficulty in terms of clause and clause-types. (When it comes to the detailed integration of semantics and syntax within a particular theoretical framework, the selection of sentences or clauses as basic, and in what sense of 'basic', does of course make a difference. But at the level of generality at which we are operating in this introductory.work this is something we need not be concerned with.) Jn order to make explicit the possibility of adopting an alternative view, I have 'included 'clause-type' in the section heading, and I have occasionally added the terms 'clause' and 'clause-type' in brackets.

There is a connexion between sentence-type (or clause-type) and mood. But type and mood are partly independent dimen­sions of the grammatical structure of sentences (and clauses), and it is important not to confuse them. In particular, it is important not to confuse or to conflate 'declarative' with 'indi­cative', as philosophers and even linguists do at times. A sen­tence cannot be simultaneously interrogative and declarative; but in many languages it can be both interrogative and indica­tive (as these terms are traditionally understood): i.e., it can be interrogative in sentence-type and contain, as its sole or princi­pal clause, one that is indicative in mood. But it can also be, in some languages if not in English, both interrogative and sub­junctive. For example, the Latin sentence

(42) 'Quid faceret?',

which is in the imperfect subjunctive, differs grammatically and semantically from

(43) 'Quid faciebat?',

 

 

1 78 Sentence-meaning and prepositional content

which is in the imperfect indicative. Both (42) and (43) can be translated into English according to context in various ways: e.g.. as

(42a) 'What was he/she to do?'

or

(43a) 'What was he/she doing?'.

It is important to realize that the semantic difference between (42) and (43) in Latin is exactly parallel with the difference between

(42b) 'Quid faciam?' ('What am I do to?')

and

(43b) 'Quid facio?' ('What am I doing?'),

in which the verbs are in the present tense subjunctive and indi­cative, respectively, and the subject is in the first person. Sen­tences such as (42) and (42b) can also be analysed as having the same prepositional content as (43) and (43b) respectively, but as combining with this a non-propositional - truth-condition-ally unanalysable - expressive, and more particularly subjec­tive, component of meaning (see 10.6). The English translations of (42) and (42b) which I have given above are potentially misleading in that they dp not grammaticalize this subjective component of utterances by means of the category of mood in a one-clause sentence, and they encourage the semanti-cist to look for a non-subjective analysis involving the embed­ding of the prepositional content of one clause within that of another. Modern English, in most dialects, makes very little use of the distinction between the indicative and the subjunctive even in subordinate clauses.

Just as, in some languages, a sentence can be both inter­rogative and non-indicative, so too there are languages in which a sentence can be declarative without being indicative. Indeed, there are languages (notably, members of the American-Indian Siouan family) in which there are various kinds of non-indicative declarative sentences, but no indicative

6.6 Sentence-type, clause-type and mood 179

sentences at all. Speakers of such languages, when they use a sen­tence to make a statement cannot but encode in the verbal com­ponent of their utterance, by the choice of one grammatical mood rather than another, some subjective qualification of their commitment to the truth of the proposition they express or some other indication of what may be referred to later as its epistemic status. (What is meant by 'epistemic' and 'subjective qualifica­tion' will be explained in sections 8.4 and 10.5.) In so far as the sentences in question are members of a class (a sentence-type) which is associated, characteristically, with making statements, they are declarative. But none of the subclasses is indicative (in mood), because none of the moods in these languages is asso­ciated with the neutral (objective or non-subjective) expression of prepositional content (in the making of statements, the asking of questions, or whatever). The indicative, in those languages which have such a mood, is traditionally regarded as the mood of factuality. Obviously, one can not only assert or deny, but also query, presuppose, or even simply consider (in soliloquy or thought), the factuality of a proposition.

An indicative sentence (or clause) is by definition a sentence (or clause) in the indicative mood, as an imperative, subjunctive br optative sentence (or clause)¹ is a sentence (or clause) in the imperative, subjunctive or optative mood, in those languages which have any or all of these moods. Mood, as_; a grammatical category of the sentence (or clause), is frequently encoded infiec-tionally, throughout the languages of the world (as it is in Latin and Greek and the other Indo-European languages), in the grammatically distinct - more precisely, morphosyntactically distinct - forms of the verb in the sentence (or clause) of which the verb is the head. It is for this reason that mood is often defined, in traditional grammars, as a category of the verb. But this association of mood with verbal inflection is, in principle, contingent. As we shall see later, mood is best defined as that category which results (in those languages which have it) from the grammaticalization of subjective modality and other kinds of expressive meaning, including some part of what is nowadays commonly referred to as illocutionary force (8.3). Much of this, in English, is encoded in the modal verbs, which