Ambiguity and vagueness in semantic

Ambiguity and vagueness

Ambiguity could be meant that both words and sentences can have more than one meaning, and the semantic rules a linguist sets up must state correctly for each language which words and sentences have more than one meaning. A little problem in deciding of a given sentence whether or not it is ambiguous is count as ambiguity. There are many cases where it is not at all clear whether the word, phrase or sentence in question is ambiguous or not.

For Instance: She has good legs.

Take the word good .Is it ambiguous? This sentence can either mean that she has healthy legs (no varicose veins, no broken or badly mended bones, no weak ankles, etc), or it can mean that she has beautiful legs, or it can mean that she has legs which function well (as an athlete’s, or a gymnast’s and etc).

So, we can conclude that the word good may be used in sentences with different interpretation. The problem is compounded when we look at other phrases containing good. A good student describes either someone who behaves well, or even someone who works haphazardly but shows a high level of ability. Then in other sentence containing good is A good film. This sentence can either means one which gives enjoyment or one which is thought to be of lasting value. What has to be decided is whether the meaning of good is homogeneous and neutral between all these different specifications, or whether good has different meanings according to its use in describing different things. In more general terms, this presents an example of the difficulty of distinguishing ambiguity from lack of specification or vagueness.

A.      Four types of vagueness

To see the extent of the problem of distinguishing ambiguity from vagueness, let us consider the different types of vagueness. There four types are not unrelated to each other:

1.      Referential vagueness

Referential vagueness, where the meaning of the lexical item is in principle clear enough, but it may be hard to decide whether or not the item can be applied to certain objects.

For example: city and town. Presumably we can at least roughly agree that a city is a place where a large collection of people live, and it is made up of a large number of houses; whereas a town is simply any place where a collection of people live, made up of a certain number of houses. Town can be small or large, but cities are big by definition. If we can agree that the meanings of the items need to have a specification along these lines, we shall certainly find difficulty in individual cases in deciding whether or not some place is city or town. Is Bradford a city? Notice that it will not do to specify as part of the meaning of the item that a city must contain a minimum number of inhabitants, for we can talk of Roman cities where the numbers might scarcely exceed that of a present-day village.

2.      Indeterminacy of meaning

The second type of vagueness is Indeterminacy of the meaning of an item or phrase, where the interpretation seems itself quite intangible and indeterminate.

For instance: Possessive construction – John’s book.

John’s book can be used to describe the book John wrote, the book he owns, the book he has been reading, the book he has been told to read, the book he was carrying when he came into the rooms, etc. in the face of this variety, it seems clear that we can say little about the meaning of possessive construction other than that there must be some relation of association between the possessor and the possessed. The meaning is otherwise quite indeterminate.

3.      Lack of specification in the meaning of an item

This is the third type of vagueness, where the meaning though in principle quite clear is very general.

For example: neighbour.

This word is unspecified for sex, or for that matter, race or age, etc.

4.      Disjunction in specification of the meaning of an item.

This is the type where the meaning of an item involves the disjunction of different interpretation. Disjunction within a single lexical item leads to a prediction that where more than one of the disjunction can be interpreted, then such interpretation should be possible simultaneously.

For instance: To see the validity of this type of characterization consider what is perhaps the central example: or.

a.      The applicants for the job either had a first class degree or some teaching experience.

b.      All competitors must either be male or wear a one-piece swimming costume.

In each of these cases, the implication that or contributes to the sentence as a whole is that one of the conjuncts is true. In (1), the applicants are implied to have had either a first-class degree but no teaching experience, or teaching experience but not a first-class degree, or possibly both. That is to say there is an interpretation in which both implications can be held simultaneously. In (2), the implication is similar. The utterer of such a sentence would certainly not be excluding the possibility of both of the conjuncts being true, for this would imply that a male competitor had either to wear nothing a two piece costume! On the contrary, the sentence allows the following types of competitor: male competitors (whether wearing one-piece costume or not) and non-male competitors wearing one piece costume. This disjunction in the characterization of or can be stated more formally in terms of truth conditions.

            P and Q each represent sentence and v correspond to or. P v Q will be true if and only if either P is true, or Q is true, or P and Q are true. It can be true under different conditions.

P	Q	P v Q
T T F F	T F T F	T T T F

Another important example of disjunction in a single semantic representation is provided by negation.

B.      An ambiguity test

In order to be certain of separating out cases of vagueness from cases of ambiguity, we need a test which distinguishes clear cases of vagueness and ambiguity, and which will give us some basis for deciding on the less clear cases. Let us look first at the preliminary truth-conditional definition of ambiguity: does this provide a basis for distinguishing the two phenomena? Unfortunately the answer is clearly 'No'. Our definⁱtion of ambiguity, which is a standard truth conditional definition, is that a sentence is ambiguous if it can be true in quite different circumstances. But this would predict that in all cases where the meaning is unspecified, the sentence in question would be as many ways ambiguous as the contrasting circumstances which that unspecified meaning allowed the sentence to be true in. There is an alternative, equivalent formulation of this definition: that a sentence is ambiguous if it can be simultaneously true and false, relative to the same state of affairs. But this alternative characterization is no more helpful in unclear cases. For suppose we are uncertain whether a given sentence is ambiguous with respect to some contrast, or merely unspec_ified as to that contrast.

Take for example John killed Bill. Is this sentence am­biguous, one interpretation being that John killed Bill intentionally, the other interpretation being that John killed Bill by accident? Or is the sentence merely unspecified as to whether the action is intentional or not. The sentence can certainly be used to describe these two rather different kinds of events. It can in other words be true in these two rather different sets of circumstances. We in fact distinguish lexically between murder and manslaughter which are speci­fied as to intentionality on the part of the agent. Suppose one linguist claims that the sentence Johan killed Bill has no specification in its mean­ing as to whether the action implied is intentional or not. He would anticipate that the sentence would be true both in circumstances in which the action was unintentional, and in which the action was inten­tional. He would argue that the question of intentionally is simply not relevant to the assessment of the truth value of the sentence. But suppose also that some other linguist disagrees, claiming that the sentence is ambiguous between an intentional interpretation and an unintentional interpretation. This linguist will say that in circumstances where the action was unintentional, the sentence is true on the uninten­tional interpretation and, simultaneously, false on the intentional interpretation. In circumstances where the action was intentional, that same linguist would say, conversely, that the sentence is true on the intentional interpretation and, simultaneously, false on the unintentional interpretation. Since, he would argue, this sentence meets the require­ment that a sentence be ambiguous if it is simultaneously true and false relative to the same state of affairs, it must be ambiguous. Now these linguists have reached an impasse. The characterization of ambiguity as the simultaneous assignment to a sentence of the values true and false has not provided a criterion for deciding unclear cases; it merely accentuates the point of disagreement.

For a more helpful way of distinguishing sentences which are am­biguous from those which are not, we have to turn to anaphoric pro­cesses, processes which refer back to an earlier part of the sentence. One example of this is the expression to do so too. This is used where the action described has already been specified and is being referred to again. For example the sentence John hit Bill and Jason did so too implies that Jason also hit Bill. In more linguistic terms, the uses of the expression do so too demands identity of meaning of the two verb phrases in question. Now this provides us with a test for ambiguity. If some verb phrase (the traditional expression of predicate phrase is equivalent to verb phrase) is two-ways ambiguous, then we can predict that when it is conjoined to a do so or other verb phrase pro-form expression, the entire sentence will be two ways ambiguous – whichever interpretation is implied, the do so expression must be identical to that interpretation. More formally, a sentence which is two-ways ambiguous must be given two semantic representations to characterize its two meanings. Since a do so expression or any other verb phrase pro-form demands identity of meaning, a two-ways ambiguous sentence together with such an expression can only be two-ways ambiguous – in both of the two representations of the sentence's meaning, the pro-form expression will always be identical to it. So for example we predict that (3) is only two-ways ambiguous.

(3) Johnny saw her duck and Will did so too.

Either it means that Johnny saw the duck which belonged to her and Will also saw the duck which belonged to her; or it means that Johnny saw her quickly lower her head and Will also saw her quickly lower her head. What we predict that it cannot mean is that Johnny saw the duck which belonged to her and Will saw her quickly lower her head, because in such a case, the meaning of the two verb phrases would not be identical. And so it is. Except as a pun, there is no possibility of such crossed interpretations when the verb phrase to which do so is added is ambiguous. In the case of an unspecified or vague verb phrase, we have a contrary prediction. Do so expressions require identity of meaning, and where the meaning in question is unspecified with respect to some contrast, there is no reason to expect that non-identical interpretations are excluded. For example, the sentence John is my neighbour and Sue is too does not imply that because Sue is also my neighbour she must have all the properties that John has being, say, a six-foot male West Indian. Or, to take our previous example of do the room, the painter has done the sitting-room and the carpet-man has too does not imply that the carpet-man must also have painted the sitting-room. On the contrary, the natural interpretation is that different actions have been carried out. If the expression to do the sitting-room were said to be ambiguous according as the actions it described differed, we would predict that such different interpretations of the expression could not be conveyed in the above example. But they can; and they can because the expression to do the sitting-room is not ambiguous but merely unspecified.

We are now in a position to see how this test works in slightly less obvious cases. Let us return to kill and the problem of the specification of unintentionality. Given that kill can be used to describe actions which are intentional on the part of the instigator and actions which are quite accidental, the point of disagreement is whether the word kill is corres­pondingly ambiguous, or whether it is merely unspecified as to inten­tionality. If it is ambiguous, one should not be able to interpret sentence (4) as having conflicting interpretations of intentionality on the part of Johnny and Susie. If kill is merely unspecified as to whether or not the action of killing is intentional, then such conflicting interpretations will be possible.

(4) Johnny killed a bird today, and so did Susie.

Can this sentence be used to describe an occasion on which Susie came in heart-broken because she had ridden her bicycle over a lark's nest quite by mistake and killed a young lark; but Johnny, the little horror, was thrilled when he finally managed to shoot down a pigeon with his air-gun? It surely can. Similarly there is nothing odd in  (5) despite the fact that, of the two actions described, only one was intentional.

(5) Gesualdo killed his wife, and so did Orpheus.

To take another somewhat unclear case, which has been used as the basis for an argument in the recent syntax—semantics controversy, consider the word almost. The sentence John almost killed the hostages can be used to describe an occasion on which John was on the point of carrying out some action which would have caused the hostages to die, or it can be used to describe an occasion on which John did carry out some action which brought the hostages to the point of death. What we have to decide is whether the sentence is ambiguous, and has two quite separately specifiable meanings, or whether it has a meaning which does not specify exactly how almost interacts with the remainder of the sentence. For example, what does sentence (6) mean?

(6) John almost killed the hostages and so did Manuel.

As a first approximation let us agree that the hostages were almost brought to the point of death by both John and Manuel. But can it be used to describe an occasion on which John severely wounded the hostages and Manuel was on the point of finally killing them when the police burst in and tore the gun away from him? It seems clear that it can: there is nothing contradictory about the sequence of sentences in (7).

(7) John almost killed the hostages and so did Manuel. John first severely wounded them and then Manuel was on the point of finally killing them when the police burst in and tore the gun from him.

Yet if the sentence John almost killed the hostages was ambⁱguous such a sequence would be contradictory since the do so expression would be being used where there was no identity of meaning. The test therefore seems to show that John almost killed the hostages is not ambiguous, but merely unspecified. Whether this non-ambiguity involves complete lack of specification or a representation of disjunct possibilities (analogies to or) remains an open question. But what the tests indicate quite clearly is that though almost can be used in a sentence to convey rather different interpretations, such a sentence is not ambiguous.

C.      Ambiguity and negation

What of negation? In the previous chapter I argued that the semantic representation of negation had to represent the claim that the conditions for the truth of the corresponding positive sentence were not met, and that this representation had to be in the form of a disjunction of the negation of each of the conditions for the truth of the corresponding positive sentence. So for example I suggested that the interpretation of the sentence It wasn't a woman had to characterize the implication that either the item described was not female or not adult or not human, this being a disjunction of the truth conditions of its positive congener. I pointed out at the end of that chapter that such a characterization of negation conflicted with the truth-conditional definition of ambiguity that a sentence is ambiguous if it is true under different sets of condi­tions. But we have just seen in this chapter that that characterization is in any case insufficient in that it predicts that all cases of only generally specified interpretations are ambiguous. What prediction does the verb phrase pro-form test make about negation? We have seen that negative sentences, at least in general, have a single representation of meaning, given by a disjunction. This being so, we should predict that negative sentences are unambiguous; and this the pro-form test confirms.

(8) On Monday it wasn't a woman that came to the door, and on Tuesday it wasn't either: on Monday it was a man and on Tuesday it was a young girl.

In (8), the sentence It wasn't a woman that came to the door is used for two purposes — firstly to assert that the reason why on Monday it was false that a woman came to the door was that the person who came was not a female adult but a male; secondly to assert that the reason why on Tuesday it was false that a woman came to the door was that the person who came was not a female adult, but a non-adult female. Thus there are claimed to be different bases for the truth of It wasn't a woman that came to the door, in the first place that the condition of femininity required for the truth of the positive sentence was not met, in the second_. place that the condition of adult-hood also required for the truth of the positive sentence was not met. Yet this difference does not demonstrate a difference in the meaning of the negative sentence, in question. The phenomenon we are dealing with here is called the scope or negation, the scope of negation being those elements to the negative element is applying. In the case of It wasn't a woman to the door - it was a man the scope of negation is restricted to the condition of feminity - no other part of the sentence is denied: in the case of It wasn't a woman that came to the door -- it was a young girl the scope of negation is restricted to the condition of adult-hood. The pro-form test for ambiguity shows clearly that differing scope of nega­tion, at least for sentences of this type, does not result in ambiguity. Now this is an important result for it is a common mistake among linguists to argue for a conclusion on the basis of scope of negation ambiguity. But these are non-arguments, for at least in general, negative-sentences are not ambiguous with respect to variations in the scope of negation. (9)-(11) provide us with further^- demonstration of this,

(9) Edwin didn't kill the mice and Bill didn't do so either. Edwin is always kind to animals and wouldn't have anything to do with the experiment and though Bill used to make theme very ill, they never actually died.

(10) The professor didn't accuse her of taking drugs and her tutor didn't do so either. The professor didn't say anything at all because he didn't think she was taking them and her tutor, who also takes them, merely suggested that she should be more careful about it in future

 (11) The chairman didn't sell any shares to the new firm and the secretary didn't do so either. I know the chairman didn't because he specifically told me that he had given them some as a free gift, and the secretary didn't because he didn't have any to sell.

In (9) we have a case of a negative sentence containing kill in which the scope of negation differs in the two sentences, in the  first applying to the whole complex representation of meaning of kill, in the second applying to merely a sub-part of it: the fact that Bill carried out some action on the mice which caused some reaction in them is not negated ; what is negated is the causation specifically of death. This difference is not however sufficient to exclude the identity-requiring do so verb phrase. In (10) we have a difference of scope in a sentence containing accuse. Now it is arguable that a characterization of the meaning of accuse must include the implications that the referent of the subject of the verb assume that the action involved was bad and that the referent of the subject of the verb state that the person accused was responsible for the action in question. And in (10) the scope of negation varies across these two implications: the first conjunct is taken to imply that the second of these implications falls within the scope of negation; the second conjunct implies that the first of these implications falls within the scope of negation. Again this difference in scope provides no evidence of consequent ambiguity of the negative sentence. (11) is parallel. The selling of shares by both the chairman and the secretary is denied but for different reasons - firstly the scope of negation is restricted to the trans­action of money involved in selling (this was a gift); secondly the scope of negation encompasses the whole action depicted by the item sell (there was no exchange of any sort - either of goods or money). In each of these cases, though the scope of negation varies, the sentences, according to the test, are unambiguous. Thus our representation of negative sentences as involving a single semantic representation which is itself a disjunction of conditions receives confirmation from this test..

Reference:

Kempson, Ruth M. 1977. Semantic Theory. New York: Cambridge University Press.