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Ivan Franko National University in Lviv

1, Universytetska Str.

79000 Lviv, Ukraine
In the present article the correlation between the concepts of causativity and transitivity are analysed. Both concepts are surveyed in syntactical and semantic way. Transitivity as a primary syntactical category is specific because of its fixed arguments: subject and direct object. Causativity is originally defined as the semantic “ground-effect”correlation between the causing and caused entities. On the one hand, the analysis of the ancient Greek name for the accusative case, in which the direct object is usually used, shows that the meaning of causation is present in the transitive construction. The semantic treatment of the concept of transitivity brings similar results. On the other hand, the government of a subject and a direct object by all the (lexical) causatives without exception indicates their transitivity. Using basic predicates and the criterion of the causative argument frame makes it possible to show the semantic derivation of transitivity from causativity and to describe causative verbs as a prototype of transitive ones.
Key words: causativity; transitivity; object.


Mieszko Tałasiewicz
University of Warsaw, Poland
Rules of meaning for vague expression always contain a pragmatic part that makes us consider the circumstances of utterance when applying the expression. Sometimes this pragmatic part becomes dominant and it makes us apply or not apply the expression regardless the absolute value of the most relevant property or aspect of object, which usually decides whether the expression is applicable. Therefore the sorites paradox cannot be established – first, the conditional premise is not the matter of course and it should be rejected on pragmatic grounds, second, we may reject the categorical premise of the paradox. Further, it is questioned that vagueness permeates all natural language. Personal and impersonal discourse is distinguished; vagueness can be ruled out from the latter (for every statement belonging to such discourse there is an authority to make relevant regulations). In personal discourse it is assumed that the speaker always applies given expression to objects that certainly belong to positive extension. Statements in such utterance are normally true or false. The problem may arise if for the receiver the objects belong to borderline, but it turns out to be a pragmatic problem of interpretation, not logical problem of truth-value.
Key words: vagueness; pragmatics.
A. Vagueness is told to be so mysterious, that philosophers do not know not only how to cope with it, but even how to describe it adequately. However, there are some quite commonly accepted headlines to begin with:20
1. Vague expressions definitely refer to some objects (which amount to positive extension), definitely do not refer to some other objects (negative extension) and there are some objects such that it is essentially impossible to decide, whether these expressions refer to them or not (borderline). In other words, there are some objective, semantic rules that prescribe, for instance, that a man who stands six feet two inches is tall; prescribe that a man of five feet six inches is not tall; and do not prescribe whether a man of five feet ten inches is tall or not.

1a. In fact, not only the borderline between positive extension and negative extension is blurred: so is the line between positive extension and the first-order borderline and between this borderline and negative extension. This amounts to higher-order vagueness and (in further research) it brings a heap – excusez le mot – of troubles to semantic accounts.

2. Vagueness corresponds with a relatively well discriminated, gradually changing property or aspect of things – like the number of hairs, size or colour.

3. Vagueness permeates almost all natural language and is unavoidable.

Generally speaking, vagueness is responsible for two kinds of troubles.

Point 1 amounts to the situation that some statements with vague expressions are apparently true, some are apparently false but some are undecided as to the truth-value – and this challenges the principle of the excluded middle or even the principle of bivalence.

Points 1 and 2 give rise to so called sorites paradox. A classic example of such paradox is the paradox of a bald man. A man who has no hair on his head is certainly bald (categorical premise, founded on point 1). If someone who has n hairs is bald then someone who has n+1 hairs is also bald (conditional premise, founded on point 2). The principle of induction makes us to admit then that everyone is bald. (Different patterns of reasoning, for example these adopting numerous modus ponens principles, do not change much in the picture.)

Point 3 says that these problems are serious problems. By “serious problems” I mean problems for the languages of science.

The aim of the article is to question all the points 1 - 3 and outline a sketch of solution to the main problems on these grounds.
B. Let us begin with 2. I am not going to attack it totally, I just want to point out, that it holds quite rarely, in fact – and only in very unnatural, sophisticatedly arranged situations. Never – or almost never – in normal, everyday communication.

Normally the applicability of vague expressions depends on many – and furthermore, usually indeterminately many – properties or aspects of potential designates that amount to, say, image or appearance of these objects. Baldness, for instance, does not depend only on the number of hairs on one's scalp, but on their density, colour, haircut or length. It is perfectly conceivable that of two men one has n hairs and the other n+1 and one of them is bald and the other is not or is a case of the borderline. Moreover, it is conceivable that of two men who both have n hairs on their scalps one is bald and the other is not. Thus, the conditional premise of the paradox is by no means the matter of course – unless thanks to some special action a ceteris paribus clause is established.

C. That applicability of vague expressions depends on some imprecise image is only the first step, however. It depends also on many – and furthermore, usually indeterminately many – pragmatic aspects of the situation, the extralinguistic context of utterance. Baldness of a man, for instance, depends also on what people that surround him look like, and what kind of people the person who is applying the word knows. Richness depends not only on the amount of cash and estate, but on the place in which the speaker and the person in question live, standard of neighbours, needs, aspirations and the chances they have had in their past. How many objects make a heap also depends on situation. Some mountain trails, for instance, are marked with heaps of stones. Quite often it is appropriate to call just one stone a heap, if only it looks like put down by a human hand.

This brings us close to rejecting point 1. There are no purely semantic rules that point out some objects as designates and some as counter-designates of vague expressions. In some cases it seems to be no positive extension, borderline and negative extension in general at all. It is not so, for instance, that a man of five feet ten is a certain case of borderline of the expression “tall”. He is a certain case of positive extension when he is among the pygmy and a certain case of negative extension among the bushmen. He is a certain case of borderline in Europe, that’s it.

To make the last step and reach finally formerly announced rejecting of point 1 we need to consider an objection that perhaps the rules are just more flexible than we usually think, but still they are. A man three feet “tall” is not tall in any circumstances. 21

Well, still there are at least some quite evident cases where applicability of given vague predicate ceases completely to correspond with absolute values of certain properties of its potential designates. Tell me any distance; I will provide you with situations in which it is correspondingly long distance, short distance and a borderline. On the other hand, in given situation, the information, for instance, that there will be emitted two signals, one short and one long, is properly comprehensible no matter how long – absolutely – the signals in fact are: only their relative length matters.22 A 1-second signal is long, when the other lasts 0.1 second and perfectly identical signal is short, when the other lasts 10 seconds.

Anyway, it is quite plausible to assume, I suppose, that semantics for vague expressions is more or less pragmatically governed. In other words, vague expressions are indexicals of a sort. A vague word without any situational context lacks the meaning. The rules of meaning always contain a clause (implicitly, of course) saying that the expression is applicable if something in the world occurs and is not if occurs something else. Most often it is required that the object in question should be clearly distinguishable from other objects contended in the situation on the grounds of relevant aspect or image. The examples from the previous paragraph show that at least sometimes there are rules that make us apply the expression, in special occasion, completely regardless to the absolute value of the relevant property of the pointed out designate.

This yields the rejection of point 1. In some cases not a single object can be described as definite designate or counterdesignate of the expression – without taking context into consideration.

D. Having this, I would venture to approach the paradox. In most cases we can undermine the conditional premise or the ceteris paribus clause – on the grounds of what was said in paragraph B. Note that I do not insist there are sharp thresholds in meaning, like the epistemicists do – I do insist that usually there are sharp thresholds in the situation. People of the same number of hairs usually differ quite extensively, even in the aspect of baldness. These thresholds could be laboriously planed off – at the cost of getting far from any common intuition – but really threatening paradox should now be formulated in much more detailed and sophisticated way (than usually it is), contain specific restrictions etc.

Faced by such an elaborated form of paradox I would gather all my courage and say, that I do reject the categorical premise. If I were put into so extremely bizarre situation as ten thousand people in line, ordered by the number of their hairs (ceteris paribus!) I would admit that the standard conceptual frame of common, everyday language fails to address the situation properly. And I would say that in this situation I cannot call “bald” even the first man in the line, the one of no hairs.

I realise that it sounds strange. But in my opinion it is not far from the cases described above. If sometimes we must apply certain word to an object regardless to the absolute value of its relevant property then it is conceivable that in some other cases we must not apply certain word to given object, regardless to the absolute value of its relevant property. In an extreme case we must not call ‘bald’ a man who has no hair: that is bizarre, but the paradoxical situation itself is bizarre. In normal situations, I have insisted above, we could perfectly well reject the conditional premise.

Perhaps one more remark would make my view clearer. Imprecision related to vagueness is often contrasted with imprecision of measurement. It is said that imprecision of measurement can be wiped off e.g. by employing some more precise instruments or more minute observation, whereas imprecision due to vagueness is not possible to get rid of. I consider this contrast unfair. Imprecision of measurement seems to me in the same degree correctable or incorrectable as imprecision of description related to vagueness. We cannot make a vague expression precise (without changing its meaning) but either we cannot make more precise any measurement already made. It is as it is. If necessary, we can just make another measurement, a more precise one. And, as well, we can withdraw insufficiently precise expression and use a more precise one. Note that it is not a logical correction of meaning but pragmatic correction of usage. The word 'bald' is not fit to describe correctly a man of no hairs if the man is lined up with 10 000 people ordered by the number of their hairs. The proper reaction for the question 'Is the first man in the line bald?', is: “Well, it is better to say that he is of no hairs”.

Shortly, I propose to believe that the pragmatic part of the rules of meaning for vague expressions includes a clause – a commandment – “you will not use this word unless it describes your object well enough to communicate smoothly”.
E. Let us now examine point 3. Vagueness permeates all natural language. Does it, really? Standard argumentation for this is usually following. All – or nearly all – expressions of any natural language are more or less vague since their meaning is more or less directly founded in ostensive procedure, which is regarded as the main source of vagueness. To make such a word precise is to change its meaning. So vagueness is unavoidable.

Yes, probably vagueness is unavoidable without changing meanings. But what is so horrifying in changing meanings? Definition, esp. scientific definition is a standard logical tool since Socrates at least; some definitions are intended just to make meanings precise – at the reasonable cost of a slight meaning change.

Such definitions are part – in many occasions an essential part – of natural language. Perhaps they are rare in everyday, common language. But not all natural language – as opposed to formal languages – is everyday language of everyday communication. Many specialised jargons or dialects belong to natural language as well. “Language” of law, history, sociology, philosophy – these are all parts of natural language and in all of them regulative definitions are welcome or necessary. Natural language is a conglomerate of many parts, sometimes very different in character. It is possible, I believe, to get rid of vagueness in some of these parts, the more “scientific” ones – at least in the crucial points.

Let us look at this issue in a more precise way. I think the following idealisations would not take us too far from reality:

In natural language there is personal discourse and impersonal discourse23 Every statement belonging to personal discourse is a concrete utterance – necessarily having a speaker and usually a hearer, addressee. Every utterance has a definite pragmatic context (although some essential parts of the situation may be unknown or unrecognised). Examples of such discourse: a talk, a discussion, a novel etc. Examples of relevant statements: ‘Would you pass me this apple, please? The red one, I mean’, ‘Come on, Henry is as bald as a coot’, ‘A good student need not to worry about the exam’ etc.

Statements belonging to impersonal discourse don’t have any definite speaker (the circumstance that they are usually formulated or redacted by some person does not matter; that is not a real utterance). Here we have languages of all scientific disciplines (without their formal parts) and many institutional jargons: official or legal “dialect”, instructions of usage or assembling something, safety guidelines or some advertisements. Examples of statements: “Physical bodies attract each other with the force proportional to the product of their masses...”, “The poll was taken at the representative sample of philosophy students”, “No smoking”, “Office hours every first Monday of quarter, from 3 p. m. till 3.15 p.m.” etc.

For every statement belonging to impersonal discourse there is an official or quasi-official authority (personal or impersonal) entitled to provide binding interpretation of this statement – regulative interpretation if necessary. It could be a legal bill or a judge, an officer in charge or some regulation codex, a scientist (original author) or a group of scientists (influential research team), a commonly recognised handbook, a specialist dictionary and so on.

The principal value of impersonal discourse is precision and objectivity; effectiveness or economy of speech is far less important. Since vagueness affects precision and introduces subjective variations it should be erased from here at any cost. Fortunately enough, in the light of above assumptions it seems natural to conclude that thanks to necessary intervention of relevant authority, which provides some regulative definitions, vagueness can be ruled out of impersonal discourse. For example, originally vague word “adult” is regulated by law as “being at least 18 years old” (in Europe – as far as I know in the USA the line of shadow is drawn at the age of 21).

F. Having this, I would attempt to explore the problem of truth-value of statements containing vague expressions.

Vagueness is essential only in personal discourse – since there is no authority to make necessary changes in meaning (and since there is a need for vague expressions as they are helpful in effective communication, effectiveness being the principal value of personal discourse). But on the other hand, we have here pragmatic context. The question: what is – in general – the truth-value of a given statement in personal discourse is in my opinion misleading. Such a statement may be differently interpreted in different situations, and in the same situation – by the speaker and the receiver. The latter difference is due to the fact that the pragmatic context of utterance consists partially in personal idiosyncrasies, a sort of private historical database of paradigmatic examples. A person grown up among declared bald-heads would be less liberal in using the word ‘bald’ than someone living with mop-heads.24

I would insist here that in normal, serious conversation (personal discourse) the speaker always applies vague expressions to objects belonging to their positive extensions25 General statements, like ‘Tall and handsome men are stupid’, mean that in every case one is ready to apply the subject, he is also ready to apply the predicate.

This thesis, although certainly an idealisation of the real situation, expresses an intuitive – according to my intuition, at least – belief that people rather do not call “bald” a man whom they do not consider as bald. If necessary they would rather apply some other word. It has to be stressed here that there is no changing of meaning or making words precise. The word remains vague – it is only applied to an instance of its positive extension in given situation.

Statements that predicate vague expressions of objects belonging to positive extensions do not affect the principle of bivalence or the principle of the excluded middle. They are just true, in normal sense.26 From the point of view of the speaker there is no problem of truth-value, then. Certainly, there can be a problem from the point of view of the receiver. The problem arises if the speaker applies a vague predicate to the object that is not an instance of positive extension in the receiver’s opinion.

It seems, however, that it is not a problem of truth-value but of the proper meaning of the uttered phrase. Vague statements refer to very broad situations, part of which are personal “databases of paradigmatic examples” of the participants in conversation. Thus, some part of the pragmatic context co-founding the meaning of used expression is unavailable for the receiver. The “private” part is not very significant, though, so that difficulties in communication are not very extensive. Nevertheless in case of such difficulty the problem for the receiver is not what is the truth-value of the uttered statement (standard assumption is that the statement is true according to the speaker’s meaning), but how exactly the speaker understands used expressions. Hearing Smith’s enunciation “Mark is bald” reasonable Jones would not answer “That’s not true”. He would rather say “Why do you consider Mark as bald, he has quite many hairs yet, hasn't he?”. He would namely regard the statement as true in the Smith’s meaning and at the same time would question this meaning, suggesting him a correction of the conceptual frame.

To sum up the question of truth-value. In personal discourse vague expressions could be statements par excellence only in concrete utterance. They are just true then as they are applied only to positive extensions (or false as some general statements or lies). From abstract, logical point of view they should be considered not as statements at all, but as a sort of higher-order sentential functions, where the predicate letter represents not a real predicate but a predicate-variable, with pragmatically co-established variation range.

Such interpretation would be disastrous in every scientific discourse. Such a discourse is impersonal; relevant statements have no determined speaker with whom one could negotiate meanings; sometimes they have no intended addressee either. They are abstract; it is expected that everyone would understand them in the same way regardless to the concrete circumstances – and that they would be real statements, which truth-value would be (in principle) possible to establish. Essential vagueness would destroy this expectation; but vagueness is not essential in impersonal discourse – at least if we admit the institution of “definition authorities” and do not insist on preserving all initial, common meanings unchanged. There are a lot of examples of such authorities; and one could hardly find any word in science that preserved its original meaning. Public life is also full of legal definitions; and its language is permeated by scientific terminology, filtered through many sorts of journals or other mass-media.

This is the outline of pragmatic conception of vagueness. There is something behind that, however. It is quite apparent, I suppose, that in the polemic context there are numerous variations of so called semantic conceptions: supervaluation, subvaluation, three-valued logic and so on. Once got to know them, I was stunned by their sophistication and subtle distinctions they evoked. Eventually I came to believe, however, that they are too sophisticated.

Vagueness is a property of common, everyday language. I think that for this language formal concepts of semantics are misconceived. Notions of T-convention, levels of meta-language, valuations, models, etc. were originally designed (by A. Tarski) for languages of formal sciences, for mathematics and mathematical logic in the first place. There are already serious difficulties to employ them for the task of examining the languages of empirical sciences (e.g. different notions of semantic and physical model). It is hopeless – in my opinion – to make sense of them in natural, everyday language. There is no distinction of object-language and metalanguage in everyday speech; there are many functions of language mixed together, description being not the most important; there are perlocutions, illocutions and so on.

All this makes me believe that conceptual frame of formal semantics does not match this language well; that the very idea of employing such a theory as formal semantics to everyday language is seriously counter-intuitive – to say nothing of the results.

  1. 1. Kotarbińska J. Wyrażenia okazjonalne [Indexicals], Z zagadnień teorii nauki i teorii języka. Warszawa, 1990. 2. Odrowąż-Sypniewska J. Zagadnienie nieostrości [The Problem of Va­gueness]. Warszawa 2000. 3. Przełęcki M. W sprawie terminów nieostrych [On vague terms]. Filozofia Nauki 2-3/1993. 4. Sainsbury R. M. Paradoxes. Cambridge, 1995. 5. Wójcicki R. Ajdukiewicz:. Teoria znaczenia [Ajdukiewicz’s. Theory of Meaning].Warszawa, 1999. 6. http://www.st-andrews.ac.uk/academic/philosophy/arche/vagueness.shtml

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