A symbol, broadly speaking, is something that stands for something else. Subordinate questions arise: what sorts of things can stand for things? for what sorts of things? and how do they do so? Also, certain reservations need to be made.
A £5 note once stood for five gold sovereigns, serving the same purposes. Usually a symbol stands for its object in a less robust way: it reminds us of it. It may do so by resembling it, or by standing to it in a known causal relation, or by some conventional connection of whatever origin — hence
C. S. Peirce's trichotomy of 'signs' into 'icons' (e.g. a diagram), 'indices' (e.g. a thermometer), and 'symbols' in a narrower sense (e.g. a name).
Whereas association itself is symmetrical, the relation of symbol to object is not; it is limited to situations in which the object commands more interest than the symbol. The fish symbolizes Jesus, because the Greek ίχθύζ is an acrostic of a five-word description of Jesus, but it does so in churches, not kitchens. The relation is asymmetrical and intermittent.
A physical object, or state, may stand for a physical object or state: a fish for a man, an inscription for a man, a map for a province, a mercury level for a temperature. Often, the symbol is better seen as a whole class, such as that of ichthyomorphic carvings. A name, indeed, may be seen as the class of its inscriptions and utterances. Sometimes, as when gods are said to have symbolized seasons, or Janus to have symbolized wholeness, the symbols are evidently neither physical objects nor states nor classes of such; it is hard to categorize them otherwise than as ideas. A better account might take nominalistic lines, appealing to visual patterns and linguistic expressions.
The heat and wind activate their symbolic indices, the thermometer and weathervane. But primitive peoples have believed, conversely, in an efficacy of symbols upon their objects — thus effigies and the magic of names. Thus also, presumably, the cave paintings of 30,000 years ago.
Fanciful subconscious resemblances must be assumed between symbol and symbolized, if we are to make sense of iconography or of
Sigmund Freud. The flights of creative imagination in our
dreams are undeniable, but their mechanism remains a mystery. Such symbolism must have figured in the origins of language. The surgeon Sir James Paget (1814–99) had an imaginative theory of private gestures within the mouth, private muscular contortions that bore a subjective resemblance to some visible traits of objects. It is in language, at any rate, that symbolism attains the age of discretion. Let us look to its workings.
One way in which a linguistic expression often stands for something is by
designating it. Designation is the relation that the names 'Plato' and 'Wales' bear to Plato and Wales, and that the phrases 'the author of
Waverley' and 'Whittington's cat' bear to Sir Walter Scott and Whittington's cat. Symbols that purport to designate are
singular terms. Some fail — for example, 'Pegasus' — for want of a designatum.
A way in which symbols more commonly stand for things is by
denoting them. A
general term, typically a common noun or adjective or intransitive verb, denotes each of the things it is true of. Thus 'horse' denotes each horse, 'green' each green thing, 'swim' everyone who swims.
There has been since antiquity an urge to view general terms as designating. Thus 'horse' was seen as designating some trumped-up abstract object, a universal — the property equinity — besides denoting each horse. This facile positing of universals was deplored by the medieval nominalists, as a confusion.
It was in part a happy confusion. In mathematics, and to some degree elsewhere in science, abstract objects serve theoretical purposes that cannot, evidently, be served by just talking of general terms and denotation. Classes do suffice in lieu of properties, but they are next of kin. Still, there is no need to view the general terms themselves as designating universals in addition to their job of denoting. If properties or classes are to be designated, we do have singular terms for the purpose: 'equinity', 'horsekind'.
General terms are meaningful, surely, and the urge to accord designata to them was due partly to confusing designation with meaning. Meaning is not designation, even among singular terms. The terms 'the Evening Star' and 'the Morning Star' (Frege's example) designate the same thing but differ in meaning. 'Pegasus' is meaningful, though designating nothing.
The notion of meaning is elusive.
Jeremy Bentham appreciated that meaning accrues primarily to whole sentences, and only derivatively to separate words. Setting aside emotive or poetic meaning, and looking only to the cognitive meaning of declarative sentences, we may say that the meaning of a sentence consists in its truth conditions. We know the meaning of a sentence insofar as we know in what circumstances the sentence counts as true. To understand a sentence is to know when to affirm it.
There are sentences, such as 'It's raining', 'This is red', 'That's a rabbit', that count as true only in circumstances observable at the time of utterance. Their meanings can be learned by conditioning, unaided by auxiliary sentences. To proceed from these beginnings to higher levels of language, unaided by translation from another language already known, is an impressive feat, but the child achieves it. He exploits analogies: from the apparent role of a word in one sentence he guesses its role in another. Also, he discovers that people assent to a sentence of some one form only contingently upon assenting to a corresponding sentence of some related form. Exploring, thus, the interrelations of sentences, and corrected by his elders, he learns how to compose innumerable sentences and when to affirm them.
Once he is well started, we could teach him harder sentences by constructing a dictionary along the following lines. Each entry explains some word — for example, 'putative' — by general systematic instructions for paraphrasing all possible sentential contexts of 'putative' into sentences lacking 'putative'. Each word in the paraphrase is either a word of the old sentence or a word more frequently heard than 'putative'. Words very frequently heard are left unexplained. Thus, though meaning belongs to sentences, words serve in generating it. The concept of a dictionary, just presented, shows how.
The sentential contexts of some words can be paraphrased simply by substituting some more frequent word, or some phrase. That word or phrase is then said to have the same meaning as the original word, and thus it is that the notion of word meanings is derivable from that of sentence meanings. Two expressions have the same meaning if substituting one for the other never disturbs truth conditions of sentences.
We saw that singular terms have their designata, when all goes well, and general terms their denotata. Many words claim neither — thus 'or', 'to', 'however', 'which', 'very'. Scholastics called these syncategorematic: lacking in intrinsic meaning, and meaningful only derivatively, through their contribution to the meaning of the containing sentences. There is a trace here of the confusion between meaning and designation, or denotation; words were thought to forfeit intrinsic meaning by not purporting to denote or designate. But let us take it that words generally are meaningful only through their contribution to the meaning of the containing sentences. Then we may keep the term 'syncategorematic' for the words that do not purport to denote or designate, but without thereby imputing any distinctive shortage of meaning.
Consisting, as it does, primarily in the truth conditions of sentences, meaning is pretty thin stuff. In the special case of observation sentences, it can be inculcated by sensory conditioning, or direct demonstration, for the rest, only by other sentences, paraphrases. We give the meaning of a sentence by explaining the sentence, and the meaning of a word by explaining how it works in sentences. Serious confusions could have been avoided if a practice had been made of speaking thus of explanatory activities, rather than of meanings as somehow separable entities that symbols might stand for.
The meaning of a symbol was often confused, we saw, with the designatum. When it was not, it was usually viewed as an idea. This circumstance doubtless delayed the demise of an uncritically mentalistic psychology. Meanings had to be admitted, it seemed, on pain of rendering language meaningless; and it was not easy to see what meanings could be, if not ideas. Hence a dualism of symbol and idea, language and thought.
John Horne Tooke denounced this dualism as early as 1786, protesting that
John Locke would have done well to write 'word' in place of 'idea' throughout his
Essay. The way was opened for
J. B. Watson to identify thought primarily with language, subvocal speech. The medium becomes, in Marshall McLuhan's phrase, the message. The incipient muscular tugs that constituted the thinking process, according to Watson, were not indeed wholly confined to the speech apparatus; the inarticulate painter or engineer must think partly in his fingers. Without language, however, thought would be meagre.
Mathematics affords the ultimate example of the power of notation as a way of thought. In school, when we did problems about rowing across the current, the hard part was putting them into equations; that was the programming, and algebra was the computer. The boon of arabic numeration goes without saying, and the mere use of brackets to unify a complex expression is a cornerstone of mathematics. It is the use of brackets, together with the variable, that enables us to extrapolate our laws and iterate our operations beyond all finite bounds.
(Published 1987)— Willard V. Quine
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- Watson, J. B. (1919). Psychology from the Standpoint of a Behaviorist.