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In this essay the author proposes a non-circular definition for language derived from one undefined term and three axioms.
It is appropriate to begin this essay with a statement about that which the author does not propose to address: His objective is not to consider the origins of language: whether the human race evolved in the way it has because of the nature of language—as has been hypothesised by some authorities—or whether language evolved in the way it has because of the nature of the human race—as has been suggested by others. Nor is he asking the reader to consider cognitive processes involved in communications between individual humans or whether something such as a universal grammar exists. His interest is solely in an unambiguous, non-circular definition for language.
The author is a lecturer in Mathematics at a further education college in the United Kingdom. In his efforts to try to understand why many people, particularly young people, seem to have so much difficulty understanding and applying mathematical concepts, even, for example, something as apparently simple as manipulating fractions, he has become interested in the dynamics of language, particularly similarities and differences between the language of mathematics and the lingua franca.
It is convenient to think about language as a process or system, and crucial to the consistency of any such system is a set of unambiguous, non-circular definitions for terms and operations that define the system.
All definitions for language examined by the author are circular (see, for example, Britannica, 1962): Language. The whole body of words and of methods of combining them; Words. Speech, utterance, verbal expression; Speech. The utterance of words or sentences; Utterance. The action of uttering with the voice, vocal expression, speaking, speech; Vocal. Produced by the voice, of the nature of words or speech. Under the assumption the total number of words in this dictionary is finite, any examination such as this which begins with language must necessarily return at some point to language (the reader is invited to confirm this is, in fact, true).
This circularity may be acceptable when interest is in how a word is presently used by people within a language culture, but fully unacceptable as the basis for any philosophical enquiry.
Accordingly, the author proposes this definition for language:
This existence of symbols is assumed. Symbols shall be taken to describe discrete and distinct vocal activities—sounds—uttered by human beings and related non-verbal activities such as pauses, stress and changes in pitch, and other body-related activities such as gestures, and arm and hand movements.
Also, since it is safe to assume that prehistorically vocal symbols preceded written symbols (Wilson, 1941, pp. 174-180), it is appropriate to treat written symbols as attempts to represent specific antecedent vocal symbols.
Symbols are purely arbitrary; symbols, in and of themselves, are meaningless.
Few, if any, readers question that a symbol such as, for example, horse is arbitrary and meaningless until the people of a culture in which it is uttered attach a meaning to it. However, it is sometimes the case that users feel that other sorts of symbols such as, for example, 2 + 2 = 4 or e = mc2, are not arbitrary and meaningless but express intrinsic truths about the universe in which they live. According to this axiom, the latter two are no different in this respect from the first.
A communication takes place when one individual, a sender, displays, transmits or otherwise directs a set of symbols to another individual, a receiver, with the aim of changing something, either something the receiver is doing (or not doing) or changing his or her world view. This set of symbols is typically described as a message.
A conversation between two individuals is obviously consistent with this definition. However, the reader may appropriately question how such activities as the recitation of poetry, the performance of rock music or the delivery of a university lecture comply with it. Further to any pecuniary considerations, an individual recites, performs or delivers because he or she has a need to send a message of some sort to another member of his or her culture.
A communication always take place between two individuals: a sender and a receiver.
Many example of communication from familiar circumstances appear to take place between groups of people rather than between individuals. The concert by the rock group and lecture cited above are two. Another is the delivery by a committee spokesperson of a report compiled by the entire committee. Although others are present, and in some cases acting simultaneously as either senders—the rock group—or receivers—unversity students listening to a lecture, nevertheless, each communication must necessarily be between two individuals.
A communication exists only when the sender and receiver agree on the meanings assigned to the symbols used.
If the aim of the sender of a message is to effect a change in something the receiver is doing, then there must be an expectation the message will have meaning for the receiver: that the receiver will make sense of the message and act in some way consistent with the aim of the sender. This can only happen when both agree on the meanings assigned to the symbols that form the message and the schema used to arrange them.
Language is the process or set of processes used to ensure there is agreement between the sender and receiver for meanings assigned to the symbols and the schema for combining them used for each communication.
The symbols themselves, although typically not the accompanying non-verbal activity, are usually described as words. The schema for combining them is usually described as a grammar.
There are two further considerations that are discussed here in anticipation of many readers' comments: the language of animals and the metalanguage used in this essay.
Firstly, if investigations support an hypothesis that animals of any particular species send and receive unique messages then according to this definition they are using language.
Secondly, when considering, for example, a mathematics topic such as the development of the real number system, one works with a deductive system of logic starting with a number of undefined terms and unproven axioms. These are the basis of the language of the system being created and are stated in a metalanguage chosen by the author of the system. For this essay, the definition for language is stated in English which is also the metalanguage used. This will no doubt provide a basis for some criticisms, particularly by philosophers among readers. The author offers no rebuttal for these anticipated criticisms except to invite definitions optional to his.
Consider the subtitle of this essay, Three Grand Over the Truckstop. Unless the reader is, or was at some time in the past a glider pilot flying from Bandel Field in southwestern Pennsylvania, this set of symbols—this message—is meaningless. To any reader other than members of this group this is not language even though he or she will be familiar with the individual symbols: there has been no agreement between the sender, in this case the author, and the receiver, in this case the reader, for the meanings of the symbols being used.
The reader is invited to cite examples from his or her own experience.
Britannica World Language Edition of the Oxford Dictionary (1962), Oxford: Clarenden Press.
Wilson, R.A. (1941) The Miraculous Birth of Language, London: The British Publishers Guild.
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Originality = 6.25, importance = 6.25, overall quality = 56.25
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Rice-Johnston, W. (2008). Language: A Definition from First Principles - Three Grand Over the Truckstop. PHILICA.COM Article number 136.
1 Peer review [reviewer #79826] added 13th December, 2008 at 11:53:56
Interdisciplinarity is a good thing. I appreciate it very much that a mathematician writes about language. However, he should have read at least some introductory literature about linguistics, semiotics or language philosophy before, rather than just a popular dictionary from 1962.
The word language has got several meanings, and for each of these meanings there are several non-circular definitions.
William Rice-Johnston has chosen to understand language as ‘any system of communication’ (including animal communication, rather than concentrating on human communication, which from my point of view would have been much more interesting). At the same time his definition of language as a “process or set of processes” blurrs the well-established differentiation between language as a process (which Saussure  has termed “parole” and Chomsky  “performance”) and language as a system (“langue” or “competence”, respectively).
The most important mistake in Rice-Johnston’s definition of language is that the only function of language seems to be “to ensure there is agreement between the sender and receiver for meanings assigned to the symbols and the schema for combining them”, i.e. the so-called metalinguistic function in Jakobson’s (1960) system of six basic functions of language. Now even a speed-limit sign is designed for more than just agreeing with the driver on what the number and the red circle on it mean. Its main function is to transfer a message (in this case: ‘Slow down if you are faster than this’). (In contrast to this definition of language, the author’s definition of communication seems to include only Jakobson’s  conative or Bühler’s  appellative function.)
The author’s final remark about the utterance three grand over the truckstop appears especially odd. I am certain that most people in the world would agree that, if this conveys a certain meaning for certain people, it must be language. How can it depend on the reader if something is language or not? Did the Chinese in the streets of Beijing who addressed me in Chinese not speak a language just because I did not understand it?
For those interested in the question who are themselves not experts on the subject, the part of Rice-Johnston’s definition that is neither new nor wrong is that language is a system of symbols for communication. However, communication is not an end in itself but aims to transmit a message (see Bühler’s  “organon model” for the main functions of communication). In contrast to other systems of symbols, language consists of a finite set of discrete symbols (cf. the infinite set of continuous symbols in the bees’ waggle dance) and is characterized by so-called “double articulation” (i.e. messages are combinations of meaningful elements [morphemes or words], which in turn are combinations of meaningless elements [phonemes/graphemes or sounds/letters], cf. Martinet ).
All these definitions of language are non-circular, and all these descriptions of language offer more insights into what language really is that this article.
Bühler, Karl (1934). Sprachtheorie: Die Darstellungsfunktion der Sprache. Jena.
Chomsky, Noam (1965). Aspects of the theory of syntax. Cambridge/MA.
Jakobson, Roman (1960). Linguistics and poetics. In: Style in language. Ed. Thomas A. Sebeok. Cambridge/MA.
Martinet, André (1965). La linguistique synchronique: Etudes et recherches. Paris.
Saussure, Ferdinand de (1916). Cours de linguistique générale. Lausanne, Paris.
Originality: 1, Importance: 1, Overall quality: 3