ONT Re: Quine -- Two Dogmas Of Empiricism
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TDOE. Note 10
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| 2. Definition (concl.)
|
| The word "definition" has come to have a dangerously reassuring sound,
| owing no doubt to its frequent occurrence in logical and mathematical
| writings. We shall do well to digress now into a brief appraisal of
| the role of definition in formal work.
|
| In logical and mathematical systems either of two mutually antagonistic
| types of economy may be striven for, and each has its peculiar practical
| utility. On the one hand we may seek economy of practical expression --
| ease and brevity in the statement of multifarious relations. This sort
| of economy calls usually for distinctive concise notations for a wealth
| of concepts. Second, however, and oppositely, we may seek economy in
| grammar and vocabulary; we may try to find a minimum of basic concepts
| such that, once a distinctive notation has been appropriated to each of
| them, it becomes possible to express any desired further concept by mere
| combination and iteration of our basic notations. This second sort of
| economy is impractical in one way, since a poverty in basic idioms tends
| to a necessary lengthening of discourse. But it is practical in another
| way: it greatly simplifies theoretical discourse 'about' the language,
| through minimizing the terms and the forms of construction wherein the
| language consists.
|
| Both sorts of economy, though prima facie incompatible, are valuable in
| their separate ways. The custom has consequently arisen of combining
| both sorts of economy by forging in effect two langauges, the one
| a part of the other. The inclsuive language, though redundant
| in grammar and vocabulary, is economical in message lengths,
| while the part, called primitive notation, is economical in
| grammar and vocabulary. Whole and part are correlated by
| rules of translation whereby each idiom not in primitive
| notation is equated to some complex built up of primitive
| notation. These rules of translation are the so-called
| 'definitions' which appear in formalized systems. They
| are best viewed not as adjuncts to one language but as
| correlations between two languages, the one a part of
| the other.
|
| But these correlations are not arbitrary. They are supposed
| to show how the primitive notations can accomplish all purposes,
| save brevity and convenience, of the redundant language. Hence
| the definiendum and its definiens may be expected, in each case,
| to be related in one or another of the three ways lately noted.
| The definiens may be a faithful paraphrase of the definiendum
| into the narrower notation, preseving a direct synonymy* as
| of antecedent usage; or the definiens may, in the spirit
| of explication, improve upon the antecedent usage of the
| definiendum; or finally, the definiendum may be a newly
| created notation, newly endowed with meaning here and now.
|
| In formal and informal work alike, thus, we find
| that definition -- except in the extreme case of the
| explicitly conventional introduction of new notations --
| hinges on prior relations of synonymy. Recognizing then
| that the notion of definition does not hold the key to
| synonymy and analyticity, let us look further into
| synonymy and say no more of definition.
|
|*According to an important variant sense of "definition", the relation
| preserved may be the weaker relation of mere agreement in reference;
| see below, p. 132. But definition in this sense is better ignored in
| the present connection, being irrelevant to the question of synonymy.
|
| Quine, "Two Dogmas", pp. 26-27.
|
| W.V. Quine,
|"Two Dogmas of Empiricism", 'Philosophical Review', January 1951.
| Reprinted as pages 20-46 in 'From a Logical Point of View',
| 2nd edition, Harvard University Press, Cambridge, MA, 1980.
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