Approaches to description in modern linguistics

Textual
Exemplificatory
Transformative-generative

Halliday, Michael A.K. (1961). Categories of the Theory of Grammar. WORD, 17:2. S.241-292.

There have been in the main two approaches to description in modern linguistics: the „textual“ and the non-textual or, for want of a better word, „exemplificatory.“ More recently a third has been added, primarily in grammar but lately also in phonology, the „generative“ (strictly „transformative-generative,“ since generation does not presuppose transformation). Some linguists have gone so far as to suggest that transformative generation should replace other types of description I as a linguistic method of making statements about language. Others, myself included, feel that all three approaches have a fundamental place in linguistics; that they do different things, and that the third is a valuable supplement to the first two.
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Most, if not all, of the points made in this section can be brought together under Chomsky’s observation that „a linguistic theory should not be identified with a manual of useful procedures, nor should it be expected to provide mechanical procedures for the discovery of grammar.“ The point is a familiar one to British linguists, who have for some time stressed the theoretical, as opposed to procedural, character of their own approach. But is it true that „it is unreasonable to demand of linguistic theory that it provide anything more than a practical evaluation procedure for grammars“? This it must do. But it can be asked to do more: to provide a framework of logically interrelated categories (so that it can be evaluated as a theory, and compared with other theories) from which can be derived methods of description, whether textual, exemplificatory, or transformative-generative, which show us something of how language works.