A Logical Statement of Grammatical Theory: As Constained in Halliday's 'Categories of the Theory of Grammar'

Abstract

1. Introductory. 'If we regard language activity, in its formal aspect, as the repeated selection of one from among a number of possible events-or, so as to formulate it more simply, of items from sets of items which are risk under certain conditions, the total selection situation (items and conditions) varies along a cline. At one end of the scale, there are a very large number of sets, in very complex interrelations, but with very few items in each: this is grammar. At the other end, there are few sets, in simple relations, but with large inventories of items making them up: this is lexis. There is no sharp line between them, though the extremes are clearly distinct. Since patterning of the first type lends itself to much greater abstraction, we can make the theory of grammar much more powerful than the theory of lexis. So the linguist tries to bring as much as possible of linguistic form into his grammatical statements-though there is a theory of lexis too, which has a part in the total description.'1 Thus, of the two demi-levels at the level of form, grammar can be supplied with a theory which is more compact and more intricately structured than any possible theory of lexis. And so a fully descriptive theory of grammar must be fairly complex. For this reason the methods and procedures of symbolic and other types of logic can be usefully employed in the statement of such a theory. In this way a statement can be made which is concise, complete and, most important, fully explicit. The nature of such a statement precludes any possible ambiguities which might be present in the reader's interpretation of a more discursive statement. This paper,2 then, presents a logical statement of the General Theory of Grammar which is described in M. A. K. Halliday's 'Categories of the theory of grammar', Word 17.241-92 (1961); sections 3 to 7 of that paper contain the nucleus of the theory and correspond to the present statement. Thus this statement is merely a rephrasing of the theory. Both Halliday's paper and the present one are concerned with the identical theory of grammar; it is only the methods of description which differ. The two statements will in fact complement each