H. P. Grice on P. F. Strawson on 'not'

Laws (6) and (7), taken together, show that any truthfunctional sentence or formula in which the main constant is a 4 ~ 9 sign is the contradictory of the sentence or formula which results from omitting that sign. We have seen that a standard and primary use of * not 9 in a sentence is to assert the contradictory of the statement which would be made by the use, in the same context, of the same sentence without the word * not \ l This identification, then, involves only those minimum departures from the logic of ordinary language which must always result from the formal logician's activity of codifying rules with the help of verbal patterns : viz., (i) the adoption of a rigid rule when ordinary language permits variations and deviations from the standard use (cf. rules (6) and (9) and the discussions in Chapter 1, Section B, and Chapter 2, Section 9); (ii) that stretching of the sense of * exemplify ' which allows, us, e.g., to regard * Tom is not mad ' as well as 4 Not ail bulls are dangerous ' as ' exemplifications ' of * not-p ' So we shall call 4 ^ ' the negation sign, and read * ~ * as * not '. One might be tempted to suppose that declaring formulae (6) and (7) laws of the system was the same as saying that, as regards this system, a statement cannot be both true and false and must be either true or false. But it is not. The rules that (6) and (7) are analytic are not rules about 4 true ' and " false ' ; they are rules about * ~ '. They say that, given that a statement has one of the two truth-values, then it is logically impossible for both that statement and the corresponding statement of the form 4 ~p * to be true, and for both that statement and the corresponding statement of the form 4 ~p "* to be false.