Denial, contradiction and truth-value gaps

Abstract

Since Russell gave his theory of definite descriptions and Strawson reacted to it in his famous "On Referring", the issue of truth-value gaps has never ceased to occupy the attention of philosophers. Strawson questioned the orthodox conformity of Russellian analysis to the traditional logic, particularly to the law of excluded middle. What, for Russell, was part of the meaning of a proposition like "the present monarch of the U.S.A. is honest", is only a presupposition for Strawson. That there is a monarch of the U.S.A. at present, is on Russellian analysis, one of the things asserted by this proposition and thus its falsity is sufficient to make the whole proposition false, whereas on Strawsonian analysis this existential sentence is presupposed, and in a very special sense implied, by the proposition in question, and therefore its falsity, instead of making the proposition false, makes the very question of its falsity out of place. For Strawson if a presupposition of a proposition is false, the question of its truth or falsity does not arise, and hence the proposition is neither true nor false. Obviously, such a possibility is not admitted by the law of excluded middle, and if it is regarded as genuine, as Strawson does, then the taw of excluded middle (LEM) will have to be given up. Such 'exceptions' to the LEM are called the cases of 'truth-vahie gaps'. That a proposition like "the present monarch of the U.S.A. is honest" (M) or like "the third World War has stopped" (W) is un-true, is undisputed. What is disputed is whether it is not false as well. Strawson's main reason for saying that it is false neither, is that a proposition is false if and only if its opposite is true. But