Abstract

A tempting solution to problems of semantic vagueness and to the Liar Paradox is an appeal to truth-value gaps. It is tempting to say, for example, that, where Harry is a borderline case of bald, the sentenceHarry is baldis neither true nor false: it is in the ‘gap’ between these two values, and perhaps deserves a third truth-value. Similarly with the Liar Paradox. Consider the following Liar sentence: is false.That is, sentence says of itself that it is false. If we accept the Tarskian schema S is true iff pwhere ‘S’ is a name of a sentence ‘p,’ we are led into paradox. Both the assumption that is true, and the assumption that is false lead us, via, to is true if and only if is false.Given this result, a natural reaction is to place in a ‘gap’ between true and false.