Theories of Truth and the Liar Paradox

Abstract

In his famous paper "Outline of a Theory of Truth, " Kripke claimed that in order to say that a theory of the liar paradox is presented, one should set up a formal language which contains its own truth predicate. In fact Kripke himself set up such a language (i. e his theory of truth). Since then, many theories of truth have been presented as theories of the liar paradox. But what relationship is there between such a formal language and the liar paradox? In this paper I explain this relation and consider problems of those theories of truth. I take up two problems. The first is the problem about proof theory, and the second is the problem of the Revenge Liar. I shall show that the problem of the Revenge Liar is extremely difficult and that the solution of this problem is hardly possible.