Problems of deflationism: liar paradox

Two alternatives are considered with regards of deflationism and the liar paradox: (1) revisiting of the principles of logic (in particular, in the framework of dialeteism), (2) adding an external pragmatic principle to deflationism. Tarski suggested that the truth definition for a given language should be formulated in the appropriate meta-language that allows one to define semantic concepts of semanti-cally-open languages. In general, this approach can be used within deflationism. Kripke and Hintikka solved the Tarski's problem - the problem of an infinite hierarchy of languages and truth definitions for them, but they did not managed to solve the problem of the liar paradox. One can use the substitution interpretation of quantifiers to solve the problem of liar paradox, but the consequence of it is that strict completeness and compactness become unprovable without special modifications of a given logical system. Field offers to define dialeteism as a point of view, according to which both, sentence and its negation are accepted by a given speaker. In fact, dialeteism can be understood as a special case of the pragmatic variant of deflationary theory of truth. The solution of the paradox of the liar in this case would be complete only when deflationism is accompanied with some external explanation of the conditions under which the speaker is willing to make the substitution according to deflationary scheme. By means of this pragmatic principle we are able to epistemically define the concept of meaning. The problem of solving the liar paradox should be solved not by some particular theory of truth, and by a more general logical or logico-metaphysical theory. Therefore, the liar paradox threatens deflationism only in the cast that a liar paradox solution in a more general theory leads to a revision of the latter, which would no longer be consistent with deflationism.

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