Some Liar-like paradoxes

Abstract

. The classical Liar paradox is as follows We can construct several Liar-like paradoxes, for instance of meaninglesness: An additional principles: A is meaningful  A is meaningful; A is meaningful if and only if A is true or false; is not meaningful; is true  is not meaningful; Assume that is true; hence is not meaningful; but is meaningful as true; Assume that is false; hence is meaningful, but  jest meaningful and true; hence   is meaningful; hence  is not meaningful; hence we return to the former case; Analogical paradoxes can be formulated for rationality, testability, etc. A general lesson: If a principle P establishes meaning of a predicate W referring to properties of sentences such that T-scheme is applicable, we can expect that the predicate in question can generate a Liar-like paradox. However, it does not mean that philosopher must resign from P. Generalizing the truth case P is formulated in ML and apply to items formulated in L. The only moral is that the criteria from L have to be supplemented by something else.

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Jan Wolenski
Jagiellonian University

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