Some Liar-like paradoxes

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Wolenski, Jan
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Abstract. The classical Liar paradox is as follows We can construct several Liar-like paradoxes, for instance of meaninglesness: (a) An additional principles: A is meaningful  A is meaningful; A is meaningful if and only if A is true or false; (b) (1) (1) is not meaningful; (c) (1) is true  (1) is not meaningful; (d) Assume that (1) is true; hence (1) is not meaningful; but (1) is meaningful as true; (e) Assume that (1) is false; hence (1) is meaningful, but (1) jest meaningful and true; hence (1)  (1) is meaningful; hence (1)  (1) is not meaningful; hence we return to the former case; Analogical paradoxes can be formulated for (un)rationality, (un)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.