The fact that the famous Godel incompleteness theorem and the archetype ofall logical paradoxes, that of the Liar, are related closely is, of course, notonly well known, but is a part of the common knowledge of logician community.Actually, almost every more or less formal treatment of the theorem (including,for that matter, Godel's original paper as well) makes a reference to thisconnection. In the light of the fact that the existence of this connection is acommonplace, all the more surprising that very little can be learnt about itsexact nature. Now, it emerges from what we do in this paper that the generalideas underlying the three central limitation theorems of mathematics, thoseconcerning the incompleteness and undecidability of arithmetic and theundefinability of truth within it can be taken as different ways to resolve theLiar paradox. In fact, an abstract formal variant of the Liar paradoxconstitutes a general conceptual schema that, revealing their common logicalroots, connects the theorems referred to above and, at the same time,demonstrates that, in a sense, these are the only possible relevant limitationtheorems formulated in terms of truth and provability alone that can beconsidered as different manifestations of the Liar paradox. On the other hand,as illustrated by a simple example, this abstract version of the paradox opensup the possibility to formulate related results concerning notions other thanjust those of the truth and provability.
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