  The fact that the famous Godel incompleteness theorem and the archetype of
all logical paradoxes, that of the Liar, are related closely is, of course, not
only 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 this
connection. In the light of the fact that the existence of this connection is a
commonplace, all the more surprising that very little can be learnt about its
exact nature. Now, it emerges from what we do in this paper that the general
ideas underlying the three central limitation theorems of mathematics, those
concerning the incompleteness and undecidability of arithmetic and the
undefinability of truth within it can be taken as different ways to resolve the
Liar paradox. In fact, an abstract formal variant of the Liar paradox
constitutes a general conceptual schema that, revealing their common logical
roots, connects the theorems referred to above and, at the same time,
demonstrates that, in a sense, these are the only possible relevant limitation
theorems formulated in terms of truth and provability alone that can be
considered as different manifestations of the Liar paradox. On the other hand,
as illustrated by a simple example, this abstract version of the paradox opens
up the possibility to formulate related results concerning notions other than
just those of the truth and provability.
