Godel Goofed?

[olcott <olcott@qwest.net>]

Postulate:
If the narrative descriptions of Godel's incompleteness
theorem are analogous to the theorem itself, then Godel's
Incompleteness Theorem is analogous to the Liar paradox.

Assertion:
The Liar Paradox is an ill formed statement because
it lacks an object to attach a truth value to. All
statements must be about something, and the Liar
paradox does not meet this requirement.

Assertion + Postulate = Godel's theorem is based on
an ill formed statement.

To refute the reasoning you have several bases:
(1) The narrative description of the Theorem
leaves out crucial details of the Theorem itself,
thus is not sufficiently representative of the actual
underlying reasoning, therefore is actually not
analogous to the Liar Paradox.
(specifically point out which details are missing).

(2) Even if details are not missing, the self reference
of the Incompleteness theorem is entirely different
that the self reference in the Liar Paradox, thus
these two are not comparable at all.
(Specifically point out exactly how these two differ,
and why they are not comparable).

(3) The liar paradox is a perfectly valid statement,
there is no requirement that statements be about
anything, this requirement is not true.
(This seems utterly absurd to me.)

(4) The liar paradox is about something it is about
itself, and the infinitely recursive nature of this
self reference in no way invalidates that the
liar paradox is a valid statement.
(What I assume will be your fundamental basis)