Re: Godel Goofed?

[russotto@wanda.pond.com (Matthew Russotto)]

In article <3A85CF73.E6391B92@qwest.net>, olcott  <olcott@qwest.net> wrote:
>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.

Only if the analogy is perfect.  Which it is not.  Your reasoning
fails, even without considering the truth of the postulate and the
assertion.  Go directly to jail, do not pass Go, do not collect $200.

>(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).

Already have, actually.  The Liar paradox is
"This sentence is false".
The Goedel theorem is analagous to
"This statement cannot be proven"

The Liar paradox cannot assume a truth value without contradiction.
The Goedel theorem can assume a truth value of "true" without contradiction.



-- 
Matthew T. Russotto                                russotto@pond.com
"Extremism in defense of liberty is no vice, and moderation in pursuit
of justice is no virtue."