Re: Godel Goofed?

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

In article <3A85EC63.9C0C968E@qwest.net>, olcott  <olcott@qwest.net> wrote:
>
>
>Matthew Russotto wrote:
>
>> 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.
>
>What are the specific imperfections?

One is not a statement in a formal system of reasoning.  The meaning
of the statements (as I've pointed out time and time again) are not
quite the same.  One of the statements does not express a paradox; it
can take a truth value without contradiction.

>> >(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 relevant analogous attributes of BOTH of
>these is that they BOTH propose to be well
>formed statements, additionally they BOTH
>fail to be well formed statements for the
>same reason, infinitely recursive self reference.

Self reference ("infinitely recursive self-reference" is tautological)
is not forbidden by the formal system involved.
-- 
Matthew T. Russotto                                russotto@pond.com
"Extremism in defense of liberty is no vice, and moderation in pursuit
of justice is no virtue."