Re: Goedel - interesting problem?

From: |-|erc (gotcha_at_beauty.com)
Date: 06/06/04 

Date: Sun, 06 Jun 2004 07:03:21 GMT

"Chris Menzel" <cmenzel@remove-this.tamu.edu> wrote
> On 5 Jun 2004 13:23:08 -0500, Acme Diagnostics
> <LFinezapthis@partpostmark.net> said:
> >
> > Torkel Franzen <torkel@sm.luth.se> wrote:
> > You said:
> > >>there are statements that can be formulated within the theory, but
> > >>neither proved nor disproved in the theory
> >
> > Which is superseded in all respects of explanation by Dolan's:
> > >>>Goedel's incompleteness theorem only shows that some true
> > >>>math facts cannot be proved within math, not that none of
> > >>>them can.
>
> Acme, in all sincerity, Torkel's formulation is about as accurate a
> statement of Godel's theorem as you'll get in nontechnical language.
> Dolan's "explanation" is really quite bad. Most notably, the reference

No, Dolan's is fine though its hardly his own work, much of Torkel's critisism is weak.

<unsnip>
"Torkel Franzen" <torkel@sm.luth.se> wrote in
> I thought you might. It's complete nonsense, though. While it is no
> doubt true that experts tend to be over-critical of popular summaries
> of theories and results, the text by Kent Paul Dolan that you quote
> promotes misconceptions quite unnecessarily. If, instead of the
> confused and confusing "true in that set of axioms", we just say that
> there are statements that can be formulated within the theory, but
> neither proved nor disproved in the theory, much is gained, and the
> experts will to a large extent be mollified.

if "this statement G has no proof" is "formulated within the theory",
"but neither proved nor disproven in the theory" then G is true, by semantic investigation.
</unsnip>

Going to lower ground that godel statements are not true, or declaring the meaning
of the godel statement, or not declaring the godel statement is true is *pointless*.

If this is your replacement text
> there are statements that can be formulated within the theory, but
> neither proved nor disproved in the theory

then I'll stick with Dolan, he understands that that above implies the godel
statement is TRUE.

Herc