Re: Goedel - interesting problem?

From: Chris Menzel (cmenzel_at_remove-this.tamu.edu)
Date: 06/03/04 

Date: 3 Jun 2004 17:39:26 GMT

On 3 Jun 2004 01:30:20 -0500, Acme Diagnostics
<LFinezapthis@partpostmark.net> said:
> As part payment for your recent worthy criticism, I offer these
> wonderful resources provided me by one of my favorite posters, Kent
> Paul Dolan (aka xanthian).
> ...
> Second, is Kent's masterpiece of concise and precisely worded
> explanatory text on the effect of the theorem (compiled from two
> posts):
>
> - - - - -
> [Goedel] proved that any set of axioms at least as rich as the axioms
> of arithmetic has statements which are true in that set of axioms,
> but cannot be proved by using that set of axioms.
 
To which "axioms of arithmetic" is the poster referring? There is no
such thing as THE axioms of arithmetics (and, as Aatu has already
clearly and helpfully pointed out, no such thing in logic as being true
in a set of axioms).

> It isn't all that complicated to follow the proof, either,
> since it uses only the axioms of arithmetic to achieve its
> goal.

That is really very far from true (though I'd agree that even still the
proof is not terribly complicated as deep results in mathematics go).

> The above is also most useful as an unambiguous definition to be
> included in argumentation about the Goedel theorem.

Not if you're interested in arguments that are both sound and
informative.

Cheers.

Chris Menzel

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