Re: Goedel - interesting problem?

From: |-|erc (gotcha_at_beauty.com)
Date: 06/07/04 

Date: Mon, 07 Jun 2004 00:28:36 GMT

"Daryl McCullough" <daryl@atc-nycorp.com> wrote
> |-|erc says...
>
> >You are being selective on what formula you accept.
> >
> >G = "this statement has no proof"
> >~G -> ~"this statement has no proof" -> G has a proof -> G
> >[contradiction] -> G
>
> Your reasoning here is almost correct, except that you
> left out one assumption. The implication
>
> G has a proof -> G
>
> is true only if your system is sound (that is, it only proves
> true sentences). But no system of axioms can *prove* its
> own soundness. So your proof of G must be done in a different
> proof system than the one used to formalize "G has a proof".
>
> In the case of the Godel statement G for Peano arithmetic,
> G actually is true, but its truth cannot be proved within
> Peano arithmetic.

you're an exemplary scholar of these notions, but look at the entire load of
jibberish it forces you to output. what a load of crap, there is nothing
you are doing here that peano + modus ponens can't do exactly the same.
in your mass halucinagenic induced state you all summon G as undeniably
true and concoct local_truthity as its conduit.

I understood godels proof for a decade, there is no use explaining what I now
understand is a wrong proof to me, if you don't listen to why its wrong and go into
parrot mode repeatedly I can't help you. G pops up in every such a consistent
model, I know BIG DEAL. Whats you definition of consistent? It has *a*
solution either true or false. In those models G will pop up as a valid formula ture,
and "this statement P is false" will nicely get truncated from the forumula list, added
to syntactically erronous formula when its syntax is on par with G.

Just think, ALL PROVEN TRUE THINGS HAVE A PROOF.

Why don't you accept that as a true formula? it pops up everywhere too, it craps on G.

Herc

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