Re: usenet kooks and a crank scale

From: |-|erc (h_at_r.c)
Date: 01/15/05 

Date: Sat, 15 Jan 2005 23:03:53 +1000

-------------------------------------s-o-s------------------------------------
"Aatu Koskensilta" <aatu.koskensilta@xortec.fi> wrote in ...
> Aatu Koskensilta wrote:
>
> > |-|erc wrote:
> >
> >> All the components of the sentence have an equivalnet to the formula,
> >> "THIS SENTENCE" is just as colloquial as "ME".
> >> YOU CANT PROVE ME has identical godelian derivation, by extension it
> >> is equivalent.
> >
> >
> > I can't make head or tails out of this. I'm a little slow. Could you
> > outline in detail how the sentence "YOU CAN'T PROVE ME" is expressed in
> > the language of first order arithmetic?
>
> To clarify: I have no problem constructing for any property P
> expressible in the language of first order arithmetic a sentence F, such
> that F is equivalent to its Gödel number having the property P. What
> puzzles me is how to define "provability" in the language of arithmetic.
> Pray tell! The language of set theory - indeed any mathematically
> defined language - would do equally well, of course, if you wish to have
> recourse to these.
>
>

I told you

> "This sentence isn't provable in the formal theory T" can be expressed
> in the language of first order arithmetic
<->
"this sentence, me, can't be proved to people by reading formal theory T" can be expressed in FOL
->
"You, such a person, can't prove this sentence, me" can be expressed in FOL
->
"You can't prove me" can be expressed in FOL

G = "this sentence isn't provable in the formal theory T"
if G is proven in T then it is true
if G is true it isn't proven in T
contradiction
therefore G has no proof in T
therefore G is true

g = "you can't prove me"
if you prove g, then g is true
if g is true then you can't prove g
contradiction
therefore you can't prove g
therefore g is true.

By proof extension, G <=> g.

Therefore.... BELIEVE IT OR NOT

<schoolyard girly voice>

 YOU CANT PROVE ME

</schoolyard girly voice>

is the entire reason mathematicians gave up on formalism.

shame on you all too!
Herc

Relevant Pages

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