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From: melsi on 26 May 2010 23:49
ou say

Nope. Goedel showed

Truth does not equate with derivation

wrong
godels theorem is about proof
ie there are true mathematical which cant be proven
note the word is proven
not derivation

this is the word version of his theorem
note it talks about true statements which cant be proven--not derivation


http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#First_incompleteness_theorem
Gödel's first incompleteness theorem states that:

Any effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true,[1] but not provable in the theory (Kleene 1967, p. 250).

thus
it is shown by colin leslie dean that Godels theorem ends in paradox
>
> it is said godel PROVED
> "there are mathematical true statements which cant be proven"
> in other words
> truth does not equate with proof.
>
> if that theorem is true
> then his theorem is false
>
> PROOF
> for if the theorem is true
> then truth does equate with proof- as he has given proof of a true
> statement
> but his theorem says
> truth does not equate with proof.
> thus a paradox
From: William Hughes on 27 May 2010 07:24
On May 27, 4:48 am, byron <spermato...(a)yahoo.com> wrote:
> On May 27, 5:42 pm, byron <spermato...(a)yahoo.com> wrote:
>
>
>
> > On May 27, 4:44 pm, William Hughes <wpihug...(a)hotmail.com> wrote:
>
> > > On May 27, 2:16 am, byron <spermato...(a)yahoo.com> wrote:
>
> > > > it is shown by colin leslie dean that Godels theorem ends in paradox
>
> > > > it is said godel PROVED
> > > > "there are mathematical true statements which cant be proven"
> > > > in other words
> > > > truth does not equate with proof.
>
> > > > if that theorem is true
> > > > then his theorem is false
>
> > > > PROOF
> > > > for if the theorem is true
> > > > then truth does equate with proof- as he has given proof of a true
> > > > statement
> > > > but his theorem says
> > > > truth does not equate with proof.
> > > > thus a paradox
>
> > > Nope.  Goedel showed
>
> > >      Truth does not equate with derivation
>
> > > He gave a derivation of
>
> > >      G: G does not have a derivation,
>
> > > He argued that G is true, but did not give a derivation
> > > of the fact.  No paradox
>
> > >                -William Hughes
>
> > ou say
>
> > Nope. Goedel showed
>
> > Truth does not equate with derivation
>
> > wrong
> > godels theorem is about proof
> > ie there are true mathematical which cant be proven
> > note the word is proven
> > not derivation
>
> ou say
>
> Nope. Goedel showed
>
> Truth does not equate with derivation
>
> wrong
> godels theorem is about proof
> ie there are true mathematical which cant be proven
> note the word is proven
> not derivation
>
> this is the word version of his theorem
> note it talks about true statements which cant be proven--not
> derivation
>
> http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#F...
> Gödel's first incompleteness theorem states that:
>
>     Any effectively generated theory capable of expressing elementary
> arithmetic cannot be both consistent and complete. In particular, for
> any consistent, effectively generated formal theory that proves
> certain basic arithmetic truths, there is an arithmetical statement
> that is true,[1] but not provable in the theory (Kleene 1967, p.
> 250).


The phrase "provable in the theory" has a very specific meaning:
a statement is provable in a theory iff it has a derivation in the
theory. Showing outside the theory, that something
is not "provable in the theory" is not a contradiction.

The common informal statement "Goedel showed that there
are true theorems that are not provable" is contradictory
if the wrong interpretation is given to "provable". However,
claiming that Goedels theorem is contradictory based on
one interpretation of an informal rendering is stupid.

- William Hughes




From: J. Clarke on 27 May 2010 08:05
On 5/27/2010 1:16 AM, byron wrote:
> it is shown by colin leslie dean that Godels theorem ends in paradox
>
> it is said godel PROVED
> "there are mathematical true statements which cant be proven"
> in other words
> truth does not equate with proof.
>
> if that theorem is true
> then his theorem is false
>
> PROOF
> for if the theorem is true
> then truth does equate with proof- as he has given proof of a true
> statement
> but his theorem says
> truth does not equate with proof.
> thus a paradox

No paradox. "x is true but can't be proven" is not an equivalent
statement to "x which has been proven can nonetheless be false".

From: HallsofIvy on 27 May 2010 04:39
1) That is NOT what Godel said- he did not use the concept of "truth" at all. What he said was that there are some statements which cannot be proved and such that their negations cannot be proved.

2) Even with your statement, that is a false counter-example. You are saying there are SOME true statements that cannot be proved, not that ALL true statements cannot be proved. Simply exhibiting one true statement the CAN be proved does not contradict that.
From: byron on 27 May 2010 23:38
On May 27, 10:39 pm, HallsofIvy <GeorgeI...(a)netzero.com> wrote:
> 1) That is NOT what Godel said- he did not use the concept of "truth" at all. What he said was that there are some statements which cannot be proved and such that their negations cannot be proved.
>
>  2)  Even with your statement, that is a false counter-example.  You are saying there are SOME true statements that cannot be proved, not that ALL true statements cannot be proved.  Simply exhibiting one true statement the CAN be proved does not contradict that.

you say

That is NOT what Godel said- he did not use the concept of "truth" at
all. What he said was that there are some statements which cannot be
proved and such that their negations cannot be proved.

2) Even with your statement, that is a false counter-example. You
are saying there are SOME true statements that cannot be proved, not
that ALL true statements cannot be proved. Simply exhibiting one true
statement the CAN be proved does not contradict that.





the word formulation of his syntactic theorem is quite clear

this is the word version of his theorem
note it talks about true statements which cant be proven

http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems#F...
Gödel's first incompleteness theorem states that:

Any effectively generated theory capable of expressing elementary
arithmetic cannot be both consistent and complete. In particular, for
any consistent, effectively generated formal theory that proves
certain basic arithmetic truths, there is an arithmetical statement
that is true,[1] but not provable in the theory (Kleene 1967, p. 250).

thus
it is shown by colin leslie dean that Godels theorem ends in paradox

you say

Simply exhibiting one true statement the CAN be proved does not
contradict that.



fact is truth is not equated with proof
poof canot of a statement be in any way since godel a be regarded as
makeing something a statement true
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