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From: byron on 27 May 2010 23:41
On May 28, 1:38 pm, byron <spermato...(a)yahoo.com> wrote:
> 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

fact is truth is not equated with proof
poof of a statement cannot be in any way since godel a be regarded
as makeing a statement true
From: byron on 27 May 2010 23:55
On May 28, 1:41 pm, byron <spermato...(a)yahoo.com> wrote:
> On May 28, 1:38 pm, byron <spermato...(a)yahoo.com> wrote:
>
>
>
> > 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
>
> fact is truth is not equated with proof
> poof   of a statement  cannot be in any way since godel a be regarded
> as makeing a statement  true

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

true statements in mathematics were generally assumed to be those
statements which are provable in a formal axiomatic system.

he works of Kurt Gödel, Alan Turing, and others shook this assumption,
with the development of statements that are true but cannot be proven
within the system

http://en.wikipedia.org/wiki/Truth#Truth_in_mathematics
In addition, from at least the time of Hilbert's program at the turn
of the twentieth century to the proof of Gödel's theorem and the
development of the Church-Turing thesis in the early part of that
century, true statements in mathematics were generally assumed to be
those statements which are provable in a formal axiomatic system.

The works of Kurt Gödel, Alan Turing, and others shook this
assumption, with the development of statements that are true but
cannot be proven within the system
From: Don Stockbauer on 28 May 2010 01:07
On May 27, 10:38 pm, byron <spermato...(a)yahoo.com> wrote:
> 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

Interesting how the complexity of Godel's results cause almost
limitless discussion, thus instantiating the Global Brain.
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