[tuning] Temperment

Temperament is under uncertainty!
http://www.geocities.jp/imyfujita/wtcuncertain.html

--- In tuning@yahoogroups.com, Mocfujita@... wrote:
>
> Temperament is under uncertainty!
> http://www.geocities.jp/imyfujita/wtcuncertain.html

This page says: Kurt Gödel's Incompleteness Theorem says that ....
"any precise mathematical system must contain some statements
that are neither provable nor disprovable
by the means allowed within the system".

This is not a correct description of Gödel's famous theorem, and in
fact his Completeness Theorem provides a counterexample--in first
order predicate calculus, every logically valid formula is provable.

On 2/6/06, Gene Ward Smith <genewardsmith@coolgoose.com> wrote:
> --- In tuning@yahoogroups.com, Mocfujita@... wrote:
> >
> > Temperament is under uncertainty!
> > http://www.geocities.jp/imyfujita/wtcuncertain.html
>
> This page says: Kurt Gödel's Incompleteness Theorem says that ....
> "any precise mathematical system must contain some statements
> that are neither provable nor disprovable
> by the means allowed within the system".
>
> This is not a correct description of Gödel's famous theorem, and in
> fact his Completeness Theorem provides a counterexample--in first
> order predicate calculus, every logically valid formula is provable.

Also, what do the Incompleteness Theorems have to do with the
uncertainty principle? I think they're only superficially similar.

Keenan

--- In tuning@yahoogroups.com, Mocfujita@... wrote:
>
> Temperament is under uncertainty!
> http://www.geocities.jp/imyfujita/wtcuncertain.html
>

Precision in music seems to be a funny subject.

http://www.geocities.com/threesixesinarow/savart.htm#footfoot

(In French)

Clark