Date: Feb 11, 2013 2:50 AM
Author: mueckenh@rz.fh-augsburg.de
Subject: Re: Matheology § 222 Back to the roots

On 11 Feb., 07:43, William Hughes <wpihug...@gmail.com> wrote:
> On Feb 10, 11:11 pm, Virgil <vir...@ligriv.com> wrote:
>
>
>
>
>
> > In article
> > <c7249ee8-e019-43bf-8ce9-2a2099b91...@l13g2000yqe.googlegroups.com>,
>
> >  WM <mueck...@rz.fh-augsburg.de> wrote:
> > > On 9 Feb., 17:36, William Hughes <wpihug...@gmail.com> wrote:
> > > > > > the arguments are yours
> > > > > > and the statements are yours-
>
> > > > > Of course. But the wrong interpretation is yours.
>
> > > > How does one interpret
> > > >    we have shown m does not exist
> > > >    (your statement)
>
> > > > to mean that
>
> > > >    m might still exist
>
> > > > ?
>
> > > TND is invalid in the infinite.
>
> > As far as the vast majority of mathematics and mathematicians is
> > concerned, Tertium Non Datur is valid everywhere.
>
> > Those who claim otherwise do not speak for the vast majority of
> > mathematics and mathematicians but at most for a miniscule minority.
> > --
>

William, you must dig a lot deeper.

> Here the excluded middle is not relevant.  We know that
>      P := there exists a natural number m
> is false.

False. "There exists a natural number m" is correct.

>  It does not matter how many truth
> values P can have, we know which one we have.
> The excluded middle would only be relevant if we were trying
> to obtain P true from ~~P true or P false
> from ~~~P true.  Here we are obtaining ~P true
> from ~P  true-

There exists a natural number m such that d is line number m is false.

This is quite different from your statement.  It includes the truth of
the statement "d exists".

Since we have: There is no digit d_n of d that can be found outside of
the list, we have d, if existing, is not outside of the list. TND then
yields d is inside. And for every d_n there is a line containing
d_1 ... d_n shows d, if not being more than every d_n, is a line of
the list.

But your naive misunderstanding is valuable to the reader. It is just
this misunderstanding that has been the basis of transfinity.

Regards, WM