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