Date: Feb 11, 2013 1:43 AM
Author: William Hughes
Subject: Re: Matheology § 222 Back to the roots

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

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