```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 ofthe statement "d exists".Since we have: There is no digit d_n of d that can be found outside ofthe list, we have d, if existing, is not outside of the list. TND thenyields d is inside. And for every d_n there is a line containingd_1 ... d_n shows d, if not being more than every d_n, is a line ofthe list.But your naive misunderstanding is valuable to the reader. It is justthis misunderstanding that has been the basis of transfinity.Regards, WM
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