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.
