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. > --
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
