In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 20 Apr., 17:07, fom <fomJ...@nyms.net> wrote: > > On 4/20/2013 1:56 AM, WM wrote: > > > > > On 19 Apr., 21:37, Virgil <vir...@ligriv.com> wrote: > > > > >>>> It is not the size of any one index but the number of different indices > > >>>> that is not finite. > > > > >>> The number of indices is a number. Up to any finite index it is a > > >>> finite number. > > > > >> Then you should be aqble to give us the allegedly finite number of > > >> indices. Unless here are more of them that an finite number. > > > > > The number of indices up to index n is n (unless you count 0 as an > > > index, then the number is n + 1). The numbers of indices and the > > > values of indices are in bijection. > > > > The fact that n=n for each n is not in doubt. It is an ontological > > assumption in the standard account of identity. > > Of course. Every finite number counts its place thereby proving that > it belongs to a finite set (1, ..., n).
But unless WM can come up with a natural number which can be shown not to have a successor, or a double , or a triple, etc., what evidence does he have that the sequence must end finitely? > > > > So, to say "for every n that is a number, n is a number" and > > "if n is finite, n is finite" provides no answer. > > > But it provides the truth.
A truth > > > What has been asked for is the specific counterexample to > > Virgil's statement -- namely, that number of indices beyond > > which it can be proven that there exist no more indices. > > That is not asked for by persons who know mathematics.
It is asked by almost all mathematicians outside of Wolkenmuekenheim, and what goes on inside Wolkenmuekenheim is not mathematics. --