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). > > 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.
> 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.