On 4/20/2013 12:10 PM, WM 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).
n=n as an ontological assumption in the standard account of identity has nothing to do with the natural numbers.