On 3/17/2013 4:06 AM, WM wrote: > On 17 Mrz., 00:25, Virgil <vir...@ligriv.com> wrote: > >>>> Can WM provide an definition for natural numberss which doe not state, >>>> or at least imply, that every natural must have a successor natural? >> >>> Numbers are creations of the mind. Without minds there are no numbers. >> >> Which is not a relevant answer. > > By definition of a matheologian. >> >> Can WM provide an definition for natural numbers which doe not state, >> or at least imply, that every natural must have a successor natural? > > It is always stated or at least implicitly assumed in classical > mathematics that we are able to add 1. In reality this is an erroneous > assumption as has been shown in MatheRealism.
So, WH and Virgil do the hard work to expose the fact that WM assume's the directed set structure of the natural numbers in his statements.
I do the easy work of trying to place this into a sensible construct such as the use of a successor in Euclid's proof that there is no greatest prime so that WM's unfindable line has some sort of mangled basis in classical mathematics.
But, it is all in vain.
One can know the reality of a future moment that has not yet happened.
But, Euclid's assumption of a successor is as erroneous as anything Cantor, Dedekind, Brouwer, etc. has done.