"Sam Sung" <firstname.lastname@example.org> wrote in message news:email@example.com... > Julio Di Egidio wrote: > >> << Edward Nelson criticizes the classical conception of natural numbers >> because of the circularity of its definition. In classical mathematics >> the >> natural numbers are defined as 0 and numbers obtained by the iterative >> applications of the successor function to 0. But the concept of natural >> number is already assumed for the iteration. >> >> >> <http://en.wikipedia.org/wiki/Ultrafinitism#Main_ideas> > > So what?
You have snipped the context.
> Take any (uniquely operated) iteration and count the > steps by whichever method you like - the result is isomorphic > to N in whichever 'theory'.