> << 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? Take any (uniquely operated) iteration and count the steps by whichever method you like - the result is isomorphic to N in whichever 'theory'. Some folks who 'feel incomfortable', like the asshole idiot WM, when one defines a limit to that sort of operation, thus are unable to comprehend that abstraction, might go see a doctor or invent alternative theories - anyway, whoever drivels about something like 'physical existence' of numbers is just a plain idiot, hopefully a kind one.