[nuncanada]

A simple answer would be: the Natural Numbers can be axiomatized infinitely many different isomorphic ways in First Order Theories. Which one is the "right" one? None and according to FOM wisdom you shouldn't care. In Higher Order Theories there is a very straightforward and natural way to define the Natural Numbers. Could you create other isomorphic axiomatizions? Yes but they certainly wouldn't be as pleasant and straightforward...