ABSTRACT
1. As is well known it is very easy to teach a child to count with pebbles or apples. However, difficulties arise when one attempts to introduce pure numbers. This is evident if one but considers the history of human thought. The arithmetic of the Egyptians and the Babylonians was confined to the sphere of practical applications and therefore was entirely clear. Difficulties first arose when the Greeks created the concept of natural number. This very important step was taken in a manner which is hard to describe; nevertheless this process was certainly far less simple and clear than the related processes in the arithmetic of natural numbers. The arithmetic of the Greeks was part of metaphysics and never was separated from the disturbing problem,: how it is possible that natural numbers have independent existence?
