To bring clearly before the mind what is meant by class and to distinguish this notion from all the notions to which it is allied, is one of the most difficult and important problems of mathematical philosophy.”When Russell wrote this in 1903, he could illustrate the difficulty of the problem by his own confusing attempt at a solution. He was able to demonstrate the importance of classes for mathematical philosophy in his later work: the definition of cardinal number as a class of classes similar to a given class served him as a cornerstone for the derivation of mathematics from logic.