Hume's principle

Hume's principle is: The number of Fs is equal to the number of Gs if and only if there is a bijection between the Fs and the Gs.

Gottlob Frege used Hume's principle in his philosophy to derive from it according to Frege's theorem, the Peano axioms of arithmetic, which is the basis of neo- logicism.

Frege's conception of numbers differs from that of Georg Cantor, Frege as cardinal and ordinal numbers defined independently. However, Cantor's definition of cardinal numbers by means of the ordinals is part of theories of transfinite numbers.