HP plays a central role in Gottlob Frege's philosophy of mathematics.
)[2]Note Hume's use of the word number in the ancient sense, to mean a set or collection of things rather than the common modern notion of "positive integer".
The ancient Greek notion of number (arithmos) is of a finite plurality composed of units.
The principle that cardinal number was to be characterized in terms of one-to-one correspondence had previously been used by Georg Cantor, whose writings Frege knew.
But Frege criticized Cantor on the ground that Cantor defines cardinal numbers in terms of ordinal numbers, whereas Frege wanted to give a characterization of cardinals that was independent of the ordinals.