Editing Hume's principle (section)

== Influence on set theory ==
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 [[Gottlob Frege|Frege]] knew. The suggestion has therefore been made that Hume's principle ought better be called "Cantor's Principle" or "The Hume-Cantor Principle". But Frege criticized Cantor on the ground that Cantor defines [[cardinal number]]s in terms of [[ordinal number]]s, whereas Frege wanted to give a characterization of cardinals that was independent of the ordinals. Cantor's point of view, however, is the one embedded in contemporary theories of [[transfinite number]]s, as developed in [[axiomatic set theory]].