Influence On Set Theory
The principle that cardinal number was to be characterized in terms of one-to-one correspondence had previously been used to great effect by Georg Cantor, whose writings Frege knew. The suggestion has therefore been made that Hume's Principle ought better be called "Cantor's Principle". 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. Cantor's point of view, however, is the one embedded in contemporary theories of transfinite numbers, as developed in axiomatic set theory.
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