cardinal number was to be characterized in terms of one-to-one correspondence had previously been used by Georg Cantor, whose writings 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 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. References External links Stanford Encyclopedia of Philosophy: "Frege's Logic, Theorem, and Foundations for Arithmetic" by Edward Zalta. "The Logical and Metaphysical Foundations of Classical Mathematics." Arche: The Centre for Philosophy of Logic, Language, Mathematics and Mind at St. Andrew's University. Set theory Philosophy of mathematics Mathematical principles Concepts in logic