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.
Read more about this topic: Hume's Principle
Famous quotes containing the words influence on, influence, set and/or theory:
“Important as fathers are, their influence on children shouldn’t be exaggerated just because they were ignored so long. There is no evidence that there is something especially good about fathers as caretakers. There are no areas where it can be said that fathers must do certain things in order to achieve certain outcomes in children. The same goes for mothers.”
—Michael Lamb (late–20th century)
“We cannot spare our children the influence of harmful values by turning off the television any more than we can keep them home forever or revamp the world before they get there. Merely keeping them in the dark is no protection and, in fact, can make them vulnerable and immature.”
—Polly Berrien Berends (20th century)
“There are incalculable resources in the human spirit, once it has been set free.”
—Hubert H. Humphrey (1911–1978)
“The struggle for existence holds as much in the intellectual as in the physical world. A theory is a species of thinking, and its right to exist is coextensive with its power of resisting extinction by its rivals.”
—Thomas Henry Huxley (1825–95)