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:
“I am not sure but I should betake myself in extremities to the liberal divinities of Greece, rather than to my country’s God. Jehovah, though with us he has acquired new attributes, is more absolute and unapproachable, but hardly more divine, than Jove. He is not so much of a gentleman, not so gracious and catholic, he does not exert so intimate and genial an influence on nature, as many a god of the Greeks.”
—Henry David Thoreau (1817–1862)
“Just what is the civil law? What neither influence can affect, nor power break, nor money corrupt: were it to be suppressed or even merely ignored or inadequately observed, no one would feel safe about anything, whether his own possessions, the inheritance he expects from his father, or the bequests he makes to his children.”
—Marcus Tullius Cicero (106–43 B.C.)
“There is nothing more mysterious than a TV set left on in an empty room. It is even stranger than a man talking to himself or a woman standing dreaming at her stove. It is as if another planet is communicating with you.”
—Jean Baudrillard (b. 1929)
“Frankly, these days, without a theory to go with it, I can’t see a painting.”
—Tom Wolfe (b. 1931)