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)
“The private life of one man shall be a more illustrious monarchy,—more formidable to its enemy, more sweet and serene in its influence to its friend, than any kingdom in history. For a man, rightly viewed, comprehendeth the particular natures of all men.”
—Ralph Waldo Emerson (1803–1882)
“The joy of life consists in the exercise of one’s energies, continual growth, constant change, the enjoyment of every new experience. To stop means simply to die. The eternal mistake of mankind is to set up an attainable ideal.”
—Aleister Crowley (1875–1947)
“Freud was a hero. He descended to the “Underworld” and met there stark terrors. He carried with him his theory as a Medusa’s head which turned these terrors to stone.”
—R.D. (Ronald David)