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, set and/or theory:
“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.)
“Were it good
To set the exact wealth of all our states
All at one cast? to set so rich a main
On the nice hazard of one doubtful hour?
It were not good.”
—William Shakespeare (1564–1616)
“If my theory of relativity is proven correct, Germany will claim me as a German and France will declare that I am a citizen of the world. Should my theory prove untrue, France will say that I am a German and Germany will declare that I am a Jew.”
—Albert Einstein (1879–1955)