Biography
"A recurring concern has been whether set theory, which speaks of infinite sets, refers to an existing reality, and if so how does one ‘know’ which axioms to accept. It is here that the greatest disparity of opinion exists (and the greatest possibility of using different consistent axiom systems)."
"The requisites for the axioms are various. They should be simple, in the sense that each axiom should enumerate one and only one statement. The total number of axioms should be few. A set of axioms must be consistent, that is to say, it must not be possible to deduce the contradictory of any axiom from the other axioms. According to the logical 'Law of Contradiction,' a set of entities cannot satisfy inconsistent axioms. Thus the existence theorem for a set of axioms proves their consistency. Seemingly this is the only possible method of proof of consistency."