Finally there are simple ideas of which no definition can be given; there are also axioms or postulates, or in a word primary principles, which cannot be proved and have no need of proof. ↗
The only thing that might have annoyed some mathematicians was the presumption of assuming that maybe the axiom of choice could fail, and that we should look into contrary assumptions. ↗
The principal axiom in their theory was: Everything can be proved, and everything can be disproved; and in the process, one must profit as much from the folly of others, and from his own superiority, as he can. ↗