The great arbiters of language are the women who speak it in the presence of children. . . What the women pass on to the next generation is "right" and what they do not bother to pass on to their children sooner or later becomes "wrong.
But as the work proceeded I was continually reminded of the fable about the elephant and the tortoise. Having constructed an elephant upon which the mathematical world could rest, I found the elephant tottering, and proceeded to construct a tortoise to keep the elephant from falling. But the tortoise was not more secure than the elephant, and after some twenty years of very arduous toil, I came to the conclusion that there was nothing more that I could do in the way of making mathematical knowledge indubitable.