“In various ways, methods of approaching the mathematician's ideal were sought, and the resulting suggestions were the source of much that was mistaken in metaphysics and theory of knowledge.”

“The ideal of an “all-round” education is out of date; it has been destroyed by the progress of knowledge.”

“In science, an observer states his results along with the “probable error”; but who ever heard of a theologian or a politician stating the probable error in his dogmas, or even admitting that any error is conceivable? That is because in science, where we approach nearest to real knowledge, a man can safely rely on the strength of his case, whereas, where nothing is known, blatant assertion and hypnotism are the usual ways of causing others to share our beliefs. If the fundamentalist thought they had a good case against evolution, they would not make the teaching of it illegal.”

“The battle must be fought exactly as the battle of religious toleration was fought. And as in that case, so in this, a decay in the intensity of belief is likely to prove the decisive factor. While men were convinced of the absolute truth of Catholicism or Protestantism, as the case may be, they were willing to persecute on account of them. While men are quite certain of their modern creeds, they will persecute on their behalf. Some element of doubt is essential to the practice, thought not to the theory, of toleration.”

“If I were to suggest that between the Earth and Mars there is a china teapot revolving about the sun in an elliptical orbit, nobody would be able to disprove my assertion provided I were careful to add that the teapot is too small to be revealed even by our most powerful telescopes. But if I were to go on to say that, since my assertion cannot be disproved, it is an intolerable presumption on the part of human reason to doubt it, I should rightly be thought to be talking nonsense. If, however, the existence of such a teapot were affirmed in ancient books, taught as the sacred truth every Sunday, and instilled into the minds of children at school, hesitation to believe in its existence would become a mark of eccentricity and entitle the doubter to the attentions of the psychiatrist in an enlightened age or of the Inquisitor in an earlier time.”

“We know very little, and yet it is astonishing that we know so much, and still more astonishing that so little knowledge can give us so much power.”

“It might seem that the empirical philosopher is the slave of his material, but that the pure mathematician, like the musician, is a free creator of his world of ordered beauty.”