Science, Vol. 35 (1912), p. 110.
CHAPTER XIV
MATHEMATICS AND PHILOSOPHY
[1401]. Socrates is praised by all the centuries for having called philosophy from heaven to men on earth; but if, knowing the condition of our science, he should come again and should look once more to heaven for a means of curing men, he would there find that to mathematics, rather than to the philosophy of today, had been given the crown because of its industry and its most happy and brilliant successes.—Herbart, J. F.
Werke [Kehrbach], (Langensalza, 1890), Bd. 5, p. 95.
[1402]. It is the embarrassment of metaphysics that it is able to accomplish so little with the many things that mathematics offers her.—Kant, E.
Metaphysische Anfangsgründe der Naturwissenschaft, Vorrede.
[1403]. Philosophers, when they have possessed a thorough knowledge of mathematics, have been among those who have enriched the science with some of its best ideas. On the other hand it must be said that, with hardly an exception, all the remarks on mathematics made by those philosophers who have possessed but a slight or hasty or late-acquired knowledge of it are entirely worthless, being either trivial or wrong.—Whitehead, A. N.
Introduction to Mathematics (New York, 1911), p. 113.