=1325.= No irrational exaggeration of the claims of Mathematics can ever deprive that part of philosophy of the property of being the natural basis of all logical education, through its simplicity, abstractness, generality, and freedom from disturbance by human passion. There, and there alone, we find in full development the art of reasoning, all the resources of which, from the most spontaneous to the most sublime, are continually applied with far more variety and fruitfulness than elsewhere;.... The more abstract portion of mathematics may in fact be regarded as an immense repository of logical resources, ready for use in scientific deduction and co-ordination. --COMTE, A. _Positive Philosophy [Martineau], (London, 1875), Vol. 2, p. 439._ =1326.= Logic it is called [referring to Whitehead and Russell’s Principia Mathematica] and logic it is, the logic of propositions and functions and classes and relations, by far the greatest (not merely the biggest) logic that our planet has produced, so much that is new in matter and in manner; but it is also mathematics, a prolegomenon to the science, yet itself mathematics in its most genuine sense, differing from other parts of the science only in the respects that it surpasses these in fundamentality, generality and precision, and lacks traditionality. Few will read it, but all will feel its effect, for behind it is the urgence and push of a magnificent past: two thousand five hundred years of record and yet longer tradition of human endeavor to think aright.--KEYSER, C. J. _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.