It is precisely here, however, that another most important phase of the matter comes to light. The ingenious humanitarian fancies that he can turn the edge of the foregoing arguments completely. It was Theodor Waitz who, in his "Anthropology" (London, 1863), suggested that the relation between human culture and human faculty might be the inverse of what was commonly conceived. Instead of the culture resulting from the faculty, it might be the faculty that resulted from the culture. Accordingly, we should not say that the Greek civilization with its language, its art, its science, its philosophy, its eloquence, its literature, its civil and military life, was the outgrowth of the Greek genius, the native faculty of the Hellenic race, but rather that this genius, this spiritual faculty, this unrivalled intellectual-artistic endowment of the Greeks, was the continuous resultant at each moment in the history of the race of the collective culture-experiences through which, up to that moment, it had passed. We have tried conscientiously to state this doctrine, that race endowment is the reaction from race culture-experience, as forcibly and as plausibly as possible; but we cannot hope to have redeemed it from patent absurdity. Surely there was never a plainer case of the cart before the horse. No one denies or forgets that training and discipline do quicken and sharpen the intellectual faculties; they enable a man to make the most of himself, to realize his possibilities, to develop himself to the utmost. The power to solve a problem in algebra or geometry is the result, in part, of the previous training in those subjects. Here is the very partial and most familiar truth that lies hid away in Waitz's stupendous error. But was the ability to understand algebra and geometry given by the actual study of the same, given step by step? By no means. The knowledge necessary to understand the successive propositions does indeed grow thus step by step, but not the power. Open the book at the middle; there you may find a theorem whose proof you readily understand, because it implies very little previous knowledge. Newton at first thought Euclid's Elements a "light book," because it offered him no difficulty. But if you meet with some unfamiliar affirmation, then comes the question, why? The answer is found in some theorem already proved. Turn back to it; perhaps the proof involves some still more fundamental property, and again you ask, why? Again you must recur to some earlier theorem; and so on, until all your "whys" are answered with all possible clearness in irreducible axioms or postulates. He who has the mental ability will find this method of learning a theorem entirely practicable, and it may sometimes be found highly instructive. But it excludes all question of gradual growth of mental power through the successive "stages of culture" itself.