The World as Will and Idea, Vol. II — Arthur Schopenhauer, trans. Haldane & Kemp

like a face without eyes. They are, however, a suitable occupation for men of good capacity who yet lack the highest faculties, which would even be a hindrance to minute investigations of such a kind.

Such men concentrate their whole power and their whole knowledge upon one limited field, in which, therefore, on condition of remaining in entire ignorance of everything else, they can attain to the most complete knowledge possible; while the philosopher must survey all fields of knowledge, and indeed to a certain extent be at home in them; and thus that complete knowledge which can only be attained by the study of detail is necessarily denied him.

Therefore the former may be compared to those Geneva workmen of whom one makes only' wheels, another only springs, and a third only chains. The philosopher, on the other hand, is like the watchmaker, who alone produces a whole out of all these which has motion and significance.

They may also be compared to the musicians of an orchestra, each of whom is master of his own instrument ; and the philosopher, on the other hand, to the conductor, who must know the nature and use of every instrument, yet without being able to play them all, or even one of them, with great perfection. Scotus Erigena includes all sciences under the name Scientia, in opposition to philosophy, which he calls Soupientia.

The same distinction was already made by the Pythagoreans; as may be seen from Stobseus (Floril., vol. i. p. 20), where it is very clearly and neatly explained. But a much happier and more piquant comparison of the relation of the two kinds of mental effort to each other has been so often repeated by the ancients that we no longer know to whom it belongs. Diogenes Laertius (ii.

79) attributes it to Aristippus, Stobseus (Floril., tit. iv. no) to Aristo of Chios ; the Scholiast of Aristotle ascribes it to him (p. 8 of the Berlin edition), but Plutarch (Be Puer. Educ., c. 10) attributes it to Bio — " Qui ajebai, sicut Penelopes proci,

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FIRST BOOK. CHAPTER XII.

quum non possent cum Penelope concumbere, rem cum ejus ancillis habuissent ; ita qui philosophiam nequeunt apprehendere eos in alliis nullius pretii diciplinis sese conterere." In our predominantly empirical and historical age it can do no harm to recall this.

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CHAPTER XIII.1

ON THE METHODS OF MATHEMATICS.

Euclid's method of demonstration has brought forth from ts own womb its most striking parody and caricature in he famous controversy on the theory of parallels, and he attempts, which are repeated every year, to prove the Seventh axiom. This axiom asserts, and indeed supports ts assertion by the indirect evidence of a third interacting line, that two lines inclining towards each other for that is just the meaning of "less than two right ngles") if produced far enough must meet — a truth 'hich is supposed to be too complicated to pass as selfvident, and therefore requires a demonstration. Such a emonstration, however, cannot be produced, just because lere is nothing that is not immediate. This scruple of mscience reminds me of Schiller's question of law : — "For years I have used my nose for smelling. Have I, ten, actually a right to it that can be proved ? " Indeed seems to me that the logical method is hereby reduced absurdity. Yet it is just through the controversies )out this, together with the vain attempts to prove what directly certain as merely indirectly certain, that the lf-sufficingness and clearness of intuitive evidence apars in contrast with the uselessness and difficulty of ^ical proof — a contrast which is no less instructive than nusing. The direct certainty is not allowed to be valid Ire, because it is no mere logical certainty following from 13 conceptions, thus resting only upon the relation of the

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predicate to the subject, according to the principle contradiction. That axiom, however, is a synthetica proposition a priori, and as such has the guarantee o pure, not empirical, perception, which is just as immediat and certain as the principle of contradiction itself, fror which all demonstrations first derive their certainty Ultimately this holds good of every geometrical theoren and it is quite arbitrary where we draw the line betwee what is directly certain and what has first to be demor strated. It surprises me that the eighth axiom is nc rather attacked. "Figures which coincide with eac other are equal to each other." For " coinciding wit each other" is either a mere tautology or somethir purely empirical which does not belong to pure percei tion but to external sensuous experience. It presupposthat the figures may be moved ; but only matter is moable in space. Therefore this appeal to coincidence leav pure space — the one element of geometry — in order pass over to what is material and empirical.

1 This chapter is connected with § 1 5 of the first volume. VOL. H. X