The World as Will and Idea, Vol. II — Arthur Schopenhauer, trans. Haldane & Kemp
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The translator’s English as printed (R. B. Haldane & J. Kemp). The original-language text is not held; names are romanised as the translator printed them.
The reputed motto of the Platonic lecture-room, " Aye fieTpijTos /j.7]S€i<; ewtro)," of which mathematicians are proud, was no doubt inspired by the fact tb.at Plato i garded the geometrical figures as intermediate existenc between the eternal Ideas and particular things, Aristotle frequently mentions in his "Metaphysics" (esj cially i. c. 6, p. 887, 998, et Scholia, p. 827, ed. Ben Moreover, the opposition between those self-exist* • eternal forms, or Ideas, and the transitory individi. things, was most easily made comprehensible in geomei • cal figures, and thereby laid the foundation of the d • trine of Ideas, which is the central point of the philosor ' of Plato, and indeed his only serious and decided th • retical dogma. In expounding it, therefore, he started fr 1 geometry. In the same sense we are told that he regar< i geometry as a preliminary exercise through which a mind of the pupil accustomed itself to deal with incoi real objects, having hitherto in practical life had
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do with corporeal things (Schol. inAristot., p. 12, 15). This, then, is the sense in which Plato recommended geometry to the philosopher ; and therefore one is not justified in extending it further.
I rather recommend, as an investigation of the influence of mathematics upon our mental powers, and their value for scientific culture in general, a very thorough and learned discussion, in the form of a review of a book by Whewell in the Edinburgh Beview of January 1836. Its author, who afterwards published it with some other discussions, with his name, is Sir W. Hamilton, Professor of Logic and Metaphysics in Scotland.
This work has also found a German translator, md has appeared by itself under the title, " Uieber den Werth und Unwerth der Mathematik " aus dem Englishen, 1836.
The conclusion the author arrives at is that the /alue of mathematics is only indirect, and lies in the implication to ends which are only attainable through hem; but in themselves mathematics leave the mind vhere they find it, and are by no means conducive to ts general culture and development, nay, even a decided indrance.
This conclusion is not only proved by thoough dianoiological investigation of the mathematical ctivity of the mind, but is also confirmed by a very ;arned accumulation of examples and authorities. The nly direct use which is left to mathematics is that it in accustom restless and unsteady minds to fix their Mention. Even Descartes, who was yet himself famous 5 a mathematician, held the same opinion with regard • mathematics.
In the " Vie de Descartes par BaiLlet" 393, it is said, Liv. ii. c. 6, p. 54: " Sa propre experience ivait convaincu du pen cCutiliU des mathtmatiques, surtout rsqu'on ne les cultive que pour elles mimes. . . . II ne yait rien de moins solide, que de s'occuper de nombres tout •nples et de figures imaginaires" &c.
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CHAPTER XIV.
ON THE ASSOCIATION OF IDEAS.
The presence of ideas and thoughts in our consciousnesf is as strictly subordinated to the principle of sufficieni reason in its different forms as the movement of bodies to the law of causality. It is ju3t as little possible tha a thought can appear in the mind without an occasioi as that a body can be set in motion without a cause Now this occasion is either external, thus an impressioi of the senses, or internal, thus itself also a thought whic introduces another thought by means of association. Thi again depends either upon a relation of reason and cor sequent between the two ; or upon similarity, even mei analogy ; or lastly upon the circumstance that they wei both first apprehended at the same time, which agai may have its ground in the proximity in space of the objects. The last two cases are denoted by the woi & propos. The predominance of one of these three bom of association of thoughts over the others is characterist of the intellectual worth of the man. The first narai will predominate in thoughtful and profound minds, tl second in witty, ingenious, and poetical minds, and t third in minds of limited capacity. Not less characterisl is the degree of facility with which one thought reca others that stand in any kind of relation to it : tl constitutes the activeness of the mind. But the i possibility of the appearance of a thought without sufficient occasion, even when there is the strongest des to call it up, is proved by all the cases in which wo
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