Page:The World as Will and Idea - Schopenhauer, tr. Haldane and Kemp - Volume 2.djvu/333

do with corporeal things (Schol. in Aristot., 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 Review 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, and has appeared by itself under the title, "Ueber den Werth und Unwerth der Mathematik" aus dem Englishen, 1836. The conclusion the author arrives at is that the value of mathematics is only indirect, and lies in the application to ends which are only attainable through them; but in themselves mathematics leave the mind where they find it, and are by no means conducive to its general culture and development, nay, even a decided hindrance. This conclusion is not only proved by thorough dianoiological investigation of the mathematical activity of the mind, but is also confirmed by a very learned accumulation of examples and authorities. The only direct use which is left to mathematics is that it can accustom restless and unsteady minds to fix their attention. Even Descartes, who was yet himself famous as a mathematician, held the same opinion with regard to mathematics. In the "Vie de Descartes par Baillet," 1693, it is said, Liv. ii. c. 6, p. 54: "Sa propre expérience l'avait convaincu du peu d'utilité des mathematiques, surtout lorsqu'on ne les cultive que pour elles mêmes. ... Il ne voyait rien de moins solide, que de s'occuper de nombres tout simples et de figures imaginaires," &c.