Note (return) — Chapter IX

Thus have we, in Pythagoras, the dawn of an Idealist school; for mathematics are founded upon abstractions, and there is consequently an intimate connection between mathematics and idealism. The relations of space, and number, and determinate form, are, like the relations of cause and effect, of phenomena and substance, perceptible only in thought; and the mind which has been disciplined to abstract thought by the study of mathematics, is prepared and disposed for purely metaphysical studies. "The looking into mathematical learning is a kind of prelude to the contemplation of real being." 444 Therefore Plato inscribed over the door of his academy, "Let none but Geometricians enter here." To the mind thus disciplined in abstract thinking, the conceptions and ideas of reason have equal authority, sometimes even superior authority, to the perceptions of sense.