Nietzsche shows his nominalistic tendencies by repeatedly pronouncing the same propositions in almost literally the same words,[1] without, however, acknowledging the school in which he picked up this error. It is quite true that mathematical lines and circles are human conceptions, but they are not purely subjective conceptions, still less untruths; they are great and important discoveries. They are not arbitrarily devised but constructed according to the laws of the uniformities that dominate existence. They represent actual features of the factors which shape the objective universe, and thus only is it possible that the astronomer through the calculation of mathematical curves can predict the motion of the stars.[2] Reason is the key to the universe, because it is the reflex of cosmic order, and the cosmic order, the intrinsic regularity and immanent harmony of the uniformities of nature, is not a subjective illusion but an objective reality. When Goethe claims that all things transitory are symbols of that which is intransitory and eternal, Nietzsche answers that the idea of anything intransitory is a mere symbol, and God (the idea of anything eternal) a poet's lie. Like a mocking-bird, the nominalist philosopher imitates the ring of Goethe's well-known lines at the conclusion of the second part of "Faust," in which the "real world" of transient things is considered as a mere symbol of the true world of eternal verities: "Das Unvergangliche Ist nur dein Gleichniss. Gott der Verfängliche Ist Dichter-Erschleichniss. Weltspiel, das herrische, Mischt Sein und Schein:-- Das Ewig-Närrische Mischt uns--hinein." "The non-deciduous Is a symbol of _thy_ sense, God ever invidious, A poetical license. World-play domineeringly Mixes semblance and fact, And between them us sneeringly The Ever-Foolish has packed." In spite of Nietzsche's hunger for the realities of life, that is to say for objectivity, he was in fact the most subjective of all philosophers--so much so that he was incapable of formulating any thought as an objectively precise statement. He did not believe in truth: "There is probability, but no truth," says he in _Der Wanderer und sein Schatten_, p. 190; and he adds concerning the measure of the value of truth (ibid., Aphorism 4): "The trouble in ascending mountains is no measure of their height, and should it be different in science?" It is true that such words as "long" and "short" are relative, because dependent on subjective needs and valuations. But must we for that reason give up all hope of describing facts in objective terms? Are not meters and foot-measures definite magnitudes, whether or not they be long for one purpose and short for another? Relativity itself admits of a description in objective terms; but if a statement of facts in objective terms were impossible, the ideals of exact science (as all ideals) would be a dream.