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

fastness and importance of the objects. For example, if I know the mass of a planet and the distance of its satellite from it, I can tell with certainty tlie period of the revolution of the latter according to Kepler’s second law. But the ground of this law is, tliat with this distance only this velocity will both chain the satellite to the planet and prevent it from falling into it.

Thus it is only upon such a geometrical basis, that is, by means of an intuition or perception a priori, and also under the application of a law of nature, that much can be arrived at by means of syllogisms, for here they are merely like bridges from one sensuous apprehension to others ; but it is not so with mere pure syllogistic reasoning in the exclusively logical method.

The source of the first fundamental truths of astronomy is, however, properly induction, that is, the comprehension of what is given in many perceptions in one true and directly founded judgment. From this, hypotheses are afterwards constructed, and their confirmation by experience, as induction approaching to completeness, affords the proof of the first judgment.

For example, the apparent motion of the planets is known empirically ; after many false hypotheses with regard to the spacial connection of this motion (planetary course) the right one was at last found, then the laws which it obeyed (the laws of Kepler), and, lastly, the cause of these laws (universal gravitation), and the empirically known agreement of all observed cases with the whole of the hypotheses, and with their consequences, that is to say, induction, established them with complete certainty.

The invention of the hypotheses was the work of the judgment, which rightly comprehended the given facts and expressed them accordingly; but induction, that is, a multitude of perceptions, confirmed their truth. But their truth could fdso be known directly, and by a single empirical perception, if we could pass freely through space and had telescopic eves. Therefore, here also syllogisms are not

As a third example taken from a different sphere wo may mention that the so-called metaphysical truths, that is, such truths as those to which Kant assigns the position of the metaphysical first principles of natural science, do not owe their evidence to demonstration. What is a 'priori certain we know directly ; as the form of all knowledge, it is known to us with the most complete necessity.

For example, that matter is permanent, that is, can neither come into being nor pass away, we know directly as negative truth ; for our pure intuition or perception of space and time gives the possibility of motion ; in the law of causality the understanding affords us the possibility of change of form and quality, but we lack powers of the imagination for conceiving the coming into being or passing away of matter.

Therefore that truth has at all times been evident to all men everywhere, nor has it ever been seriously doubted ; and this could not be the case if it had no other ground of knowledge than the abstruse and exceedingly subtle proof of Kant.

But besides this, I have found Kant’s proof to be false (as is explained in the Appendix), and have shown above that the permanence of matter is to be deduced, not from the share which time has in the possibility of experience, but from the share which belongs to space.

The true foundation of all truths which in this sense are called metaphysical, that is, abstract expressions of the necessary and universal forms of knowledge, cannot itself lie in abstract principles ; but only in the immediate consciousness of the forms of the idea communicating itself in apodictic assertions a priori, and fearing no refutation.

But if we yet desire to give a proof of them, it can only consist in showing that what is to be proved is contained in some truth about which there is no doubt, either as a part of it or as a presupposition. Thus, for example, I have shown that all empirical perception implies the

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application of the law of causality, the knowledge of which is hence a condition of all experience, and therefore cannot be first given and conditioned through experience as Hume thought. Demonstrations in general are not so much for those wlio wish to learn as for those who wish to dispute. Such persons stubbornly deny directly established insight ; now only the truth can be consistent in all directions, and therefore we must show such persons that they admit under one form and indirectly, what they deny under another form and directly; that is, the logically necessary connection between what is denied and what is admitted.