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

is in view ; all this is done by the family of judgment Deficiency in judgment is silliness. The silly man fails to grasp, nidw “the^partial or ' ir^ative difference of concepts which in one aspect are identical, now the identity of concepts which are relatively or partially different.

To this “explanation of the faculty of judgment, moreover, Kant’s division of it into reflecting and subsuming judgment may be applied, according as it passes from the perceived objects to the concepts, or from the latter to the former ; in .both cases always mediating between empirical knowledge of the understanding and the reflective knowledge of the reason.

There can be no truth which could be brought out by means of syllogisms alone ; and the necessity of establishing truth by means of syllogisms is merely relative, indeed subjective. Since all demonstration is syllogistic, in the case of a new truth we must first seek, not for a demonstration, but for direct evidence, and only in the absence of such evidence is a demonstration to be temporarily made use of.

No science is susceptible of demonstration throughout any more than a building can stand in the air ; all its demonstrations must ultimately rest upon what is perceived, and consequently cannot be demonstrated, for the whole world of reflection rests upon and is rooted in the world of perception. All primal, tliat is, original, evidence is a 'perception, as the word itself indicates.

Therefore it is either empirical or founded upon the perception a priori of the conditions of possible experience. In both cases it affords only immanent, not transcendent knowledge. Every concept has its worth and its existence only in its relation, sometimes very indirect, to an idea of perception ; what is true of the concepts is also true of the judgments constructed out of them, and of all science.

Therefore it must in some way be possible to know directly without demonstrations or syllogisms every truth that is arrived at through syllogisms and communiCftterl Kv Homnnflf’.TAf'.inTia T’Viia mncf. in t.liA

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case of certain complicated mathematical propositions at which we only arrive by chains of syllogisms; for example, the calculation of the chords and tangents to all arcs by deduction from the proposition of Pythagoras. But even such a truth as this cannot essentially and solely rest upon abstract principles, and the space-relations which lie at its foundation also must be capable of being so presented a prion in pure intuition or perception that the truth of their abstract expression is directly established. But of mathematical demonstration we shall speak more fully shortly.

It is true we often hear men speak in a lofty strain of sciences which rest entirely upon correct conclusions drawn from sure premises, and which are consequently unassailable. But through pure logical reasoning, however true the premises may be, we shall never receive more than an articulate expression and exposition of what lies already complete in the premises ; thus we shall only explintly expound what was already implicitly understood. The esteemed sciences referred to are, however, specially the mathematical sciences, particularly astronomy. But the certainty of astronomy arises from the fact that it has for its basis the intuition or perception of space, which is given a priori, and is therefore infallible. All space-relations, however, follow from each other with a necessity (ground of being) which affords a priori certainty, and they can therefore be safely deduced from each other. To these mathematical properties we have only to add one force of nature, gravity, which acts precisely in relation to the masses and the square of the distance ; and, lastly, the law of inertia, which follows from the law of causality and is therefore true a priori, and with it the empirical datum of the motion impressed, once for all, upon each of these masses. This is the whole material of astronomy, which both by its simplicity and its certainty leads to definite results, which are highly interesting on account of the

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