The World as Will and Idea, Vol. I — Arthur Schopenhauer, trans. Haldane & Kemp
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The translator’s English as printed (R. B. Haldane & J. Kemp). The original-language text is not held; names are romanised as the translator printed them.
pure a priori perception, with the same right and certainty as in arithmetic. It is in fact always this necessity, known through perception in accordance with the principle of sufficient reason of being, which gives to geometry its principal evidence, and upon which in the consciousness of every one, the certainty of its propositions rests. The stilted logical demonstration is always foreign to the matter, and is generally soon forgotten, without weakening our conviction. It might indeed be dispensed with altogether without diminishing the evidence of geometry, lor this is always quite independent of such demonstration, which never proves anything we are not convinced of already, through another kind of knowledge. So far then it is like a cowardly soldier, who adds a wound to an enemy slain by another, and then boasts that he slew him himself.^
* After all this we hope there will be no doubt that the evidence of mathematics, which has become the pattern and symbol of aU evidence, rests essentially not upon demonstration, but upon immediate perception, which is thus here, as everywhere else, the ultimate ground and source of truth. Yet the perception which lies at the basis of mathematics has a great advantage over all other perception, and therefore over empirical porception. It is a priori, and therefore independent of experience, which is always given only in successive parts ; therefore everything is equally near to it, and we can start either from the reason or from the consequent, as we please. Now this makes it absolutely reliable,
^ Spinoza, who always boasts that self {substantia causa sui, <kc.), and he proceeds more f/eometricOf has in the demonstrations he allows actu^y done so more than he him- himself all the freedom of choice for self was aware. For what he knew which the nature of the wide conwith certainty and decision from the cept-spheres afford such convenient immediate, perceptive apprehension opportunity. That his doctrine is of the nature of the world, he seeks true and excellent is therefore in to demonstrate logically without his ca.se, as in that of geometry, reference to this knowledge. He quite independent of the demonstra* only arrives at the intended and pre- tions of it. Of. ch. 13 of supplemen determined result by starting from tary volume, arbitrary concepts framed by himTHE WORLD AS IDEA.
loi for in it the consequent is known from the reason, and this is the only kind of knowledge that has necessity; for example, the equality of the sides is known as established by the equality of the angles.
All empirical perception, on the other hand, and the greater part of experience, proceeds conversely from the consequent to the reason, and this kind of knowledge is not infallible, for necessity only attaches to the consequent on account of the reason being given, and no necessity attaches to the knowledge of the reason from the consequent, for the same consequent may follow from different reasons.
The latter kind of knowledge is simply induction, i.e., from many consequents which point to one reason, the reason is accepted as certain ; but as the cases can never be all before us, the truth here is not unconditionally certain. But all knowledge through sense-perception, and the great bulk of experience, has only this kind of truth.
The affection of one of the senses induces the understanding to infer a cause of the effect, but, as a conclusion from the consequent to the reason is never certain, illusion, which is deception of the senses, is possible, and indeed often occurs, as was pointed out above.
Only when several of the senses, or it may be all the five, receive impressions which point to the same cause, the possibility of illusion is reduced to a minimum ; but yet it still exists, for there are cases, for example, the case of counterfeit money, in which all the senses are deceived.
All empirical knowledge, and consequently the whole of natural science, is in the same position, except on^ the pure, or as Kant calls it, metaphysical part of it. Here also the causes are known from the effects, consequently all natural philosophy rests upon hypotheses, which are often false, and must then gradually give place to more correct ones.
Only in the case of purposely arranged experiments, knowledge proceeds from the cause to the effect, that is, it follows the method that affords certainty ; but these experiments
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