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

It is also a consequence of the scientific form, the subordination of eveiything particular under a general, and so on always to what is more general, that the truth of many propositions is only logically proved, — that is, through their dependence upon other propositions, through syllogisms, which at the same time appear as proofs. But we must never forget that this whole form of science is merely a means of rendering knowledge more easy, not a means to greater certainty. It is easier to discover the nature of an animal, by means of the species to which it belongs, and so on through the genus, family, order, and class, than to examine on every occasion the animal presented to us : but the truth of all propositions arrived at syllogistically is always conditioned by and ultimately dependent upon some truth which rests not upon reasoning but upon perception. If this perception were always as much within our reach as a deduction through syllogisms, then it would be in every respect preferable. For every deduction from concepts is exposed to great danger of error, on account of the fact we have considered above, that so many spheres lie partly within each other, and that their content is often vague or uncertain. This is illustrated by a multitude of demonstrations of false doctrines and sophisms of every kind. Syllogisms are indeed perfectly certain as regards form, but they are

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very uncertain on account of their matter, the concepts. For, on the one hand, the spheres of these are not sufficiently sharply defined, and, on the other hand, they intersect each other in so many ways that one sphere is in part contained in many others, and we may pass at will from it to one or another of these, and from this sphere again to others, as we have already shown.

Or, in other words, the minor term and also the middle can always he subordinated to different concepts, from which we may choose at will the major and the middle, and the nature of the conclusion depends on this choica Consequently immediate evidence is always much to he preferred to reasoned truth, and the latter is only to be accepted when the former is too remote, and not when it is as near or indeed nearer than the latter.

Accordingly we saw above that, as a matter of fact, in the case of logic, in which the immediate knowledge in each individual case lies nearer to hand than deduced scientfic knowledge, we always conduct our thought according to our immediate knowledge of the laws of thought, and leave logic unused.^

§ 15. If now with our conviction that perception is the primary source of all evidence, and that only direct or indirect connection with it is absolute truth ; and further, that the shortest way to this is always the surest, as every interposition of concepts means exposure to many deceptions ; if, I say, we now turn with this conviction to mathematics, as it was established as a science by Eucli^ and has remained as a whole to our own day, we cannot help regarding the method it adopts, as strange and indeed perverted. We ask that every logical proof shall be traced back to an origin in perception ; but mathematics, on the contrary, is at great pains deliberately to throw away the evidence of perception which is peculiar to it, and always at hand, that it may substitute for it a logical demonstration. This must seem to us ^ Of. Oh. 12 of Supplement,

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