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

The eirayoyyr], inductio, is with Aristotle the opposite of the airarfdrfrj. The latter proves a proposition to bt false by showing that what would follow from it is not true ; thus by the instantia in contrarium. The eTrwyar/t) on the other hand, proves the truth of a proposition bj showing that what would follow from it is true. Thus i leads by means of examples to our accepting something while the aira^tarp) leads to our rejecting it Therefor the ejrcvyaK/T), or induction, is an inference from the con sequents to the reason, and indeed modo ponente ; for fror many cases it establishes the rule, from which these case then in their turn follow. On this account it is neve perfectly certain, but at the most arrives at very gres probability. However, this formal uncertainty may yc leave room for material certainty through the number ( the sequences observed ; in the same way as in niathc matics the irrational relations are brought infinite! near to rationality by means of decimal fractions. Ti aira<yQ>yr}> on the contrary, is primarily an inference fro: the reason to the consequents, though it is afterwan carried out modo tollente, in that it proves the no: existence of a necessary consequent, and thereby destro;

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the truth of the assumed reason. On this account it is always perfectly certain, and accomplishes more by a single example in contrarium than the induction does by innumerable examples in favour of the proposition propounded. So much easier is it to refute than to prove, to jverthrow than to establish.

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CHAPTER X.

ON THE SYLLOGISM.

Although it is very hard to establish a new and correc view of a subject which for more than two thousam years has been handled by innumerable writers, ant which, moreover, does not receive additions through th growth of experience, yet this must not deter me fror presenting to the thinker for examination the followin attempt of this kind.

An inference is that operation of our reason by virtue ( which, through the comparison of two judgments a thii judgment arises, without the assistance of any knowled^ otherwise obtained. The condition of this is that the. two judgments have one conception in common, for othe wise they are foreign to each other and have no cor munity. But under this condition they become the fath and mother of a child that contains in itself something both. Moreover, this operation is no arbitrary act, b an act of the reason, which, when it has considered su judgments, performs it of itself according to its own la^ So far it is objective, not subjective, and therefore subj( to the strictest rules.

We may ask in passing whether he who draws an infl ence really learns something new from the new pro] sition, something previously unknown to him ? absolutely ; but yet to a certain extent he does. W. he learns lay in what he knew : thus he knew it also, 1 ■ he did not know that he knew it ; which is as if he 1 I something, but did not know that he had it, and thi * a tni »

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just the same as if he had it not. He knew it only implicite, now he knows it explicite ; but this distinction may be so great that the conclusion appears to him a new truth. For example :

All diamonds are stones ; All diamonds are combustible : Therefore some stones are combustible. The nature of inference consequently consists in this, that we bring it to distinct consciousness that we have already thought in the premisses what is asserted in the conelusion. It is therefore a means of becoming more distinctly conscious of one's own knowledge, of learning more fully, or becoming aware of what one knows.

The knowledge which is afforded by the conclusion was latent, ind therefore had just as little effect as latent heat has m the thermometer. Whoever has salt has also chlorine ; aut it is as if he had it not, for it can only act as chlorine f it is chemically evolved ; thus only, then, does he really Dossess it.

It is the same with the gain which a mere jonclusion from already known premisses affords : a previmsly bound or latent knowledge is thereby set free. These somparisons may indeed seem to be somewhat strained, but ret they really are not.

For because we draw many of the )ossible inferences from our knowledge very soon, very apidly, and without formality, and therefore have no disinct recollection of them, it seems to us as if no premisses or possible conclusions remained long stored up unused, >ut as if we already had also conclusions prepared for all he premisses within reach of our knowledge.

But this is ot always the case ; on the contrary, two premisses may ave for a long time an isolated existence in the same mind, ill at last some occasion brings them together, and then ae conclusion suddenly appears, as the spark comes from le steel and the stone only when they are struck together, n reality the premisses assumed from without, both for heoretical insight and for motives, which bring about reolves, often lie for a long time in us, and become, partly