Page:The World as Will and Idea - Schopenhauer, tr. Haldane and Kemp - Volume 2.djvu/318

308 of the things and relations, any single essential point has been overlooked, the correctness of all the succeeding operations of the mind cannot prevent the result from being false; for there lie the data, the material of the whole investigation. Without the certainty that these are correctly and completely collected, one ought to abstain, in important matters, from any definite decision.

A conception is correct; a judgment is true; a body is real; and a relation is evident. A proposition of immediate certainty is an axiom. Only the fundamental principles of logic, and those of mathematics drawn a priori from intuition or perception, and finally also the law of causality, have immediate certainty. A proposition of indirect certainty is a maxim, and that by means of which it obtains its certainty is the proof. If immediate certainty is attributed to a proposition which has no such certainty, this is a petitio principii. A proposition which appeals directly to the empirical perception is an assertion: to confront it with such perception demands judgment. Empirical perception can primarily afford us only particular, not universal truths. Through manifold repetition and confirmation such truths indeed obtain a certain universality also, but it is only comparative and precarious, because it is still always open to attack. But if a proposition has absolute universality, the perception to which it appeals is not empirical but a priori. Thus Logic and Mathematics alone are absolutely certain sciences; but they really teach us only what we already knew beforehand. For they are merely explanations of that of which we are conscious a priori, the forms of our own knowledge, the one being concerned with the forms of thinking, the other with those of perceiving. Therefore we spin them entirely out of ourselves. All other scientific knowledge is empirical.

A proof proves too much if it extends to things or cases of which that which is to be proved clearly does not hold good; therefore it is refuted apagogically by these. The