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

A conception is correct ; a judgment is true.; a body if real ; and a relation is evident. A proposition of immediate certainty is an axiom. Only the fundamental principle of logic, and those of mathematics drawn a priori from in tuition or perception, and finally also the law of causality have immediate certainty. A proposition of indirec certainty is a maxim, and that by means of which i obtains its certainty is the proof. If immediate certaint is attributed to a proposition which has no such certaint} this is a petitio principii. A proposition which appea directly to the empirical perception is an assertion: t confront it with such perception demands judgmeD Empirical perception can primarily afford us only pa ticular, not universal truths. Through manifold repetitic and confirmation such truths indeed obtain a certain ur versality also, but it is only comparative and prec rious, because it is still always open to attack. But if proposition has absolute universality, the perception which it appeals is not empirical but a priori. Th Logic and Mathematics alone are absolutely certs sciences ; but they really teach us only what we alrea knew beforehand. For they are merely explanations that of which we are conscious a priori, the forms of c own knowledge, the one being concerned with the for of thinking, the other with those of perceiving. Theref we spin them entirely out of ourselves. All other sci tific knowledge is empirical.

A proof proves too much if it extends to things or cf J of which that which is to be proved clearly does not 1 J good j therefore it is refuted apagogically by these.

p. 309

deductio ad absurdum properly consists in this, that we take a false assertion which has been made as the major proposition of a syllogism, then add to it a correct minor, and arrive at a conclusion which clearly contradicts facts of experience or unquestionable truths. But by some round-about way such a refutation must be possible of svery false doctrine. For the defender of this will yet 3ertainly recognise and admit some truth or other, and :hen the consequences of this, and on the other hand ;hose of the false assertion, must be followed out until ye arrive at two propositions which directly contradict jach other. We find many examples in Plato of this )eautiful artifice of genuine dialectic.

A correct hypothesis is nothing more than the true and jomplete expression of the present fact, which the origilator of the hypothesis has intuitively apprehended in ts real nature and inner connection. For it tells us only vhat really takes place here.

The opposition of the analytical and synthetical methods ve find already indicated by Aristotle, yet perhaps first istinctly described by Proclus, who says quite correctly : MeOohoi 8e irapaBiBovrac' KaWiarrj fiev f) Sta T17? ava- .uo-ea>? eir' ap^rjv ofxoXoyovfievrjv avayovaa to t^qrovfievov • v Kai IIXaTcov, to? <pa<ri, AaoSafxavTi irapeBcoKev. k. t. X." Methodi traduntur sequentes : pulcherrima quidem ea, quce er analysin qucesitum refert ad principium, de quo jam mvenit ; quam, etiam Plato Laodamanti tradidisse dicitur.) In Primum Euclidis Librum" L. iii. Certainly the anameal method consists in referring what is given to an imitted principle ; the synthetical method, on the con- ■ary, in deduction from such a principle. They are there- >re analogous to the eTrar/ayyr) and a7rajy(oyr) explained 1 chapter ix. ; only the latter are not used to establish repositions, but always to overthrow them. The analyeal method proceeds from the facts ; the particular, to the inciple or rule ; the universal, or from the consequents the reasons ; the other conversely. Therefore it would

3io FIRST BOOK. CHAPTER XII.

be much more correct to call them the inductive and the deductive methods, for the customary names are unsuitable and do not fully express the things.