Page:The World as Will and Idea - Schopenhauer, tr. Haldane and Kemp - Volume 2.djvu/300

290 falseness of the first depends upon the falseness of the second; thus that these two propositions stand in direct community as regards truth and falseness. The disjunctive judgment, on the other hand, asserts that upon the truth of one of the categorical judgments here linked together depends the falseness of the others, and conversely; thus that these propositions are in conflict as regards truth and falseness. The question is a judgment, one of whose three parts is left open: thus either the copula, "Is Caius a Roman – or not?" or the predicate, "Is Caius a Roman – or something else?" or the subject, "Is Caius a Roman – or is it some one else who is a Roman?" The place of the conception which is left open may also remain quite empty; for example, "What is Caius?" – "Who is a Roman?"

The, inductio, is with Aristotle the opposite of the. The latter proves a proposition to be false by showing that what would follow from it is not true; thus by the instantia in contrarium. The, on the other hand, proves the truth of a proposition by showing that what would follow from it is true. Thus it leads by means of examples to our accepting something while the leads to our rejecting it. Therefore the, or induction, is an inference from the consequents to the reason, and indeed modo ponente; for from many cases it establishes the rule, from which these cases then in their turn follow. On this account it is never perfectly certain, but at the most arrives at very great probability. However, this formal uncertainty may yet leave room for material certainty through the number of the sequences observed; in the same way as in mathematics the irrational relations are brought infinitely near to rationality by means of decimal fractions. The, on the contrary, is primarily an inference from the reason to the consequents, though it is afterwards carried out modo tollente, in that it proves the non-existence of a necessary consequent, and thereby destroys