The _hypothetical and disjunctive judgments_ are assertions as to the relation of two (in the case of the disjunctive judgment even several) categorical judgments to each other. The _hypothetical judgment_ asserts that the truth of the second of the two categorical judgments here linked together depends upon the truth of the first, and the 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 επαγωγη, inductio, is with Aristotle the opposite of the απαγωγη. 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 επαγωγη, 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 απαγωγη leads to our rejecting it. Therefore the επαγωγη, 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 απαγωγη, 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 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 overthrow than to establish. Chapter X. On The Syllogism.