[12] Aristotle in his logical analysis of Induction, Prior. Analytics II. 25, defines it to be “the proving the inherence of the major term in the middle (_i.e._ proving the truth of the major premiss in fig. 1) through the minor term.” He presupposes a Syllogism in the first Figure with an universal affirmative conclusion, which reasons, of course, from an universal, which universal is to be taken as proved by Induction. His doctrine turns upon a canon which he there quotes. “If of one and the same term two others be predicated, one of which is coextensive with that one and the same, the other may be predicated of that which is thus coextensive.” The fact of this coextensiveness must be ascertained by [Greek: nous], in other words, by the Inductive Faculty. We will take Aldrich’s instance. All Magnets attract iron A B C are Magnets A B C attract iron. Presupposed Syllogism reasoning from an universal. A B C attract iron (Matter of observation and experiment) All Magnets are A B C (Assumed by [Greek: nous], i.e. the Inductive faculty) All Magnets attract iron (Major premiss of the last Syllogism proved by taking the minor term of that for the middle term of this.) Or, according to the canon quoted above: A B C are Magnets. A B C attract iron. But [Greek: nous] tells me that the term Magnets is coextensive with the term A B C, therefore of all Magnets I may predicate that they attract iron. Induction is said by Aristotle to be [Greek: hoia phanton], but he says in the same place that for this reason we must _conceive_ ([Greek: noehin]) the term containing the particular Instances (as A B C above) as composed of all the Individuals. If Induction implied actual examination of all particular instances it would cease to be Reasoning at all and sink into repeated acts of Simple Apprehension it is really the bridging over of a chasm, not the steps cut in the rock on either side to enable us to walk down into and again out of it. It is a branch of probable Reasoning, and its validity depends _entirely_ upon the quality of the particular mind which performs it. Rapid Induction has always been a distinguishing mark of Genius the certainty produced by it is Subjective and not Objective. It may be useful to exhibit it Syllogistically, but the Syllogism which exhibits it is either nugatory, or contains a premiss _literally_ false. It will be found useful to compare on the subject of Induction _as the term is used by Aristotle_, Analytica Prior. II 25 26 Analytica Post. I. 1, 3, and I. Topics VI I and X.