| All Magnets attract iron | Presupposed Syllogism reasoning from an universal.
| |
| A B C are Magnets | ||
| A B C attract iron. | ||
| A B C attract iron | (Matter of observation and experiment) | |
| All Magnets are A B C | (Assumed by νοῦς, 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 νοῦς 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 διὰ πάντων but he says in the same place that for this reason we must conceive (νοεῖν) 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 premise 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.
P. 133, l. 32. The reference is made to the Post Analyt. I. II. and it is impossible to understand the account of ἐπιστήμη without a perusal of the chapter; the additions to the definition referred to relate to the nature of the premisses from which ἐπιστήμη draws its conclusions: they are to be “true, first principles, incapable of any syllogistic proof, better known than the conclusion, prior to it, and causes or it.” (See the appendix to this Book.)
P. 134, l. 12. This is the test of correct logical division, that the membra dividentia shall be opposed, i.e. not included the one by the other.
