Practically in inductive argument an opponent is worsted when he cannot produce an instance to the contrary. Suppose he admits the predicate in question to be true of this, that and the other, but denies that this, that and the other constitute the whole class in question, he is defeated in common judgement if he cannot instance a member of the class about which the predicate does not hold. Hence this mode of induction became technically known as Inductio per enumerationem simplicem ubi non reperitur instantia contradictoria. When this phrase is applied to a generalisation of fact, Nature or Experience is put figuratively in the position of a Respondent unable to contradict the inquirer.
Such in plain language is the whole doctrine of Inductive Argument. Aristotle's Inductive Syllogism is, in effect, an expression of this simple doctrine tortuously in terms of the Deductive Syllogism. The great master was so enamoured of his prime invention that he desired to impress its form upon everything: otherwise, there was no reason for expressing the process of Induction syllogistically. Here is his description of the Inductive Syllogism:—
"Induction, then, and the Inductive Syllogism, consists in syllogising one extreme with the middle through the other extreme. For example, if B is middle to A and C, to prove through C that A belongs to B."[1]
This may be interpreted as follows: Suppose a general proposition is in dispute, and that you wish to make it good by obtaining severally the admission of all the particulars that it sums up. The type of a general proposition in Syllogistic terminology is the Major Premiss, All M is P. What is the type of the particulars that it sums up? Obviously, the Conclusion, S is P. This particular is contained in the Major Premiss, All M is P; its truth is accepted as contained in the truth of All M is P. S is one of the parts of the generic whole M; one of the individuals or species contained in the class M. If you wish, then, to establish P of All M by Induction, you must establish P of all the parts, species, or individuals contained in M, that is, of all possible Ss: you must make good that this, that and the other S is P, and also that this, that and the other S constitute the whole of M. You are then entitled to conclude that All M is P: you have syllogised one Extreme with the Middle through the other Extreme. The formal statement of these premisses and conclusion is the Inductive Syllogism.
This, that and the other S is P, Major.
This, that and the other S is all M, Minor.
... All M is P, Conclusion.
This, that and the other magnet (i.e., magnets individually) attract iron.
This, that and the other magnet (i.e., the individuals separately admitted) are all magnets.
... All magnets attract iron.