observes (‘Prior Anal.’ II. xxiii.) that “induction, or the syllogism that arises from it, consists in proving the major term of the middle by means of the minor.” In other words, suppose that we are proving that animals without a gall are long-lived, we do so through our knowledge that man, the horse, and the mule have no gall. Now, in a natural deductive syllogism, we should say—
Man, the horse, and the mule, have no gall;
Therefore they are long-lived.
“Long-lived” is here the major term; but in the inductive process we prove it of the middle term, “animals without a gall,” by means of the minor term, “man, the horse, and the mule.” So we require to state the inductive syllogism thus:—
Man, the horse, and the mule are animals without a gall;
Therefore (all) animals without a gall are long-lived.
Aristotle adds that, for the validity of this reasoning, you require to have an intuition in your reason that “man, the horse, and the mule” are, or adequately represent, the whole class of animals without a gall. This is, in fact, the crucial question in the inductive process—Do the instances you have got adequately represent the whole class of similar instances, so as to give you the key to a law of nature? For instance, if it is found that in two or three cases a particular treatment cures the cholera, how can you tell whether the induction is adequate, and that you are justified
