Appendix edit
Chapter XXIII: On Induction edit
- Induction is one of the two roads to certainty. It infers the major of the middle by means of the minor term, which last must include all the individual instances of the quality denoted by the major. Induction is clearer for us, though syllogism is naturally prior and more knowable.
. . . . . . We believe in a thing as a result either of syllogism or of induction. Now induction and the inductive syllogism consist in inferring one term of the middle by means of the other (minor) term. E.g. Suppose B to be the middle term between A and C, induction proves by means of C that A is B, for that is the way we express induction. Thus let A represent ‘long-lived,’ B ‘not having gall,’ C ‘individual instances of longevity, such as Man, Horse, Mule.’ Now all B is A, for every creature without gall is long-lived; also B, not having gall, belongs to every C. If then C be convertible with B, and not more comprehensive than the middle term, A must be B. For we have shewn before that if any two qualities are predicable of the same term, and if the major term be convertible with one of them, then one of the qualities predicated will be true of the convertible term. One ought to look at C as a combination of the whole number of particular instances, for induction is based on completeness. Now inductive syllogism requires a primary and ultimate premise, for when a middle term exists, the syllogism makes use of that, when it does not, it proceeds by induction. Induction is in a manner opposed to syllogism, as the latter proves the major term of the minor by means of the middle, the former proves the major of the middle by means of the minor. Hence the syllogism which makes the middle term the instrument of proof is naturally prior and more knowable, but for us that which uses induction is clearer.
Chapter XXIV: On Example edit
- Example consists in the demonstration that the major is true of the middle term by the help of a fourth term or number of terms resembling the minor. Example bears the relation of part to part, thus differing from syllogism, while it differs from induction in using only a few instances or even one, instead of the entire number of individuals included under the common designation or term.
Example is the method used when the major term is proved true of the middle by a means of a term resembling the minor. It must already be known that the middle is true of the minor and the major of the term resembling the minor. For instance, let A be ‘a bad thing’; B ‘to make war on neighbours’; C ‘War of Athenians against Thebans’; D ‘War of Thebans against Phocians.’ If then we wish to prove that it is a bad thing [for the Athenians] to enter on war with the Thebans, we must make use of the proposition ‘It is a bad thing to make war on neighbours.’ This is supported by similar instances; e.g. by the war of the Thebans against the Phocians. Since then fighting against one’s neighbours is a bad thing, and fighting against the Thebans is fighting against neighbours, it is clearly a bad thing to fight against the Thebans.
It is plain that B is true both of C and D, for both are cases of making war on neighbours, and it is likewise clear that A is true of D, for the war against the Phocians was not favourable to the Thebans. That A is true of B will be proved by means of the term D.
The same method is applicable if several similar examples be employed to prove the major term of the middle.
It is clear then that the Example has neither the relation of part to whole nor of whole to part, but of part to part; that is to say both terms are included under the same common term, but only one of them is already known. It differs from induction, in that induction proves, by a survey of all the individual instances, that the major is true of the middle, not that it is true of the minor, while example does prove the major true of the minor, and does not make use of all the individual instances, but only of some or one.