facts certified by observation, to facts which we have not observed, and even to facts not capable of being now observed; future facts, for example; but which we do not hesitate to believe on the sole evidence of the induction itself.
Induction, then, is a real process of Reasoning or Inference. Whether, and in what sense, as much can be said of the Syllogism, remains to be determined by the examination into which we are about to enter.
Chapter II.
Of Ratiocination, Or Syllogism.
§ 1. The analysis of the Syllogism has been so accurately and fully performed in the common manuals of Logic, that in the present work, which is not designed as a manual, it is sufficient to recapitulate, memoriæ causâ, the leading results of that analysis, as a foundation for the remarks to be afterward made on the functions of the Syllogism, and the place which it holds in science.
To a legitimate syllogism it is essential that there should be three, and no more than three, propositions, namely, the conclusion, or proposition to be proved, and two other propositions which together prove it, and which are called the premises. It is essential that there should be three, and no more than three, terms, namely, the subject and predicate of the conclusion, and another called the middle term, which must be found in both premises, since it is by means of it that the other two terms are to be connected together. The predicate of the conclusion is called the major term of the syllogism; the subject of the conclusion is called the minor term. As there can be but three terms, the major and minor terms must each be found in one, and only one, of the premises, together with the middle term which is in them both. The premise which contains the middle term and the major term is called the major premise; that which contains the middle term and the minor term is called the minor premise.
Syllogisms are divided by some logicians into three figures, by others into four, according to the position of the middle term, which may either be the subject in both premises, the predicate in both, or the subject in one and the predicate in the other. The most common case is that in which [pg 127] the middle term is the subject of the major premise and the predicate of the minor. This is reckoned as the first figure. When the middle term is the predicate in both premises, the syllogism belongs to the second figure; when it is the subject in both, to the third. In the fourth figure the middle term is the subject of the minor premise and the predicate of the major. Those writers who reckon no more than three figures, include this case in the first.
Each figure is divided into moods, according to what are called the quantity and quality of the propositions, that is, according as they are universal or particular, affirmative or negative. The following are examples of all the legitimate moods, that is, all those in which the conclusion correctly follows from the premises. A is the minor term, C the major, B the middle term.
First Figure.
| All B is C | No B is C | All B is C | No B is C |
| All A is B | All A is B | Some A is B | Some A is B |
| therefore | therefore | therefore | therefore |
| All A is C | No A is C | Some A is C | Some A is not C |
Second Figure.
| No C is B | All C is B | No C is B | All C is B |
| All A is B | No A is B | Some A is B | Some A is not B |
| therefore | therefore | therefore | therefore |
| No A is C | No A is C | Some A is not C | Some A is not C |
Third Figure.
| All B is C | No B is C | Some B is C | All B is C | Some B is not C | No B is C |
| All B is A | All B is A | All B is A | Some B is A | All B is A | Some B is A |
| therefore | therefore | therefore | therefore | therefore | therefore |
| Some A is C | Some A is not C | Some A is C | Some A is C | Some A is not C | Some A is not C |
Fourth Figure.
| All C is B | All C is B | Some C is B | No C is B | No C is B |
| All B is A | No B is A | All B is A | All B is A | Some B is A |
| therefore | therefore | therefore | therefore | therefore |
| Some A is C | Some A is not C | Some A is C | Some A is not C | Some A is not C |
In these exemplars, or blank forms for making syllogisms, no place is assigned to singular propositions; not, of course, because such propositions are not used in ratiocination, but because, their predicate being affirmed or denied of the whole of the subject, they are ranked, for the purposes of the syllogism, with universal propositions. Thus, these two syllogisms—
| All men are mortal, | All men are mortal, |
| All kings are men, | Socrates is a man, |
| therefore | therefore |
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