Part III, Chapter 5: Rules, Moods, and Principles of the First Figure
THE first figure is, then, that in which the middle term is subject in the major proposition, and attribute in the minor.
This figure has only two rules.
Rule 1
The minor must be affirmative;
For, if it were negative, the major would be affirmative by the third general rule, and the conclusion negative by the fifth; therefore the greater term would be taken universally in the conclusion, since it would be negative, and particularly in the major; for it is its attribute in this figure, and would be affirmative, thus violating the second rule, which forbids us to conclude from the particular to the general. This reason holds also in the third figure, where the greater term is also attribute in the major.
Rule 2
The major must be universal;
For, the minor being affirmative, by the preceding rule, the middle term, which is its attribute, is taken particularly; therefore it must be universal in the major, where it is subject, which renders this proposition universal; otherwise it will be taken twice particularly, contrary to the first general rule.
That the first figure can have only four moods.
We have shown, in the preceding chapter, that there can be only ten valid moods; but of these ten moods, A, E, E, and A, O, O, are excluded by the first rule of this figure, viz., that the minor must be affirmative; I, A, I, and O, A, O, are excluded by the second, which is, the major must be universal; A, A, I, and E, A, O, are excluded by the fourth corollary from the general rules, for the lesser term being the subject in the minor, if it be universal, the conclusion may be universal also.
And, consequently, there remain only these four moods:
Two affirmative: A, A, A and A, I, I. Two negative: E, A, E and E, I, O.
Which was to be demonstrated.
These four moods, in order that they may be more easily retained, have been reduced to artificial words, of which the three syllables denote the three propositions, and the vowel of each syllable points out of what kind the proposition ought to be; so that these words have been of this great service in the schools, that they denote clearly, by a single word, a species of syllogism, which otherwise could not have been explained without much circumlocution:
BAR- Whoever suffers those whom he ought to support to die of hunger, is a murderer.
BA- All the rich who do not give alms in times of public necessity, suffer those to die of hunger whom they ought to support; RA. Therefore they are homicides.
CE- No impenitent thief can expect to be saved; LA- All those who die without making restitution, after having enriched themselves with the wealth of the church, are impenitent thieves; RENT. Therefore none such can expect to be saved. DA- Everything which is a help to salvation is beneficial. HI- There are some afflictions which are helps to salvation;
i. Therefore there are some afflictions which are beneficial. FE- Whatever is followed by a just repentance is not to be wished for; RI- There are some pleasures which are followed by a just repentance;
o. Therefore there are some pleasures which are not to be wished for.
Since in this figure the greater term is affirmed or denied of the middle, taken universally, and this same middle is then affirmed in the minor of the lesser term, or subject of the conclusion, it is clear that it is founded on two principles, one for the affirmative moods, the other for the negative moods.
That which belongs to an idea, taken universally, belongs also to everything of which that idea is affirmed, or which is subject of that idea, or which is comprehended under the extension of this idea; for these expressions are synonymous.
Thus the idea of animal belonging to all men, belongs also to all Ethiopians. This principle has been so clearly explained in the chapter where we treated of the nature of affirmative propositions, that it is not necessary to say more of it here. It is sufficient to state, that it is commonly expressed in the schools in the following manner:—Quod convenit consequenti, convenit antecedenti; and that, by the term consequent, is understood the general idea which is affirmed of another, and, by antecedent, the subject by which it is affirmed, since, in reality, the attribute is obtained, as a consequent from the subject,—if it be man, it is also animal.
Whatever is denied of an idea, taken universally, is denied also of everything of which that idea is affirmed.
Tree is denied of all animals; it is, therefore, denied of all men, since they are animals. It is commonly expressed in the schools, thus:—Quod negatur de consequenti, negatur de antecedenti. What we have said, in treating of negative propositions, renders it unnecessary to say more here.
It must be remarked, that it is only in the first figure that we obtain a conclusion in all the four—A, E, I, O.
And that it is in the first alone that we obtain a conclusion in the form of A; the reason of which is, that in order to make the conclusion a universal affirmative, the lesser term must be taken generally in the minor, and, consequently, be its subject, and the middle term its attribute; whence it happens that the middle is there taken particularly. It must, therefore, be taken generally in the major by the first general rule, and, consequently, be its subject. Now the characteristic of the first figure is, that the middle term be subject in the major proposition, and attribute in the minor.