Part III, Chapter 7: Rules, Moods, and Principles of the Third Figure
IN the third figure the middle term is twice taken as subject, whence it follows:—RULE 1.
That the minor proposition must be affirmative;
This we have already proved by the first rule of the first figure, since in both the attribute of the conclusion is also the attribute of the major.
The conclusion must be particular.
For the minor being always affirmative, the lesser term, which is its attribute, is particular. Therefore, it cannot be universal in the conclusion, where it is subject, since this would be to infer the general from the particular, contrary to the second general rule.
That there can be no more than six moods in the third figure.
Of the ten valid moods, A, E, E, and A, O, O, are excluded by the first rule of this figure, which is, that the minor be not negative.
A, A, A, and E, A, E, are excluded by the second rule, which is, that the conclusion cannot be general. There remain, therefore, these six moods:
3 affirmative: A, A, I; I, A, I; A, I, I. 3 negative: E, A, O; O, A, O; E, I, O.
Which was to be demonstrated.
These six moods have been reduced to the following artificial words, though in a different order: —
DA- The infinite divisibility of matter is incomprehensible; RA- The infinite divisibility of matter is most certain; PTI. Therefore there are, therefore, some things most certain which are incomprehensible.
FE- No man is able to abandon himself; LA- Every man is an enemy to himself; PTON. There are, therefore, some enemies which he cannot abandon.
Di- There are some wicked men in the highest state;
SA- All wicked men are miserable;
MIS. Therefore, there are some miserable who are in the highest state.
DA- Every servant of God is a king;
TI- Some servants of God are poor;
SI. Therefore some poor are kings.
Bo- There is some anger which is not blameworthy;
CAR- Every kind of anger is a passion;
DO. Therefore some passions are not blameworthy.
FE- No folly is eloquent;
RI- There is some folly put into figures;
SON. Therefore there are figures which are not eloquent.
The two terms of the conclusion being attributed, in the premises, to a single term, which serves as the middle, we may reduce the affirmative moods to this figure to the following principle: —
When two terms may be affirmed of the same thing, they may also be affirmed taken particularly.
For, being united together in that thing, since they belong to it, it follows that they are sometimes united together, so that they may be affirmed the one of the other particularly. But in order that we may be sure that these terms have been affirmed of the same thing, which is the middle term, it is necessary that this middle term be taken once universally at least; for if it were taken twice particularly, they might be two different parts of a common term, which would not be the same thing.
When of two terms one may be denied, and the other affirmed, of the same thing, they may be denied particularly of each other.
For it is certain they are not always joined together, since they are not joined in this thing; therefore we may sometimes deny them of each other, that is to say, we may deny them of each other, taken particularly. But it is necessary, for the same reason, in order to its being the same thing, that the middle term be taken universally once at least.