Part III, Chapter 6: Rules, Moods, and Principles of the Second Figure
THE second figure is that in which the middle term is taken twice as attribute; whence it follows, that, in order to its concluding necessarily, it must observe these two rules,—RULE 1.
One of the two propositions must be negative, and, consequently, the conclusion also, by the sixth general rule;
For, if both propositions were affirmative, the middle, which is here always attribute, would be taken twice particularly, contrary to the first general rule.
Rule 2
The major proposition must be universal;
For, the conclusion being negative, the greater term, or attribute, is taken universally. Now, this same term is subject in the major; therefore it must be universal, and, consequently, render the major universal.
That there can be only four moods in the second figure.
Of the ten valid moods the four affirmative are excluded by the first rule of this figure, which is, that one of the premises must be negative.
O, A, O, is excluded by the second rule, which is, that the major must be universal.
E, A, O, is excluded for the same reason as in the first figure; for the lesser term is also subject in the minor.
There remain, therefore, of these ten moods, only these four —
Two general: E, A, E and A, E, E. Two particular: E, I, O and A, O, O.
Which was to be demonstrated.
These four moods have been comprehended under the following artificial words: —
CE- No liar is to be believed; SA- Every good man is to be believed; RE. Therefore no good man is a liar. CA- All those who are followers of Jesus Christ crucify the flesh; MES- All those who lead an effeminate and voluptuous life do not crucify the flesh; TRES. Therefore none such are followers of Jesus Christ.
FES- No virtue is contrary to the love of truth;
TI- There is a love of peace which is opposed to a love of truth;
NO. Therefore there is a love of peace which is not a virtue.
BA- Every virtue is accompanied with discretion.
RO- There is a zeal without discretion;
CO. Therefore there is a zeal which is not a virtue.
It would be easy to reduce all these different sorts of reasonings to a single principle, by a little explanation; but it is more beneficial to reduce two of them to one principle, and two to another, since their dependence on these two principles, and the connection they have with them, is more clear and immediate.
1. PRINCIPLES OF THE ARGUMENTS IN Cesare AND Festino.
The first of these principles is that which serves also as a basis for the negative arguments of the first figure, to wit, that which is denied of a universal idea is denied also of everything of which that idea is affirmed, that is to say, of all the subjects of that idea; for it is clear that the arguments in Cesare and Festino are established on this principle. In order to show, for example, that no good man is a liar, I affirmed, to be believed of every good man, and I denied liar of every man who was to be believed, by saying that no liar is to be believed. It is true that this aspect of denying is indirect, since, in place of denying liar to be believed, I denied to be believed of liar. But, as universal negative propositions are converted simply by denying the attribute of a universal subject, we deny that universal subject of the attribute.
This shows, notwithstanding, that the reasonings in Cesare are, in some sort, indirect, since that which is denied of them is only denied indirectly; but as this does not prevent the mind from comprehending, easily and clearly, the force of the argument, they may be considered as direct, understanding by this term reasonings, clear and natural. This also shows that the two moods, Cesare and Festino, differ from Celarent and Ferio of the first, only in having their major reversed. But though we may say that the negative moods of the first figure are more direct, it often happens, nevertheless, that these two of the second figure, which answer to them, are more natural, and that the mind more readily employs them. For example, in that which we have given, although the direct order of negation require us to say, No man is to be believed who is a liar, which would have made an argument in Celarent, the mind is, nevertheless, naturally led to say, No liar is to be believed.
PRINCIPLES OF THE ARGUMENTS IN Camestres AND Baroco.
In these two moods the middle term is affirmed of the attribute of the conclusion, and denied of the subject, which shows that they are established directly on this principle: Nothing that is comprehended under the extension of a universal idea belongs to any of the subjects of which that idea is denied, the attribute of a negative proposition being taken in the whole of its extension, as we have proved in the Second Part.
True Christians are comprehended under the extension of charitable, since every true Christian is charitable; charitable is denied of those who are pitiless towards the poor; therefore true Christian of those who are without mercy towards the poor;—which makes this argument
Every true Christian is charitable;
None who are without pity for the poor are charitable;
Therefore none who are without pity to the poor are true Christians.