Part III, Chapter 10: A General Principle by which we may judge of the Excellence or Defect of any Syllogism
WE have seen how we may judge whether complex arguments are conclusive or vicious, by reducing them to the form of more common reasonings, in order, then, to judge of them by the common rules. But as it does not appear that our minds need this reduction in order to make this judgment, we were led to think that there must be rules more general on which these common ones themselves were founded, by which we might recognise more easily the excellencies or defects of all kinds of syllogisms, and the following is what has occurred to us in relation to this matter. When we wish to prove a proposition, the truth of which is not evident, it appears that all we have to do is to find a proposition, better known, which confirms the other, which, for this reason, may be called the proposition containing. But since it cannot contain it expressly in the same terms, because, if it did, it would not differ from the other, and thus be of no service in making it clearer, it is necessary there should be yet another proposition which may show that which we called containing, does, in reality, contain what we wish to prove, and this one may be called applicative.
In affirmative syllogisms, it is often indifferent which of the two is called containing, since they both in some sort, contain the conclusion, and each serves to show that the other contains it.
For example, if I doubt whether a vicious man is unhappy, and reason thus —
Every one who is the slave of his passions is unhappy;
Every vicious man is the slave of his passions;
Therefore every vicious man is unhappy.
Whichever proposition you take, you may say that it contains the conclusion, and that the other shows it; for the major contains it, since slave of his passions contains under it vicious, that is to say, that vicious is contained under its extension, and is one of its subjects, as the minor shows; and the minor contains it also, since slave of his passions, comprehends in its idea that of unhappy, as the major shows.
Nevertheless, as the major is almost always the more general, it is commonly regarded as the proposition containing, and the minor as the proposition applicative.
In relation to negative syllogisms, as there is only one negative proposition, and as the negation is properly contained in the negation alone, it appears that we ought always to take the negative proposition as the containing, and the affirmative as the applicative exclusively, whether the negative be the major, as in Celarent, Ferio, Cesare, Festino, or whether it be the minor, as in Camestres and Baroco.
For if I prove by this argument that no miser is happy: Every happy man is content; No miser is content; Therefore no miser is happy;
it is more natural to say, that the minor, which is negative, contains the conclusion, which is also negative, and that the major serves the purpose of showing that it contains it. For this minor, no miser is content, separating, totally miser from content, separates from it also happy, since, according to the major, happy is contained in the whole extension of content.
It is not difficult to prove that all the rules which we have given serve only to show that the conclusion is contained in one of the first propositions, and that the other shows this; and that arguments are vicious only when we fail to observe this; that they are always good when it is observed, for all these rules may be reduced to two principles, which are the foundations of the others: one, that no term can be more general in the conclusion than in the premises. Now this clearly depends on the general principle that the premises ought to obtain the conclusion, which could not be, if the same term, being in the premises and in the conclusion, had less extension in the premises than in the conclusion, for the less general does not contain the more general,—some man does not contain all men.
The other general rule is, that the middle term ought to be taken at least once universally, which depends again on this principle, that the conclusion ought to be contained in the premises. For, supposing we wished to prove that some friend of God is poor, and were to employ, for this purpose, this proposition, some saint is poor, I say that we shall never be able clearly to see that this proposition contains the conclusion, except by another proposition in which the middle term, which is saint, is taken universally, for it is clear that in order that this proposition, some saints are poor, may contain the conclusion, some friend of God is poor, it is both necessary and sufficient that the term some saint, contain the term, some friend of God, since, in relation to the other, they have it in common. Now, a particular term is of no determinate extent, and it contains certainly only that which is involved in its comprehension and idea.
And consequently, in order that the term, some saint, may contain the term, some friend of God, it is necessary that friend of God be contained in the comprehension of the idea of saint.
Now, all that is contained in the comprehension of an idea, may be universally affirmed of it: all that is contained in the comprehension of the idea of triangle may be affirmed of every triangle; all that is contained in the idea man, may be affirmed of every man; and consequently, in order that friend of God, may be contained in the idea of saint, it is necessary that every saint be the friend of God, whence it follows that this conclusion, some friend of God is poor, can be contained in this proposition, some saint is poor (where the middle term, saint, is taken particularly), only in virtue of a proposition in which it is taken universally, since it must be shown that friend of God is contained in the comprehension of the idea saint, which can only be shown by affirming saint of God. Taken universally,—every saint is a friend of God, and consequently none of the premises will contain the conclusion, when the middle term is taken particularly in one of the propositions, unless it be taken universally in the other.—Q. E. D.