Part III, Chapter 11: Application of this General Principle to many Syllogisms which appeared to be involved
KNOWING, therefore, by what has been already said in the Second Part, what is meant by the comprehension and extension of terms, by which we may determine when one proposition contains, or does not contain another, we may judge of the excellency or defect of every syllogism without considering whether it is simple or compound, complex or incomplex, without paying any attention to figures or moods, exclusively by this general principle, That one of the two propositions must contain the conclusion, and the other show that it contains it. This will be better understood by some examples.
I am in doubt whether this reasoning be good, —
The duty of a Christian is not to praise those who commit criminal actions;
Now those who engage in a duel commit a criminal action; Therefore it is the duty of a Christian not to praise those who engage in duels.
Now, I need not trouble myself as to the figure or mood to which this may be reduced. It is sufficient for me to consider whether the conclusion is contained in one of the two first propositions, and if the other shows it, and I find at once that the first having nothing different from the conclusion, except that in the one, those who commit criminal actions, and in the other, those who engage in duels, that in which there is commit criminal actions, will contain that in which there is engage in a duel, provided that committing criminal actions contains engaging in duels.
Now it is clear by the sense that the term those who commit criminal actions, is taken universally, and that it extends to all those who commit any such actions whatever; and thus the minor, those who engage in a duel commit a criminal action, showing that to engage in a duel is contained under this term, commit criminal actions, shows also that the first proposition contains the conclusion.
I doubt whether this reasoning be good,—The gospel promises salvation to Christians; Some wicked men are Christians; Therefore the gospel promises salvation to wicked men. In order to determine this, I need only consider that the major cannot contain the conclusion unless the word Christians be taken generally for all Christians, and not for some Christians only. For if the gospel promises salvation only to some Christians, it does not follow that it promises it to wicked men, who may be Christians, since these wicked men may not be among the number of those Christians to whom the gospel promises salvation. Hence this reasoning is sufficiently conclusive (but the major is false), if the word Christians be taken in the major for all Christians, and it is not conclusive if it be taken for some Christians only, for then the first proposition will not contain the conclusion.
But in order to determine whether it was taken universally, we must judge it by another rule, which is given in the Second Part, viz., Except in relation to facts, that of which we affirm is taken universally when it is expressed indefinitely. Now, although those who commit criminal actions, in the first example, and Christians, in the second, form part of an attribute, they nevertheless take the place of subject in relation to another part of the same attribute. For it is of them that we affirm, in the one case, that we ought not to praise them, and in the other, that salvation is promised to them. And, consequently, not being restricted, they ought to be taken universally, and thus both arguments are good in form; but the major of the second is false, unless we understand by the word Christian, those who live conformably to the gospel, in which case the minor will be false, since there are no wicked men who live conformably to the gospel.
It is easy to see, by the same principle, that this reasoning is worth nothing, —
The divine law commands us to obey secular magistrates;
Bishops are not secular magistrates;
Therefore the divine law does not command us to obey bishops.
For neither of the first propositions is contained in the conclusion, since it does not follow that because the divine law does not command one thing it has not commanded another; and thus the minor shows well enough that bishops are not comprised under the term secular magistrates, and that the commandment to honour secular magistrates does not include bishops. But the major does not say that God has made no other commandments besides this, as it ought to do in order to guarantee the conclusion in virtue of this minor. This is the case in the following argument, and renders it valid: —
Christianity obliges servants to obey their masters in those things only which are not contrary to the law of God;
Now, unlawful traffic is contrary to the law of God;
Therefore Christianity does not oblige servants to obey their masters in an unlawful business.
For the major contains the conclusion, since the minor, unlawful traffic, is comprised in the number of things which are contrary to the law of God, and the major being exclusive, it is as though we said, The divine law does not oblige servants to obey their masters in anything that is contrary to the law of God.
We may, by this same principle, easily refute the following common sophism: —
He who says that you are an animal speaks truly;
He who says that you are a goose, says that you are an animal; Therefore he who says that you are a goose speaks truly.
For it is enough to say that neither of the two first propositions contain the conclusion; for if the major contained it (differing from the conclusion only in this, that there is animal in the major, and goose in the conclusion), animal must contain goose; but animal is taken particularly in this major, since it is the attribute of this affirmative incidental proposition, you are an animal, and consequently, it could contain goose only in its comprehension: to show which, the word animal must be taken universally in the minor by affirming goose of every animal, which cannot be done, and is not either, since animal is again taken particularly in the minor, being there, as well as in the major, the attribute of this incidental proposition, you are an animal.
By this, too, we may refute that ancient sophism referred to by St Augustine: —
You are not what I am;
I am a man;
Therefore you are not a man.
This argument is unsound by the rules of the figures—since it is of the first,—and the first proposition, which is its minor, is negative. But it is enough to say that the conclusion is not contained in the first of these propositions, and the other proposition, I am a man, does not show that it is contained in it. For the conclusion being negative, the term man is there taken universally, and thus is not contained in the term what I am, since he who speaks is not every man, but only some man, as appears from his saying, in the applicative proposition, I am a man, in which the term man is restricted to a partial signification, since it is the attribute of an affirmative proposition; now the general is not contained in the particular.