Part III, Chapter 12: Of Conjunctive Syllogisms
ALL syllogisms are not conjunctive whose propositions are conjunctive or compound, but those only whose major is so compounded that it contains the whole of the conclusion. These may be reduced to three kinds—conditional, disjunctive and copulative.
Conditional syllogisms are those in which the major is a conditional proposition which contains all the conclusion: as, —
If there is a God, he ought to be loved; Now there is a God; Therefore he ought to be loved.
The major has two parts: first, the antecedent, if there be a God; second, the consequent, he ought to be loved.
This syllogism may be of two kinds, since from the same major we may form two conclusions.
The first is, when, having affirmed the consequent in the major, we affirm the antecedent in the minor, according to this rule—In positing the antecedent, we posit the consequent: —
If matter cannot move of itself, its first motion must have been given to it by God; Now matter cannot move of itself; Its first movement must therefore have been given to it by God.
The second kind is, when we take away the consequent, in order to take away the antecedent, according to this rule—In taking away the consequent, we take away the antecedent: —
If any of the elect perish, God is deceived; But God is not deceived; Therefore none of the elect perish.
This is the reasoning of St Augustine: Horum si quisquam perit, fallitur Deus; sed nemo eorum perit, quia non fallitur Deus.
Conditional arguments are vicious in two ways.
The one is, when the major is an irrational condition, of which the consequent is contrary to the rules: as if I conclude the general from the particular in saying, If we deceive ourselves in anything, we deceive ourselves in all things.
But this falsehood in the major of these syllogisms regards rather the matter than the form; thus we consider them as vicious in relation to the form, when the conclusion is wrongly deduced from the major, whether it be true or false, reasonable or unreasonable; which is done in two ways:
First, when we infer the antecedent from the consequent: as if we say —
If the Chinese are Mohammedans, they are infidels;
Now they are infidels;
Therefore they are Mohammedans.
The second kind of conditional arguments which are false, is when, from the negation of the antecedent, we infer the negation of the consequent: as in the same example, —
If the Chinese are Mohammedans, they are infidels; They are not Mohammedans; Therefore they are not infidels.
There are, however, some of these conditional arguments which appear to have this defect, which are, nevertheless very good, because there is an exclusion understood in the major, though not expressed. Example: Cicero having published a law against those who bought suffrages, and Murena being accused of buying them, Cicero pleaded for him, justifying himself from the reproach which Cato brought against him, of acting in this defence contrary to his own law, by this argument: Etenim si largitionem factam esse confiterer, idque recte factum esse defenderem, facerem improbe, etiam si alius legem tulisset; cum vero nihil commissum contra legem esse defendam, quid est quod meam defensionem latio legis impediat? This argument would seem to resemble that of a blasphemer, who should say in self-defence, If I denied there was a God, I should be a wicked man; but although I blaspheme, I do not deny there is a God; therefore I am not a wicked sinner. This argument proves nothing, because there are other crimes besides atheism, which render a man wicked; but that which makes Cicero’s good, although Ramus has given it as an example of a bad reasoning, is, that it contains in sense a particle exclusive, and may be reduced to these terms: —
I could only be reasonably reproached with acting contrary to my law, if I maintained that Murena bought the votes, and nevertheless justified his action; but I maintain that he did not buy the votes—consequently I do nothing opposed to my law.
The same may be said of this reasoning of Venus, in speaking to Jupiter in Virgil: —
Si sine pace tua, atque invito numine Troes
Italiam petiere, luant peccata, neque illos
Juveris auxilio: sin tot responsa secuti,
Quae superi manesque dabant: cur nunc tua quisquam
Flectere jussa potest? aut cur nova condere fata?
For this reasoning may be reduced to these terms:—If the Trojans have come into Italy contrary to the will of the gods, they are punishable;
But they have not come contrary to the will of the gods; Therefore they are not punishable.
It is therefore necessary to supply something, otherwise it will resemble the following, which certainly is not conclusive: —
If Judas entered into the apostleship without being called, he ought to have been rejected by God; But he did not enter without being called; Therefore he ought not to be rejected by God. But that which preserves the reasoning of Venus, in Virgil, from being vicious, is that we must consider the major as exclusive in meaning, as though it had been—The Trojans then alone would have been punishable, and unworthy the help of the gods, if they had come into Italy contrary to their will; Therefore, &c. Or we may say, which is the same thing, that the i. affirmative, si sine pace tua, &c., involved in it this negative: —
If the Trojans came into Italy only by the will of the gods, it is not just to reject them;
Now they did come by order of the gods alone;
Therefore, &c.
Those syllogisms are called disjunctive of which the first proposition is disjunctive, that is to say, whose parts are joined together by vel, or, as the following of Cicero:—Those who have slain Caesar are paricides, or defenders of liberty;
Now they are not paricides; Therefore they are defenders of liberty. There are two kinds of these,—the first when we take away one part in order to preserve the other, as in that which we have given, or the following: —
All wicked men must be punished, either in this world or in another; Now there are some wicked men who are not punished in this world;
Therefore they will be in another.
There are sometimes three members in this sort of syllogism, and then we take away two in order to keep one, as in this argument of St Augustine, in his Book on Lying (chap. 8): Aut non est credendum bonis, aut credendum est eis quos credimus debere aliquando mentiri, aut non est credendum bonis aliquando mentiri. Horum primum perniciosum est; secundum stultum; restat ergo, ut nunquam mentiantur boni.
The second, but less natural kind, is when we take one of the parts, in order to take away the other, as if we say: —
Saint Bernard, affirming that God had confirmed, by miracles, his preaching the crusade, was either a saint or an impostor; Now, he was a saint; Therefore he was not an impostor.
These disjunctive syllogisms are rarely false, except through the falsity of a major, through which the division is not exact, leaving a mean between the opposed members: as if I were to say —
We must either obey princes when they command those things which are contrary to the law of God, or rise against them; Now, we must not obey them when they command things contrary to the law of God; Therefore we must rise against them. Or, Now we must not rise up against them; Therefore we must obey them in that which is contrary to the law of God.
Both reasonings are false, because there is a mean in this disjunction, which was observed by the first Christians, who patiently suffered all things rather than do anything contrary to the law of God, without, however, rising in revolt against princes.
These false disjunctions are one of the most common sources of false reasonings among men.
These syllogisms are of one sort only, which is, when we take a copulative proposition, which denies, and then establish one part, in order to take away the other.
A man cannot be, at the same time, a servant of God and a worshipper of money; Now a miser is a worshipper of money; Therefore he is not a servant of God.
But such a syllogism does not conclude necessarily when we take away one part in order to posit the other, as may be seen by the following reasoning derived from the same propositions: —
A man cannot be, at the same time, a servant of God and a worshipper of money; Now, prodigals are not worshippers of money; Therefore they are servants of God.