Examples of all the Moods in the three last figures (except Baroko and Bokardo) converted to the corresponding figures

Reductio per impossible, or ad Absurdum.

This species of reduction, as already partially explained, consists in the hypothetical falsehood of that which is under discussion; and in the tracing of such a concession to its legitimate consequences, with the view of proving that what was hypothetically conceded as false, involves some palpable impossibility or absurdity.

This kind of reduction is usually confined to the moods Baroko of the second, and Bokardo of the third figure. It is equally applicable, however, to any of the three last figures, as will be shown by examples. But let us, in the first place, take Baroko and Bokardo.

In reference to Baroko and Bokardo, it is necessary to remark that the contradictory of the conclusion must be substituted for the particular negative premiss, while the universal premiss retains its original place. In other moods reducible in this way, the contradictory of the conclusion must be substituted for the major or minor premiss, as the requirements of a syllogism in the first figure may render such substitution necessary.

1. Baroko.

BA-All truly wise men live virtuously.

ROK-Some philosophers do not live virtuously; therefore, O.-Some philosophers are not truly wise men.

If instead of the minor (a particular negative) we substitute the contradictory of the conclusion, viz.,

All philosophers are truly wise men,

the middle term will be universally affirmed of the major in the major proposition, while in the new minor proposition it will be affirmed that the whole minor term is contained in the major, and by the Dictum de omni the conclusion will follow that the middle term is affirmed of the whole minor. By thus substituting the contradictory of the conclusion, in place of the minor (a particular negative), the syllogism will stand thus

Barbara.

BAR-All truly wise men live virtuously.

BA-All philosophers are truly wise men; therefore,
RA.-All philosophers live virtuously.

The conclusion of the reduct is the contradictory of the original minor premiss of the reducend, and must be false, since the premisses of the reducend were supposed to be true; and therefore one of the premisses of the reduct, from which the conclusion has been legitimately deduced, must also be false. But as the major proposition is one of the original premisses granted to be true, the falsity must be in the minor, viz., the contradictory of the original conclusion, which proves the original conclusion to be true.

2. Bokardo.

BO-Some kinds of money have not intrinsic value.
KAR—All kinds of money have adventitious value.

DO. Some things having adventitious value have not intrinsic value.

If in place of the negative premiss (the major), we substitute the contradictory of the conclusion, viz.

All things having adventitious value have intrinsic value. We shall have the following syllogism in Barbara, viz.—

All things having adventitious value have intrinsic value. All kinds of money have adventitious value.

All kinds of money have intrinsic value.

This new conclusion must be false, because it contradicts the major premiss of the reducend; therefore the substituted major premiss, from which the conclusion of the reduct is drawn, must be false, and consequently its contradictory (the conclusion of the reducend) must be true.

But although the moods Baroko and Bokardo are usually reduced, by reductio per impossible, to Barbara, they may also be ostensively reduced by contraposition or negation— the first to Ferio, and the second to Darii. Let the following syllogism be in Baroko :

Every true patriot is a friend to religion.

Some great statesmen are not friends to religion.

Some great statesmen are not true patriots.

In order to reduce this syllogism to Ferio, we first convert the major premiss by negation, and then render the minor premiss affirmative, by combining the negative particle with the predicate. Thus—

He-who-is-not-a-friend-to-religion is not a true patriot.
Some great statesmen are not-friends-to-religion.
Some great statesmen are not true patriots.

In like manner, Bokardo may be reduced to Darii. Let the following syllogism be in Bokardo :

Some systems of unjust exaction have not been followed by immediate punishment.

All systems of unjust exaction incur guilt.

Some things which incur guilt have not been followed by immediate punishment.

In reducing this example to Darii, we first transpose the premisses, and next convert the major by contraposition. Thus

All systems of unjust exaction incur guilt.

Some things which have not been followed by immediate punishment are systems of unjust exaction; therefore,

Some things which have not been followed by immediate punishment incur guilt.

It has been stated above, that the moods in the three last figures may be reduced to the first by the reductio per impossible, as well as Baroko and Bokardo. To assist the learner in the way in which this may be done, the following example is annexed:

Let the mood to be reduced be in Disamis, of the third figure.

This mood is represented by the vowel symbols, IAI. If this conclusion I is false, its contradictory E, must be true; for of contradictories one must be false, and the other true. Now, this assumed contradictory E contradicts the major premiss I. If we substitute this contradictory for I, the new premisses will be EA, from which we can legitimately deduce the conclusion E, and the new mood will be Celarent of the first figure. The falsity involved in this assumed contradictory will be best illustrated by examples of the reducend and reduct :

DI-Some infidels publish their opinions.

sA-All infidels are opposed to true religion.

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MIS. Some beings opposed to true religion publish their opinions.