English Grammar

the minor term is compared with the middle; and, 3. The Conclusion, in which the minor term is compared with the major. The Major Premise is usually placed first. When terms are said to be compared with each other, it is meant that one of them is affirmed or denied by the other.

Of the two premises, the Major is, in common discourse, called the "Principle," and the Minor Premise the "Reason."

CANONS AND RULES.

1st Canon.-Two terms which agree with one and the same third may be declared to agree with each other.

2d Canon.-Two terms, whereof one agrees and the other disagrees with one and the same third, may be pronounced to disagree with each other.

When two terms are brought together as subject and predicate of a proposition, they are described, in technical language, as agreeing or disagreeing with each other, according as the one is affirmed or denied of the other. The former of these canons applies to affirmative, the latter to negative propositions.

1st Rule.-A Syllogism must have three, and only three, Terms.

2d Rule. It must have three, and but three, Propositions. 3d Rule.-The Middle term must be one only, i. e., not double; must be unequivocal; and must be, in one at least of the premises, distributed.

4th Rule.-No Term is to be distributed in the Conclusion that was not distributed in the Premise (or there must be no "illicit" process).

5th Rule.-One at least of the premises must be affirmative; since, if both were negative, the Middle term would not be pronounced either to agree with each of the "Extremes," or to agree with one and to disagree with the other, but to disagree with both; whence nothing can be inferred; as, "No X is Y, and Z is not X," evidently affords no ground for comparing Y and Z together.

6th Rule. If one premise be negative, the Conclusion must be negative; since, inasmuch as the other premise must be affirmative, the Middle will have been assumed to agree with one of the "Extremes," and to disagree with the other.

EXERCISE.

Point out the three Propositions in each of the following Syllogisms, and name them; also each Subject, Predicate, and Copula; also the Major term, the Minor term, and the Middle term:

1. Every dispensation of Providence is beneficial; Afflictions are dispensations of Providence ; Therefore they are beneficial.

2. No predaceous animals are ruminant; The lion is a predaceous animal;

Therefore the lion is not ruminant.

3. All tyrants deserve death;

Cæsar was a tyrant;

Therefore he deserved death.

4. No one who lives on terms of confidence with another is justified in killing him;

Brutus lived on terms of confidence with Cæsar;

Brutus, therefore, was not justified in killing Cæsar. The MODE of a Syllogism is the designation of the three Propositions it contains (in the order in which they stand), according to their respective Quantity and Quality; that is, according as each proposition is universal or particular, affirmative or negative; that is, according as each proposition is A, E, I, or O. Out of sixty-four combinations obtained by 4x4x4, there are only eleven modes in which any syllogism can be expressed.

The FIGURE of a Syllogism is the situation of the Middle term in the two premises respectively with relation to the two Extremes (or Terms) of the conclusion, namely, the Major and Mi

nor terms.

Let X be the Middle term, Y the Major term, and Z the Minor term.

In the FIRST FIGURE the Middle term is made the Subject of the Major premise, and the Predicate of the Minor; as, Every X is Y; Z is X; therefore Z is Y.

All electrical phenomena (X) are measurable (Y);
Magnetism (Z) is an Electrical phenomenon (X);
Therefore it (Z) is measurable (Y).

Here the middle term is less extensive than the major, and more extensive than the minor.

In the SECOND FIGURE the Middle term is the Predicate of each Premise. In this, none but negative conclusions can be proved, since one of the premises must be negative, in order that the Middle term may be (by being the predicate of a Negative) distributed; as, No Y is X; Z is X; therefore Z is not Y. The nervous fluid will not travel along a tied nerve; Electricity will travel along a tied nerve;

Therefore Electricity is not the nervous fluid.

Here the Middle term is more extensive than the major or the minor term.

In the THIRD FIGURE the Middle term is the Subject of each premise. In this Figure none but particular conclusions can follow; as, Every X is Y; every X is Z; therefore some Z is Y. All virtuous men are conscientious;

All virtuous men are happy;

Therefore some who are happy are conscientious.

Here the Middle term, "virtuous men," is less extensive than either the major or the minor term.

The FOURTH FIGURE (Y is X; X is Z; therefore Z is Y) is omitted by some logicians as awkward and unnecessary.

§ 467. An ENTHYMEME is a syllogism with one premise suppressed. It is an abridged form of an argument. This is the ordinary form of speaking and writing. See § 465.

EXERCISE.

Draw out the following Enthymemes into regular syllogisms: 1. Cæsar was a tyrant, therefore he deserved death. 2. The Epicureans can not be regarded as true philosophers, for they did not reckon virtue as a good in itself.

3. Some reviewers do not refrain from condemning books which they have not read; they are, therefore, not candid. 4. How can ye believe who receive honor one of another?

RHETORICAL ENTHYME ME.

§ 468. The RHETORICAL ENTHYMEME is a sentence which contains the materials of a syllogism, but does not itself furnish a legitimate conclusion. The concurrence of several defective syllogisms of this sort are equivalent to a demonstrative one. In the investigation of the authorship of the Letters of Junius, the following defective Enthymemes have been employed, which, taken together, form a strong case:

The author of " Junius" wrote a particular hand;

Sir Philip Francis wrote the same kind of hand;