3rd 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 :

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

Brutus, therefore, was not justified in killing Cæsar.

The MODE of a Syllogism is the designation of the three Proposi tions 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, S, or 0. Out of sixty-four combinations obtained by 4 x 4 x 4, 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 Minor

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.

SECTION CCCCLXVII. THE ENTHYMEME.

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 Section CCCCLXV.

EXERCISE.

Draw out the following Enthymemes into regular syllogisms :

1. Cæsar was a tyrant, therefore he deserved death.

2. The Epicureans cannot 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 honour one of another?

SECTION CCCCLXVIII.-RHETORICAL ENTHYMEME.

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;

Therefore Sir Philip Francis is the author of "Junius."

The author of "Junius" made certain mistakes in correcting proof-sheets;
Sir Philip Francis made the same mistakes;

Therefore Sir Philip Francis is the author of "Junius."

The author of "Junius" had a particular style;

Sir Philip Francis had the same style;

Therefore Sir Philip Francis is the author of "Junius."

The author of "Junius" is guilty of an anomalous use of certain words;

Sir Philip Francis is guilty of the same;

Therefore Sir Philip Francis is the author of "Junius."

The author of "Junius" employs certain images ;

Sir Philip Francis employs the same;

Therefore Sir Philip Francis is the author of "Junius."

The author of "Junius" ceased to write at a particular time;

Sir Philip Francis must have ceased to write at the same time;
Therefore Sir Philip Francis is the author of "Junius."

SECTION CCCCLXIX.-CONDITIONAL SYLLOGISMS.

In a Conditional Proposition there are two members (categorical propositions), whereof one is asserted to depend on the other. That on which the other depends is called the Antecedent; that which depends on this, the Consequent; as, If

Antecedent.

Consequent.

"this man is a murderer," "he deserves death." The Antecedent being assumed to be true, the Consequent is granted as true also. And this may be considered from two points of view:-1st. Allowing that the Antecedent is true, the Consequent must be true; 2nd. Supposing the Antecedent were true, the consequent would be true. Hence there are two kinds of conditional syllogisms,-namely, the Constructive and the Destructive. If A is B, X is Y. Let this be the Major Premise. Then if you add, "but A is B, therefore X is Y," this forms a Constructive Syllogism. If you say X is not Y, therefore A is not B, this is a Destructive Syllogism. Thus, "If this river has tides, the sea into which it flows must have tides;" then, if I add, "this river has tides," it follows, in conclusion, "that the sea into which it flows has tides," which is a Constructive Syllogism. If I add, "the sea into which it flows has not tides," it follows, that "this river has not tides," which is a Destructive Syllogism.

SECTION CCCCLXX.-SORITES.

SORITES is a series of Arguments in which the Conclusion of each is made one of the Premises of the next.

EXERCISE.

1. A is B; B is C; C is D; D is E; ... A is E.

2. The Epicurean Deities are without action; Without action there is no virtue;

Without virtue there is no happiness;

The Epicurean Deities are therefore without happiness.

3. Wilkes was a favourite with the populace;

He who is a favourite with the populace must know how to manage them ;

He who knows how to manage them must well understand their character;
He who well understands their character must hold them in contempt;
Wilkes must, therefore, have held the populace in contempt.

SECTION OCCCLXXI.-DILEMMA.

DILEMMA is an argument equally conclusive by contrary suppositions. It implies a double antecedent :

1. If you have in the major premise several antecedents, all with the same consequent, then these Antecedents, being (in the minor) disjunctively granted (i. e., it being granted that some one of them is true), the one common consequent may be inferred.

If A is B, C is D; if X is Y, C is D; but either A is B, or X is Y; therefore C is D. "If the blessed in heaven have no desires, they will be perfectly content; so they will if their desires are fully gratified; but either they will have no desires, or have them fully gratified; therefore, they will be perfectly content."

2. But if the several antecedents have each a different consequent, then the Antecedents being, as before, disjunctively granted, you can only disjunctively infer the consequents. If A is B, C is D; and if X is Y, E is F; but either A is B, or X is Y; therefore, either C is D, or E is F. "If Eschines joined in the public rejoicings, he is inconsistent; if he did not join, he is unpatriotic; but he either joined or not, therefore he is either inconsistent or unpatriotic."

3. When you have several Antecedents, with each a different consequent, which consequents, instead of wholly denying, you disjunctively deny, then, in the Conclusion, you deny disjunctively the Antecedents. If A is B, C is D; if X is Y, E is F; but either C is not

is not F; therefore, either A is not B, or X is not Y. "If this man were wise, he would not speak irreverently of Scripture in jest; and if he were good, he would not do so in earnest; but he does it either in jest or in earnest; therefore he is either not wise or not good."

In the first we have the simple constructive dilemma; in the second, the complex constructive; in the third, the destructive. Every Dilemma may be reduced into two or more simple conditional syllogisms.

This kind of Argument was urged by the opponents of Don Carlos, the pretender to the Spanish throne, which he claimed as heir-male, against his niece the Queen, by virtue of the Salic law excluding females, which was established (contrary to the ancient Spanish usage) by a former King of Spain, and was repealed by King Ferdinand. They say, "If a King of Spain has a right to alter the law of succession, Carlos has no claim; and if no King of Spain has that right, Carlos has no claim; but a King of Spain either has or has not such right; therefore (on either supposition) Carlos has no claim."

SECTION CCCCLXXII.-ANALOGY.

ANALOGICAL PROPOSITIONS are those of which one of them asserts a Principle manifesting itself in a given set of circumstances, while the other asserts the same principle as manifested in all circumstances, or, more commonly, in a different set of circumstances. And an Argument from Analogy is a direct and unconditional inference of the latter of these two propositions from the first. For example, from the principle expressed in the proposition, "By speaking ill, men learn to speak ill," may be inferred, by analogy, the two following Propositions :

:

By speaking, men learn to be able to speak.

By speaking well, men learn to be able to speak well.

SECTION CCCCLXXIII. DEDUCTION, INDUCTION, AND EXAMPLE.

DEDUCTION is the process of reasoning from a general principle to a particular case.

INDUCTION is the process of reasoning from particular cases to a general principle.

EXAMPLE is the process of reasoning from one particular case to another.

It is absurd to choose by lot an officer in whom skill is needed;

It is, therefore, absurd to choose a general by lot.

Here we have a specimen of Deductive reasoning.

It is absurd to choose by lot a musician, architect, pilot, or physician;
It is, therefore, absurd to choose by lot an officer in whom skill is needed.
Here we have a specimen of Inductive reasoning.

It is absurd to choose a pilot by lot;

It is, therefore, absurd to choose a general by lot.

Here we have a specimen of reasoning from Example.

SECTION CCCCLXXIV.-FALLACIES.

A FALLACY is a deceptive or unsound argument, by which a man is convinced, or endeavours to convince others, of what is not really proved.

The fallacy of the reasoning in these two syllogisms is evident. The middle term is not distributed. It is a rule that the middle term must be distributed once at least in the premises (i. e., by being the subject of a universal, or predicate of a negative. See Section CCCCLXVI.), and once is sufficient; since, if one extreme