2. ORDER OF PROCEDURE IN THE FORMAL TESTING OF ARGUMENTS.

In testing categorical arguments three things are essential; first, to follow a definite plan; second, to give reasons; third, to give the author the benefit of the doubt. In view of these essentials, we suggest this outline which may be helpful to the inexperienced:

We recall that to be strictly logical any categorical argument must take this form: first, major premise; second, minor premise; third, conclusion. Often in common conversation either the minor premise or conclusion is given first. Illustrations of this: (1) “He cannot be a gentleman (conclusion); for no gentleman would do such a thing (major premise), and there is no doubt but that he did it” (minor premise). (2) “He has the making of a good teacher (conclusion); because he not only knows, but he knows how to impart what he knows (minor premise), and this is a sure sign of a good teacher” (major premise). When the argument appears in this illogical form, the first duty of the student is to arrange it logically. To do this he must be able to recognize readily the premises and the conclusion. To this end these facts may be of assistance:

Suggestions relative to completing abbreviated arguments:

(1) If the conclusion is to be supplied, select the term used twice in the premises; this, the middle term, must not appear in the conclusion. The other two terms may now be connected (copulated) to form the conclusion, the narrower term (minor) being used as the subject, unless it occurs in what clearly seems to be the major premise. (2) If either premise is to be supplied, unite the middle term with the subject of the conclusion for the minor premise, and with the predicate of the conclusion for the major premise. (3) In supplying any missing proposition, care should be taken to make the argument valid, if this can be done in conformity with good English, good sense, and the rules of logic.

As regards the determination of the figure it is well to locate the middle term first, placing above it the symbol M. Then “G” (greater) may be placed above the major term and “S” (smaller) above the minor.

3. ILLUSTRATIVE EXERCISES IN TESTING ARGUMENTS WHICH ARE ALREADY COMPLETE, REGULAR, AND LOGICALLY ARRANGED.

This argument is in the first figure, the mood being A
A
A. All the propositions are affirmative and universal, consequently the rules pertaining to negatives and particulars are inapplicable. “A” distributes the subject only, hence all the subjects are underscored. The middle term “dog” is distributed in the major premise, and the minor term “greyhound,” which is distributed in the conclusion, is likewise distributed in the minor premise. The argument is, therefore, valid in form. This may be verified by referring to a list of valid moods in the first figure.

The argument is in the second figure; mood E
A
E. There is one negative premise and the conclusion is negative; no particulars. “E” distributes both terms, “A” the subject only. The middle term is distributed in the major premise. Both major and minor terms are distributed in the conclusion, but they are likewise distributed in the premises where they are used. The argument is, therefore, valid. Reference to the valid moods of the second figure confirms this conclusion.

The mood is A
A
A used in the third figure. All the propositions are A’s, hence the negative and particular rules are inapplicable. “A” distributes its subject. The middle term is distributed in both premises. “All who obey the law” is distributed in the conclusion but not in the premise where it is used. Therefore the argument is invalid. The fallacy being illicit minor. A
A
A is not found in the third figure’s list of valid moods.

The mood of this argument is A
E
E used in the first figure. One premise negative; conclusion negative; no particulars. “A” distributes the subject only; “E” both subject and predicate. The middle term, “good citizens,” is distributed in both premises. The major term, “votes,” is distributed in the conclusion but not in the premise where it is used. The argument is invalid, the fallacy being illicit major. A
E
E is not found in the first figure’s list of valid moods.

The mood of this argument is A
A
A used in the second figure. There are no negatives and no particulars. “A” distributes its subject only. The middle term, “sympathetic,” is distributed in neither premise, hence the argument is invalid. Fallacy of undistributed middle. Referring to the list of valid moods, we do not find A
A
A in the second figure.

The mood is A
A
I in the first figure. No negatives; no particulars. “A” distributes its subject only; “I” distributes neither term. Middle term, distributed in the major premise; no term distributed in the conclusion. The argument is, therefore, valid. The conclusion is weakened as it could just as well be an A. The mood A
A
I in the first figure is valid, but of little value because of the weakened conclusion.

4. ILLUSTRATIVE EXERCISE IN TESTING COMPLETED ARGUMENTS, ONE OR BOTH PREMISES BEING ILLOGICAL.

Arguments containing exclusive propositions.

Propositions introduced by such words as only, none but, alone and their equivalents are exclusive propositions. Since these distribute their predicates, but do not distribute their subjects, the most convenient way of dealing with them is to interchange subject and predicate and then regard them as “A” propositions. As the first proposition of the argument is an exclusive, we must deal with it accordingly. Interchanging subject and predicate and introducing it with all places the argument in this form:

The mood of this argument is A
A
A in the second figure. No negatives; no particulars. “A” distributes its subject only; the middle term is thus undistributed. The argument is invalid, the fallacy being that of undistributed middle.

(2) “No one but a thief would take these books without asking for them, and it has been proved that you took the books; that is the reason I have called you a thief.”

It is clear that “no one but” is equivalent to “only.” Thus the first proposition of the argument is an exclusive, and may be made logical by interchanging subject and predicate and calling it an “A.” As a result of this the argument takes the following form:

We have now had sufficient experience to recognize the validity of mood AAA in the first figure.

Making the exclusive logical and completing gives:

The mood of this argument is A
E
E used in the first figure. There is a negative premise, also a negative conclusion; no particulars. The middle term is distributed twice. The major term “brave” is distributed in the conclusion but not in the major premise; hence the argument is invalid, the fallacy being illicit major.

NOTE.—There may be some doubt in the student’s mind as to the proposition “None but the brave deserve the fair,” really meaning “All the fair deserve the brave.” This doubt may be better satisfied by treating the exclusive in the second way as indicated on page 137, to wit: Negate the subject of the exclusive, then give it the form of the regular “E.” This results in “No not-brave persons deserve the fair,” which, after first converting and then obverting becomes, “All the fair deserve the brave.”

Arguments Containing Individual Propositions.

(4) “George Washington never told a lie, but you, when tempted, yielded with no qualms of conscience.”

Completing, and arranging logically gives:

Treated properly this argument proves to be valid; the student, however, is apt to deal with such in this wise:

When placed in this mood the argument is invalid; since the major term, which is distributed in the conclusion, is not distributed in the premise where it occurs (illicit major). It is the tendency on the part of students to classify as particular, a proposition which has as its subject a singular term. Such propositions we have learned to call individual. The cause of this tendency is easily explained: Consider the propositions, (1) “This man is mortal”; (2) “Some men are mortal”; (3) “All men are mortal.” In the first instance “mortal” refers to the subject “man” which is narrower in significance than “some men” to which “mortal” of the second proposition refers. In consequence, it is very natural to infer that if, “Some men are mortal,” is particular, then, “This man is mortal,” is likewise particular. The error springs from a wrong conception of particular as used in logic; the content of the term has little to do with extension, but is chiefly concerned with indefiniteness. A particular proposition is one in which the predicate refers to only a part of an indefinite subject. If the subject is referred to as a whole, and this whole is more or less definite, then the proposition is universal. Since “mortal” refers to the whole of the definite term “this man,” as positively as it refers to the whole of “all men,” there is as much justification in calling the first proposition universal as there is in calling the third universal. It may be remembered, then, that logicians class as universal all individual propositions.

Arguments Containing Partitive Propositions.

The quantity sign “all” when used with “not” is ambiguous; it may mean “no” or “some-not.” The only way to determine which meaning is intended is to try both these quantity signs, selecting the one which seems to fit best the author’s meaning. When “all-not” means “some-not” the proposition which it introduces is called a partitive proposition; since such always suggests a complementary proposition. (See page 133.) For example, “Some glittering things are not gold,” suggests its complement, “Some glittering things are gold.” In testing the foregoing argument it is clear that “All that glitters is not gold” does not mean “No glittering thing is gold,” so much as it implies “Some glittering things are not gold.” Thus the argument takes this form:

The mood is O
A
E in the first figure. There is one negative premise (O), and the conclusion is negative. There is one particular premise (O), but the conclusion is not particular. This makes the argument invalid according to rule 8; viz.: “A particular premise necessitates a particular conclusion.” Carrying the test still further it will be seen that there is likewise the fallacy of undistributed middle.

Other arguments where one of the premises is partitive.

“All scholars are not wise and, therefore, Aristotle was not wise.” “All democrats are not free-traders, but most of the men of this particular club are democrats, and hence they are of a different faith (not free-traders).”

“All the members of the club are not good players, and James belongs to the club.”

“All educated men do not write good English; therefore, you ought not to express surprise when informed that X, though an educated man, uses poor English.”

The major premise in each of the foregoing is partitive in nature and should be changed to the following form before the argument is tested; taking these in order we have: “Some scholars are not wise”; “Some democrats are not free-traders”; “Some of the members of the club are not good players”; “Some educated men do not write good English.” Let us test the validity of the last one:

Like the first one of the list, this is invalid inasmuch as a particular premise should yield a particular conclusion, not one which is universal. The argument also contains the fallacy of undistributed middle.

Arguments Containing Inverted Propositions.

(7) “Blessed are the merciful: for they shall obtain mercy.” The first proposition, being poetical in construction, is typical of the inverted form. These are usually made logical by simple conversion. Since premises usually follow “for,” or equivalent word-signs, it is easy to see that “for they shall obtain mercy” is one of the premises; while the other, the broader of the two, is understood.

Arranged logically the argument assumes this form:

Here we have the mood A
A
A in the first figure, which we know to be valid.

Other arguments where one of the propositions is inverted.

“Blessed are the pure in heart: for they shall see God.”

“To thine own self be true, and it must follow, as the night the day, thou canst not then be false to any man.”

“A king thou art and, therefore, thy commands shall be, yea, must be obeyed.”

Taking the inverted propositions in order and making each logical, the following is the result: “The pure in heart are blessed”; “You be true to yourself, and....”; “You are a king, therefore....”

5. ARGUMENTS WHICH ARE INCOMPLETE AND MORE OR LESS IRREGULAR.

The above arguments thrown into logical form and validity or invalidity stated: (The student should test these in detail.)

In supplying suppressed premises the critic is duty bound to give the author the benefit of the doubt, if by so doing no principle in logic is violated and the proposition conforms to good English and good sense. Often it is not easy to perceive in the abbreviated argument the meaning intended; in such instances all legitimate effort should be directed to making the argument valid. To illustrate: In supplying the major premise of argument “6” it would be easy to make it, “All justice is bought by the rich”; in consequence the critic could pronounce the argument invalid as the middle term would be undistributed.

Before asserting that an argument is fallacious because it has four terms rather than three, the student must make sure that there are no synonyms or equivalents used. In argument “4,” for instance, there are apparently the four terms: (1) “foolish,” (2) “despise knowledge,” (3) “man,” (4) “fool”; but to regard “foolish” and “fool” as synonyms does not seem like undue liberty. The following arguments further illustrate this need of recognizing synonyms:

“Human beings are accountable for their conduct; brutes, not being human, are therefore free from responsibility.” (Not accountable for their conduct.)

“Not all educated men spell correctly; because one often finds mistakes in the writings of college graduates.” (Educated men.)

“Modern education is not popular in this state; for it increases the tax rate, and the popularity of everything, which touches the pocket of these frugal Yankees, (increases the tax rate) is very short lived.” (Not popular.) In common parlance the use of synonyms is so prevalent that ready ability to substitute equivalents in word, phrase, and clause form is needed by him who would be skillful in testing all kinds of arguments.

It has already become apparent to the student that the number of the noun or the tense of the verb is of small logical consequence. A very large proportion of the formal fallacies in argumentation concern the rules of distribution which are summarized in the dictum “What may be said of the whole may be said of part of that whole.”

6. COMMON MISTAKES OF STUDENTS IN TESTING ARGUMENTS.

The most common mistakes made by the student when testing arguments are as follows: (1) Using the exclusive as an “A” without interchanging subject and predicate; e. g., interpreting the proposition, “Only high school graduates may enter the training school,” as meaning “All high school graduates may enter the training school.” (2) Calling individual propositions particular; e. g., interpreting “Socrates is mortal” as an “I” rather than an “A.” (3) Signifying that partitive propositions are “A’s” rather than “O’s”; e. g., “All that glitters is not gold” interpreted as meaning that “All glittering things are gold,” rather than “Some glittering things are not gold.” (A). (4) Concluding that a fallacy of four terms has been committed when two terms are synonomous. (5) Failing to interchange the subject and predicate of inverted propositions.

7. OUTLINE.

CATEGORICAL ARGUMENTS TESTED ACCORDING TO FORM.