4. ILLUSTRATIVE EXERCISE IN TESTING COMPLETED ARGUMENTS, ONE OR BOTH PREMISES BEING ILLOGICAL.
Arguments containing exclusive propositions.
(1) Only first class passengers may ride in the parlor car,
All these are first class passengers,
∴ They may ride in the parlor car.
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 andthen 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:
A (All) The G
parlor car is reserved for M
first class passengers,
A All S
these are M
first class passengers,
A ∴ All S
these may ride in the G
parlor car.
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:
A (All) These M
books were taken by a G
thief,
A S
You took these M
books,
A ∴ S
You are a G
thief.
We have now had sufficient experience to recognize the validity of mood AAA in the first figure.
(3) “None but the brave deserve the fair,
And you are not fair.”
Making the exclusive logical and completing gives:
A (All) The M
fair deserve the G
brave,
E S
You are not M
fair,
E ∴ S
You do not deserve the G
brave.
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:
E George Washington never told a lie,
A You did tell a lie,
E ∴ You (in this respect) are not like George Washington.
Treated properly this argument proves to be valid; the student, however, is apt to deal with such in this wise:
O George Washington never told a lie,
I You did tell a lie,
O ∴ You (in this respect) are not like George Washington.
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 subjecta 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.
(5) All that glitters is not gold,
Tinsel glitters,
∴ Tinsel is not gold.
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 boththese 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:
O Some M
glittering things are not G
gold,
A S
Tinsel M
glitters,
E ∴ S
Tinsel is not G
gold.
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, Aristotlewas 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:
(6) O Some educated men do not write good English,
A X is an educated man,
E ∴ X does not write good English (uses poor English).
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:
A Those who M
obtain mercy are G
blessed,
A The S
merciful shall M
obtain mercy,
A ∴ The S
merciful are G
blessed.
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....”