3. ILLUSTRATIVE EXERCISES IN TESTING ARGUMENTS WHICH ARE ALREADY COMPLETE, REGULAR, AND LOGICALLY ARRANGED.
(1) A All M
dogs are G
quadrupeds,
A All S
greyhounds are M
dogs,
A ∴ All S
greyhounds are G
quadrupeds.
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.
(2) E No G
prejudiced person is M
open to conviction,
A All S
fair minded persons are M
open to conviction,
E ∴ No S
fair minded person is G
prejudiced.
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.
(3) A All M
good citizens G
vote,
A All M
good citizens S
obey the law,
A ∴ All S
who obey the law G
vote.
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.
(4) A All M
good citizens G
vote,
E No S
criminal is a M
good citizen,
E ∴ No S
criminal G
votes.
The mood of this argument is
A
E
E used in the firstfigure. 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.
(5) A All G
true teachers are M
sympathetic,
A All S
lovers of children are M
sympathetic,
A ∴ All S
lovers of children are G
true teachers.
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.
(6) A All M
thoughtful men are G
humane,
A All S
good citizens are M
thoughtful men,
I ∴ Some S
good citizens are G
humane.
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.