7. ILLUSTRATIVE EXERCISE TESTING HYPOTHETICAL ARGUMENTS OF ALL KINDS.
The following brief outline may be followed in testing hypothetical arguments:
1. Arrange logically.
2. Determine antecedent and consequent.
3. Apply the hypothetical rule; name fallacies giving reasons.
4. Reduce to categorical form.
5. Apply the categorical rules, giving fallacies with reasons.
(1) If a man is properly educated, he will not despise manual labor;
therefore I conclude that you have not been properly educated,
since you dislike to work with your hands.
Arranged logically and antecedent and consequent indicated:
If a man is properly educated (antecedent), he will not despise manual labor (consequent);
You despise manual labor (dislike to work with your hands),
∴ You have not been properly educated.
The minor premise denies the consequent, hence the argument is valid according to the rule, “The minor premise must affirm the antecedent or deny the consequent.” The student should note that the consequent is negative and therefore its denial must be an affirmative proposition.
Reduced to the categorical:
E A G
properly educated man will not M
despise manual labor;
A S
You despise M
manual labor,
E ∴ S
You have not been G
properly educated.
Regarded categorically this is valid. Why?
(2) “If one believes in the tenets of the democratic party, then he should vote for its candidates; and since A does believe in them I have asked him to vote for me.”
Arranged, and antecedent and consequent indicated.
If one believes in the tenets of the democratic party (antecedent), then he should vote for its candidates (consequent);
And A does believe in these tenets,
∴ He should vote for its candidates (I have asked him to vote for me).
The minor premise affirms the antecedent and thus the argument is valid according to rule.
Reduced to the categorical:
A M
One who believes in the tenets of the democratic party should vote for its M
candidates,
A S
A believes in these M
tenets,
A ∴ S
A should vote for its G
candidates.
Reduced to the categorical gives mood
A
A
A in the first figure and this we know to be valid.
(3) “If the weather had not been pleasant, I could not have come; but as the weather is pleasant, here I am.”
Arranged and antecedent and consequent indicated:
If the weather had not been pleasant (antecedent), I could not have come (consequent);
The weather is pleasant,
∴ I have come (here I am).
The minor premise denies the antecedent and consequently the argument is invalid according to the rule. (An affirmative minor premise denies a negative antecedent.)
Reduced to the categorical:
E Unpleasant weather would not permit me to come,
E This weather is not unpleasant,
A ∴ This weather enabled me to come.
Fallacy of two negative premises.
(4) “If one pays his debts, he will not be ‘black-listed’; but since you are ‘black-listed,’ I conclude that you have not paid your debts.”
Arranged logically and antecedent and consequent indicated:
If one pays his debts (antecedent), he will not be “black-listed” (consequent);
You are “black-listed,”
∴ You have not paid your debts.
The minor premise denies the consequent hence the argument is valid.
Reduced to categorical form:
E No G
one who pays his debts is M
black listed,
A S
You are M
black listed,
E ∴ S
You have not G
paid your debts.
The mood
E
A
E in the second figure is valid.
(5) “Men would do right for the sake of themselves, if they appreciated the law of retribution; but they never think of that.”
Arranged, completed, and tested:
If they appreciated the law of retribution (antecedent),men would do right for the sake of themselves (consequent);
But they do not appreciate the law of retribution (never think of that),
Hence they do not do right for the sake of themselves.
Fallacy of denying the antecedent.
Reduced to the categorical:
A The case of M
men appreciating the law of retribution, is the case of G
men doing right for the sake of themselves;
E But S
men do not M
appreciate the law of retribution,
E ∴ S
Men do not do G
right for the sake of themselves.
Fallacy of illicit major.
(6) “If an animal is a vertebrate, then it must have a backbone; but the books say that this animal is not a vertebrate, hence it cannot have a backbone.”
Since the minor premise denies the antecedent it would appear that the argument is invalid; yet common knowledge and common sense dictate that the conclusion is true. Surely no invertebrate can have a backbone. As a matter of fact the antecedent and consequent are co-extensive and therefore the hypothetical rule is not applicable.
Reduced to the categorical:
A M
Vertebrates must have G
a backbone (Co-extensive),
E This S
animal is not a M
vertebrate,
E ∴ This S
animal cannot have G
a backbone.
As co-extensive A’s distribute their predicates the possibility of there being a fallacy of illicit major is forestalled.
Categorically considered the argument is likewise valid.