A Class Room Logic / Deductive and Inductive, with Special Application to the Science and Art of Teaching

by George Hastings McNair

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.