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

by George Hastings McNair

The rectangle is not equilateral,

∴ The rectangle is not a square.

(3) If the rectangle is equilateral, then it is a square;

It is a square,

∴ The rectangle is equilateral.

(4) If the rectangle is equilateral, then it is a square;

It is not a square,

∴ The rectangle is not equilateral.

6. HYPOTHETICAL ARGUMENTS REDUCED TO THE CATEGORICAL FORM.

The hypothetical syllogism so closely resembles the categorical that it may be changed to it by a slight alteration in the wording. After testing the hypothetical by its own rule, it may be expedient to reduce the argument to the categorical form, and subject it to a second test in which the categorical rules are applied. This reduction usually necessitates two steps; first, change the propositions which represent the antecedent and consequent to a subject term and a predicate term respectively and then unite them to form the major premise; second, supply a new minor term, if necessary.