2. KINDS OF LOGICAL PROPOSITIONS.
There are three kinds of logical propositions; namely, categorical, hypothetical and disjunctive.
A categorical proposition is one in which the assertion is made unconditionally. An hypothetical proposition is one in which the assertion depends upon a condition. A disjunctive proposition is one which asserts an alternative.
THE THREE KINDS ILLUSTRATED:
(1) “Every dog has his day.” Categorical.
(2) “If you do your best, success will reward you.” Hypothetical.
(3) “He is either stupid or indolent.” Disjunctive.
(4) “All vices are reprehensible.” Categorical.
(5) “Either you are very talented or very industrious.” Disjunctive.
(6) “If capital punishment does not aid society, it should be abolished.” Hypothetical.
(7) “You may go provided your teacher is willing.” Hypothetical.
(8) “No intelligent man can ignore the practice of temperance.” Categorical.
By studying the illustrations it will be observed that the categorical propositions are direct, bold, assertive statements, whereas the hypothetical are limited by conditions which make them less forceful. In the second proposition, for example, “success will reward you,” is limitedby the condition, “If you do your best.” The disjunctive may be regarded as categorical in form, but hypothetical in meaning, because in such a proposition as, “He is either, stupid or indolent,” a direct assertion is made which suggests the categorical, and yet it may be implied that, if he is stupid then he is not indolent; this is indicative of the hypothetical.
Some logicians classify propositions as categorical and conditional, the conditional being subdivided into hypothetical and disjunctive. The first classification seems preferable, however, as it conforms to the three modes of reasoning.
The common word-signs of the categorical proposition are all, every, each, any, no and some, while those of the hypothetical are if, even if, unless, although, though, provided that, when, or any word or group of words denoting a condition. The disjunctive symbols are either—or.