(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.
3. THE FOUR ELEMENTS OF A CATEGORICAL PROPOSITION.
Every categorical proposition should have four elements; namely, the quantity sign, the logical subject, the copula and the logical predicate. In the foregoing categorical propositions the quantity signs are respectively, every, all and no. In any case the quantity sign is always attached to the subject and indicates its breadth or extension. For example, in the two propositions, “All men are mortal” and “Some men are wise,” the quantity sign all makes the term man much broader than does the quantity sign some.
The logical subject of a categorical proposition is the term of which something is affirmed or denied, whereas the logical predicate of a categorical proposition is the term which is affirmed or denied of the subject. In the two propositions, “All men are mortal” and “No men are immortal,” the term about which something is affirmed or denied is men, while the terms which are affirmed and denied of the subject are respectively mortal and immortal. “Men” is, therefore, the logical subject of each proposition, while “mortal” is the logical predicate of the first and “immortal” the logical predicate of the second. The copula is the connecting word between the logical subject and predicate and denotes whether or not the latter is affirmed or denied of the former. The copula is always some form of “to be” or its equivalent. When the predicate is denied of the subject, “not” may be used with the copula and considered a part of it. To illustrate: in the logical proposition, “Some men are not wise,” “are not” may be regarded as the copula.