An individual proposition is one which has a singular subject; e. g., Abraham Lincoln was an honest man. Peter the Great was Russia’s greatest ruler. The maple tree in my yard is dying of old age. These propositions, having a singular term as subject, are individual or singular in nature. As the predicate refers to the whole of the logical subject, individual propositions are classed as universal.
(4) Plurative Propositions.
Plurative propositions are those introduced by “most,” “few,” “a few,” or equivalent quantity signs. For example, “Most birds are useful to man”; “Few men know how to live”; “A few of the prisoners escaped,” are plurative propositions. “Most” means more than half, while “few” and “a few” mean less than half. In either case the proposition is particular. Stated logically, the illustrative propositions would take the form of “Some birds are useful to man”; “Some men do not know how to live”; “Some of the prisoners escaped.”
The reader will observe the difference in significance between few and a few. The former is negative in character and when introducing a proposition makes it a particular negative (O). The latter always introduces a particular affirmative (I).
(5) Partitive Propositions.
Partitive propositions are particulars which imply a complementary opposite. These arise through the ambiguous use of all-not, some and few. All-not may sometimes be interpreted as not all and sometimes as no. To illustrate: The proposition, “All men are not mortal,” is distinctly a universal negative or an E, while the proposition, “All that glitters is not gold,” is a particular negative or an O. The logical form of the first is, “No men are mortal,” and of the second, “Some glittering things are not gold.” When used in the “not-all” sense, the proposition is partitive because if the O-meaning is intended the I is implied. For example, “All that glitters is not gold,” is partitive because the statement implies that some glittering things are gold (I) as well as the complement, “Some glittering things are not gold” (O). A knowledge of both the affirmative and negative aspects is taken for granted in the statement of either the one or the other.
“All-not,” then, is negative in any case, but universal when it means no and particular when it means not all. Any proposition is partitive in nature when the quantity sign is not all, or all-not interpreted as the equivalent of not all.
It may be observed here that all has two distinct uses. First, it may be used in a collective sense; second, in a distributive sense. For example: All is used in the collective sense in such propositions as, “All the members of the football team weighed exactly one ton,” or “All the angles of the triangle are equal to two right angles.” Using all in the distributive sense would maketrue these: “All the members of the football team weigh more than 140 pounds”; “All the angles of a triangle are less than two right angles.” All is used collectively when reference is made to an aggregate, but distributively when reference is made to each.
The quantity sign some is likewise ambiguous, as it may mean (1) some only—some, but not all, or (2) some at least—some, it may be all or not all. When “some” is used as the quantity sign of any particular proposition which has been accepted as logical, the second meaning, “some at least,” is always implied. This interpretation of “some” will be explained more in detail in a succeeding section.
When some is used in the sense of some only, the partitive nature of the proposition is apparent, as both I and O are implied. For example, with reference to the human family, to say that “some only are wise” necessitates an investigation, which leads to the discovery that some are wise, while others are not wise. If the proposition be an I, then its complementary O is implied, or if it be an O, the I is implied.