The most important outcome of the above discussion is that a proposition ordinarily expressed in the form All S is P may be either assertoric or apodeictic. It will be found that this distinction has an important bearing on several questions subsequently to be raised.
66. Particular Propositions.—In dealing with particular propositions it is necessary to assign a precise signification to the sign of quantity some.
In its ordinary use, the word some is always understood to be exclusive of none, but in its relation to all there is ambiguity. For it is sometimes interpreted as excluding all as well as none, while sometimes it is not regarded as carrying this further implication. The word may, therefore, be defined in two conflicting senses: first, as equivalent simply to one at least, that is, as the pure contradictory of none, and hence as covering every case (including all) which is inconsistent with none ; secondly, as any quantity intermediate between none and all and hence carrying with it the implication not all as well as not none. In ordinary speech the latter of these two meanings is probably the more usual.[98] It has, however, been customary with 101 logicians in interpreting the traditional scheme to adopt the other meaning, so that Some S is P is not inconsistent with All S is P. Using the word in this sense, if we want to express Some, but not all, S is P, we must make use of two propositions—Some S is P, Some S is not P. The particular proposition as thus interpreted is indefinite, though with a certain limit; that is, it is indefinite in so far that it may apply to any number from a single one up to all, but on the other hand it is definite in so far as it excludes none. We shall henceforth interpret some in this indefinite sense unless an explicit indication is given to the contrary.
[98] We might indeed go further and say that in ordinary speech some usually means considerably less than all, so that it becomes still more limited in its signification. In common language, as is remarked by De Morgan, “some usually means a rather small fraction of the whole; a larger fraction would be expressed by a good many ; and somewhat more than half by most ; while a still larger proportion would be a great majority or nearly all” (Formal Logic, p. 58).
Mr Bosanquet regards the particular proposition as unscientific, on the ground that it always depends either upon imperfect description or upon incomplete enumeration.[99] I may, for instance, know that all S’s of some particular description are P, but not caring or not troubling to define them I content myself with saying Some S is P, for example, Some truth is better kept to oneself.[100] Contrasted with this, we have the particular proposition of incomplete enumeration where our ground for asserting it is simply the observation of individual instances in which the proposition is found to hold good.
[99] Essentials of Logic, pp. 116, 117.
[100] It is implied that a proposition of this kind might be expanded into the proposition All S that is A is P, that is, All AS is P. Mr Bosanquet gives, as an example, Some engines can drag a train at a mile a minute for a long distance. “This does not mean a certain number of engines, though of course there are a certain number. It means certain engines of a particular make, not specified in the judgment.”
It is true that the particular proposition is not in itself of much scientific importance; and its indefinite character naturally limits its practical utility. It seems, however, hardly correct to describe it as unscientific, since—as will subsequently be shewn in more detail—it may be regarded as possessing distinctive functions. Two such functions may be distinguished, though they are often implicated the one in the other. In the first place, the utility of the particular proposition often depends 102 rather on what it denies than on what it affirms, and the proposition that it denies is not indefinite. One of the principal functions of the particular affirmative is to deny the universal negative, and of the particular negative to deny the universal affirmative. In the second place, the distinctive purpose of the particular proposition may be to affirm existence; and this is probably as a rule the case with propositions which are described as resulting from incomplete description. If, for example, we say that “some engines can drag a train at a mile a minute for a long distance,” our object is primarily to affirm that there are such engines; and this would not be so clearly expressed in the universal proposition of which the particular is said to be the incomplete and imperfect expression.
The relation of the particular proposition, Some S is P, to the problematic proposition, S may be P, will be considered subsequently.
67. Singular Propositions.—By a singular or individual proposition is meant a proposition in which the affirmation or denial is made of a single individual only: for example, Brutus is an honourable man ; Much Ado about Nothing is a play of Shakespeare’s ; My boat is on the shore.