Some Logicians, seeing that the quantity of predicates, though not distinctly expressed, is recognised, and holding that it is the part of Logic “to make explicit in language whatever is implicit in thought,” have proposed to exhibit the quantity of predicates by predesignation, thus:  ‘Some men are some wise (beings)’; ’some men are not any brave (beings)’; etc.  This is called the Quantification of the Predicate, and leads to some modifications of Deductive Logic which will be referred to hereafter. (See Sec. 3; chap. vii.  Sec. 4, and chap. viii.  Sec. 3.)

Sec. 2.  As to Quality, Propositions are either Affirmative or Negative.  An Affirmative Proposition is, formally, one whose copula is affirmative (or, has no negative sign), as S—­is—­P, All men—­are—­partial to themselves.  A Negative Proposition is one whose copula is negative (or, has a negative sign), as S—­is not—­P, Some men—­are not—­proof against flattery.  When, indeed, a Negative Proposition is of Universal Quantity, it is stated thus:  No S is P, No men are proof against flattery; but, in this case, the detachment of the negative sign from the copula and its association with the subject is merely an accident of our idiom; the proposition is the same as All men—­are not—­proof against flattery.  It must be distinguished, therefore, from such an expression as Not every man is proof against flattery; for here the negative sign really restricts the subject; so that the meaning is—­Some men at most (it may be none) are proof against flattery; and thus the proposition is Particular, and is rendered—­Some men—­are not—­proof against flattery.

When the negative sign is associated with the predicate, so as to make this an Infinite Term (chap. iv.  Sec. 8), the proposition is called an Infinite Proposition, as S is not-P (or p), All men are—­incapable of resisting flattery, or are—­not-proof against flattery.

Infinite propositions, when the copula is affirmative, are formally, themselves affirmative, although their force is chiefly negative; for, as the last example shows, the difference between an infinite and a negative proposition may depend upon a hyphen.  It has been proposed, indeed, with a view to superficial simplification, to turn all Negatives into Infinites, and thus render all propositions Affirmative in Quality.  But although every proposition both affirms and denies something according to the aspect in which you regard it (as Snow is white denies that it is any other colour, and Snow is not blue affirms that it is some other colour), yet there is a great difference between the definite affirmation of a genuine affirmative and the vague affirmation of a negative or infinite; so that materially an affirmative infinite is the same as a negative.