In ordinary discourse it is not always explicitly stated whether predication is universal or particular; it would be very natural to say Lions inhabit Africa, leaving it, as far as the words go, uncertain whether we mean all or some lions. Propositions whose quantity is thus left indefinite are technically called 'preindesignate,' their quantity not being stated or designated by any introductory expression; whilst propositions whose quantity is expressed, as All foundling-hospitals have a high death-rate, or Some wine is made from grapes, are said to be 'predesignate.' Now, the rule is that preindesignate propositions are, for logical purposes, to be treated as particular; since it is an obvious precaution of the science of proof, in any practical application, not to go beyond the evidence. Still, the rule may be relaxed if the universal quantity of a preindesignate proposition is well known or admitted, as in Planets shine with reflected light—understood of the planets of our solar system at the present time. Again, such a proposition as Man is the paragon of animals is not a preindesignate, but an abstract proposition; the subject being elliptical for Man according to his proper nature; and the translation of it into a predesignate proposition is not All men are paragons; nor can Some men be sufficient, since an abstract can only be adequately rendered by a distributed term; but we must say, All men who approach the ideal. Universal real propositions, true without qualification, are very scarce; and we often substitute for them general propositions, saying perhaps—generally, though not universally, S is P. Such general propositions are, in strictness, particular; and the logical rules concerning universals cannot be applied to them without careful scrutiny of the facts.
The marks or predesignations of Quantity commonly used in Logic are: for Universals, All, Any, Every, Whatever (in the negative No or No one, see next §); for Particulars, Some.
Now Some, technically used, does not mean Some only, but Some at least (it may be one, or more, or all). If it meant 'Some only,' every particular proposition would be an exclusive exponible ([chap. ii. § 3]); since Only some men are wise implies that Some men are not wise. Besides, it may often happen in an investigation that all the instances we have observed come under a certain rule, though we do not yet feel justified in regarding the rule as universal; and this situation is exactly met by the expression Some (it may be all).
The words Many, Most, Few are generally interpreted to mean Some; but as Most signifies that exceptions are known, and Few that the exceptions are the more numerous, propositions thus predesignate are in fact exponibles, mounting to Some are and Some are not. If to work with both forms be too cumbrous, so that we must choose one, apparently Few are should be treated as Some are not. The scientific course to adopt with propositions predesignate by Most or Few, is to collect statistics and determine the percentage; thus, Few men are wise—say 2 per cent.
The Quantity of a proposition, then, is usually determined entirely by the quantity of the subject, whether all or some. Still, the quantity of the predicate is often an important consideration; and though in ordinary usage the predicate is seldom predesignate, Logicians agree that in every Negative Proposition (see [§ 2]) the predicate is 'distributed,' that is to say, is denied altogether of the subject, and that this is involved in the form of denial. To say Some men are not brave, is to declare that the quality for which men may be called brave is not found in any of the Some men referred to: and to say No men are proof against flattery, cuts off the being 'proof against flattery' entirely from the list of human attributes. On the other hand, every Affirmative Proposition is regarded as having an undistributed predicate; that is to say, its predicate is not affirmed exclusively of the subject. Some men are wise does not mean that 'wise' cannot be predicated of any other beings; it is equivalent to Some men are wise (whoever else may be). And All elephants are sagacious does not limit sagacity to elephants: regarding 'sagacious' as possibly denoting many animals of many species that exhibit the quality, this proposition is equivalent to 'All elephants are some sagacious animals.' The affirmative predication of a quality does not imply exclusive possession of it as denial implies its complete absence; and, therefore, to regard the predicate of an affirmative proposition as distributed would be to go beyond the evidence and to take for granted what had never been alleged.
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 [§ 5]; [chap. vii. § 4], and [chap. viii. § 3].)
§ 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. § 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.
Generally Mill's remark is true, that affirmation and denial stand for distinctions of fact that cannot be got rid of by manipulation of words. Whether granite sinks in water, or not; whether the rook lives a hundred years, or not; whether a man has a hundred dollars in his pocket, or not; whether human bones have ever been found in Pliocene strata, or not; such alternatives require distinct forms of expression. At the same time, it may be granted that many facts admit of being stated with nearly equal propriety in either Quality, as No man is proof against flattery, or All men are open to flattery.