When a proposition is given in the indesignate form, we can generally tell from our knowledge of the subject-matter or from the context whether it is meant to be universal or particular. Probably in the majority of cases indesignate propositions are intended to be understood as universals, e.g., “Comets are subject to the law of gravitation”; but if we are really in doubt with regard to the quantity of the proposition, it must logically be regarded as particular.[104]
[104] In the Port Royal Logic a distinction is drawn between metaphysical universality and moral universality. “We call metaphysical universality that which is perfect and without exception; and moral universality that which admits of some exception, since in moral things it is sufficient that things are generally such” (Port Royal Logic, Professor Baynes’s translation, p. 150). The following are given as examples of moral universals: All women love to talk ; All young people are inconstant ; All old people praise past times. Indesignate propositions may almost without exception be regarded as universals either metaphysical or moral. But it seems clear that moral universals have in reality no valid claim to be called universals at all. Logically they ought not to be treated as more than particulars, or at any rate pluratives.
70. Multiple Quantification.—The application of a predicate to a subject is sometimes limited with reference to times or conditions, and this may be treated as yielding a secondary quantification of the proposition; for example, All men are 106 sometimes unhappy, In some countries all foreigners are unpopular. This differentiation may be carried further so as to yield triple or any higher order of quantification. Thus, we have triple quantification in the proposition, In all countries all foreigners are sometimes unpopular.[105]
[105] For a further development of the notion of multiple quantification see Mr Johnson’s articles on The Logical Calculus in Mind, 1892.
In this way a proposition with a singular term for subject may, with reference to some secondary quantification, be classified as universal or particular as the case may be; for example, Gladstone is always eloquent, Browning is sometimes obscure.
71. Infinite or Limitative Propositions.—In place of the ordinary twofold division of propositions in respect of quality, Kant gave a threefold division, recognising a class of infinite (or limitative) judgments, which are neither affirmative nor negative. Thus, S is P being affirmative, and S is not P negative, S is not-P is spoken of as infinite or limitative.[106] It is, however, difficult to justify the separate recognition of this third class, whether we take the purely formal stand-point, or have regard to the real content of the propositions. From the formal stand-point we might substitute some other symbol, say Q, for not-P, and from this point of view Some S is not-P must be regarded as simply affirmative. On the other hand, Some S is not-P is equivalent in meaning to Some S is not P, and (assuming P to be a positive term) these two propositions must, having regard to their real content, be equally negative in force.
[106] An infinite judgment, in the sense in which the term is here used, may be described as the affirmative predication of a negative. Some writers, however, include under propositiones infinitae those whose subject, as well as those whose predicate, is negative. Thus Father Clarke defines propositiones infinitae as propositions in which “the subject or predicate is indefinite in extent, being limited only in its exclusion from some definite class or idea: as, Not to advance is to recede” (Logic, p. 268).
Some writers go further and appear to deny that the so-called infinite judgment has any meaning at all. This point is closely connected with a question that we have already discussed, namely, whether the negative term not-P has any meaning. If we recognise the negative term—and we have endeavoured to 107 shew that we [ought] to do so—then the proposition S is not-P is equivalent to the proposition S is not P, and the former proposition must, therefore, have just as much meaning as the latter.
The question of the utility of so called infinite propositions has been further mixed up with the question as to the nature of significant denial. But it is better to keep the two questions distinct. Whatever the true character of denial may be, it is not dependent on the use of negative terms.