(b) Mr Welton repeats several times that a proposition which relates to a non-existent subject must be a mere jumble of words, a predication in appearance only. “That the meaning of a universal proposition can be expressed as a denial is true, but this is not its primary import. And this denial itself must rest upon what the proposition affirms. Unless SaP implies the existence of S, and asserts that it possesses P, we have no data for denying the existence of SPʹ. For if S is non-existent the denial that it is non-P can have no intelligible meaning” (Logic, p. 241). The examples which we have already given are sufficient to dispose of this objection; but it may be worth while to add a further argument. According to Mr Welton, an E proposition implies the existence of its subject but not of its predicate. We cannot then infer PeS from SeP because we have no assurance of the existence of P. But in accordance with the position taken by Mr Welton, we ought to go further and say that PeS must be a mere jumble of words unless we are assured of the existence of P. It is impossible, however, to regard PeS as a mere unmeaning jumble of words, a predication in appearance only, when SeP is a significant and true proposition. PeS may be false, or it may be an unnatural form of statement, but it cannot be meaningless if SeP has a meaning. Take, for example, the propositions—No woman is now hanged for theft in England, No person now hanged for theft in England is a woman. The second of these propositions is false if it is taken to imply that there are at the present time persons who are hanged for theft in England, but how it can possibly be regarded as meaningless I cannot understand.
(c) Miss Jones argues that if some carries with it an implication of existence, when used with a subject-term, it must do so equally when used with a predicate-term; but the predicate of an A proposition being undistributed is practically qualified by some ; hence, if Some S is P implies the existence of S and therefore of P, All S is P must imply the existence of P and therefore of S. In reply to this argument it may be pointed out, first, that a distinction may fairly be drawn without any risk of confusion between a term explicitly quantified by the word some and a term which we can shew to be undistributed but which is not explicitly quantified at all; and, secondly, that the position which we have taken is based upon a consideration of the import of propositions as a whole, not upon the force of signs of quantity considered in the abstract. The irrelevancy of the argument will be apparent if it is taken in connexion with the reasons which we have urged for holding that particulars should be interpreted as implying the existence of their subjects.
163. The Existential Import of Modal Propositions.—Of apodeictic propositions it may be said still more emphatically than of assertoric universals that they do not necessarily imply the existence of their subjects. For they assert a necessary relation between attributes, the ground of which is frequently 245 to be sought in abstract reasoning rather than in concrete experiences. And the same is true of the denial of apodeictic propositions. We may on abstract grounds assert the possibility of a certain concomitance (or non-concomitance) of attributes without having had actual experience of that concomitance (or non-concomitance), and without intending to imply its actuality. Hence we should not interpret the proposition S may be P, any more than the proposition S must be P, as by its bare form affirming the existence of S.
It has been shewn that in order that the propositions All S is P and Some S is not P may be true contradictories, one or other of them must be interpreted as implying the existence of S. It follows, however, from what has been said above that the same condition need not be fulfilled in order that S must be P and S need not be P may be true contradictories.[266]
[266] It is because Dr Wolf identifies the ordinary particular proposition with the problematic proposition that he is led to the conclusion that SaP and SoP are true contradictories although neither of them is interpreted as implying the existence of S.
But to this it has to be added that, in order that these two propositions may be true contradictories, one or other of them must be interpreted as implying the possible existence of S. This line of thought has been suggested in section [160], and it will be pursued farther in sections [176] and [179].
EXERCISES.
164. The particular judgment has, from different stand-points, been identified (a) with the existential judgment, (b) with the problematic judgment, (c) with the narrative judgment. Comment on each of these views. [C.]
The student may find that to write a detailed answer to this question will help to clear up his views respecting the particular proposition. No detailed answer will here be given; but attention may be called to one or two points.
(a) Two kinds of existential judgments may be distinguished.
(i) Those which affirm existence indefinitely, that is, 246 somewhere in the universe of discourse; for example, There are white hares, There is a devil.
(ii) Those which affirm existence with reference to some definite time and place; for example, It rains, I am hungry.
The particular may perhaps be identified with (i), hardly with (ii).
(b) We may be justified in affirming the problematical S may be P, when we cannot affirm the particular Some S is P. There are reasons for interpreting the latter judgment existentially as regards its subject, which do not apply to the former judgment.
(c) The narrative judgment need not have the indefinite character of the particular. We may, however, hold that the two kinds of judgment have this in common that there are grounds for interpreting both existentially as regards their subjects.
165. Discuss the relation between the propositions All S is P and All not-S is P.