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142 ways. First we may call attention to the ambiguities latent in the copula, and second we may compare with it the case of a quantified predicate. In regard to first of these, the universal proposition, "All men are mortal," may only express the empirical fact of mortality in connection with man, and may not imply any thing regarding the nature of that connection. The copula "is," in such cases, expresses no more than a fact. But if the proposition be conceived as identical with "Man is mortal," the copula has a latent implication regarding the nature or the necessity of the connection between man and mortality, so that the denial of it must apply to the whole class, as it would in its equivalent abstract. But in regard to the comparison between ordinary universals and those with a quantified predicate the case is still more clear. Take Hamilton's forms, and the quantified universal would be "All men are all the mortals." Now it is to be noticed that the contradictory of this is not necessarily "Some men are not all the mortals," or "Some men are not mortals," but maybe "All men are not all the mortals." The case depends wholly upon the question whether it is the subject or the predicate that is denied. This is perfectly clear in such propositions, and it only indicates what must hold good in the case between the extensive and the intensive import of any universal judgment. The denial is not necessarily limited to its quantity, that is, the quantity of the subject, but may be applied to the relation between subject and predicate conceived as a necessary one. But apart from the truth of this claim in regard to ordinary universals, there can be no question regarding abstract propositions that are singular in their import. In them the relation between quantity and quality is such that a particular is impossible, and hence the contradictory will take no account of quantity. When the meaning of ordinary universals, therefore, becomes abstract, as it is very often, they are subject to this law.

It does not require any argument to show the value of all this. If a large, and perhaps the largest part of our reasoning, consists of singular, abstract, and universal propositions taken