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] is a virtue," and in order to give this statement a quantitative meaning I must conceive it as denoting "All individual cases of charity are virtuous." But this is not what I necessarily mean by my proposition. The abstract form means to convey the idea that the essential quality of concrete instances is virtuous or a virtue. So when I say "Science is useful," I do not necessarily mean that "All sciences are useful," but only that the method at the basis of the concrete sciences is useful, and this is by its very nature a singular quality or object. Abstract propositions, therefore, such as "Charity is virtuous," "Psychology is a mental science," "Truth is valuable," must be treated as singulars, and so can have only contradictories and neither contraries nor subalterns. Thus the contradictories of the above would be "Charity is not virtuous," "Psychology is not a mental science," etc. Nor will it do to reply to this claim, that the true contradictories are "Some charity is not virtuous," "Some truths are not valuable," because, while this may be true with a change of interpretation of the original propositions, it does not apply to the conceptions expressed by them as abstract propositions. The rejoinder to any such claim would be that the concrete cases denoted by the terms "some charity," "some truths," etc., are not instances of "charity" or "truth" at all, taken in the abstract sense, but only denominations of their incidents. That is only to say that the terms are used in different senses and so cannot be properly compared for logical purposes. It is not to be denied that such propositions can be given a universal import to suit the rules. But the fact that they are ambiguous and can just as well be interpreted as abstract singular propositions shows that in the latter interpretation they must come under the special law of opposition applicable to such cases.

The importance attaching to such facts is that the proportion of discourse turning upon the use of abstract propositions is so great that the ordinary courses of opposition do not apply to it. This proportion is much greater than that of the concrete singular propositions. Within the domain of pure