science, philosophy, and theology, the entire discussion may be made up of such propositions or conceptions. Refutation and contradiction in such cases must, therefore, take the form oftotally denying the relation between subject and predicate. This fact, of course, is due to the circumstance that such propositions are singular, and unambiguous in their logical import.
The whole difficulty with ordinary opposition is the fact that it is complicated with two very different properties in propositions which are not related in the same way to opposition. They are the quantity and quality of judgments. In the universal proposition there are both the quantity of the subject and the fact or quality of its connection with the predicate to be dealt with. The denial of the one does not involve the denial of the other, and hence the psychological illusion of mistaking E for the contradictory of A, and vice versa is a very natural one, not being an illusion at all when considered from the standpoint of quality. Thus if I deny the proposition, "All men are trees," I may mean to dispute the universality of its truth, and in that instance I require to prove no more than that "Some men are not trees." But I may also mean to deny the connection between the two conceptions taken as denoting an essential element of identity between them, or as indicating that the essential quality of man is found in trees, or that he could not be man without it. The denial in this case must extend to the whole class, because it in toto denies the essentiality of the connection. Ordinarily, of course, the emphasis upon the quantity of such propositions is so distinct that the denial applies only to their universality, and not to their quality. This liability to illusion does not occur with singular propositions, because their quantity is either invariable or cannot be said to exist at all, so that their quality is the only feature that can be altered by a denial or contradiction. But with the ordinary universal there is both the quantity and the quality to be taken into account, and the denial of the former does not involve the denial of the other. To illustrate, if I deny the proposition, "All men are white," I may mean to
