deny the universality of the connection between subject and predicate, in which case I could only assure myself that "Some men are not white." But I may mean to deny the connection itself, or the assertion that white is any part of man at all, in which case I should mean that "No men are white." Every such proposition may be interpreted in two ways, in its extension and in its intension. Its extension has to do with the numerical value of the subject, and its intension with the qualificative relation between subject and predicate. The difference between these two aspects of the same proposition can be well illustrated by the difference between the propositions "All men are white" and "Man is white," the former being unmistakably quantitative in its primary meaning and the latter singular and signifying in its primary meaning that white is so essential a quality of man that he cannot exist without it. In the former case the contradictory must be "Some men are not white," and in the latter "Man is not white," this being determined by what is denied in the case. Hence if the universal or quantitative proposition be given the double interpretation, as it well may, it will have two contradictories, one based upon its quantity and the other on its quality. This explains why there is a temptation to regard E as a contradictory of A. Then the fact that propositions like "All men are white" can be conceived as denoting the same as "Man is white," in which the quantitative import is not predominant, shows how the meaning may affect Opposition in determining the relation conceived. Perhaps the case is better illustrated in such propositions as "All the sciences are useful" and "Science is useful." The denial or contradictory of the former might have some of the sciences as useful, but the denial of the latter would not, because it is not only a singular proposition in its real meaning, but indicates what is essential to all the sciences, or that the denial of it must deny the whole in effect. Hence if the universal be given the abstract import, its denial must be of its quality, and not its quantity.
This liability of universal propositions to a double import which permits different contradictions is illustrated in two
