Page:Mind (New Series) Volume 12.djvu/504

 490 G. E. T. BOSS: exclusive we have to prefix "merely" to the terms, should indicate that naturally it is not exclusive. It is, of course, matter of fact that, when we use the judgment symbolised by "A is either B or C," very fre- quently B and C are exclusive, but what I wish to maintain is that this is owing to the nature of those terms, and is not to be inferred from the form of the judgment. When we make a disjunction, we, more often than not, divide a genus into its species, and of course co-ordinate species are mutually exclusive ; they would not be species unless they were exclusive, but frequently the predicate concepts are not of species but of attributes not known to be specific, and then we cannot say that they are exclusive of each other. No doubt one of the aims of science is to divide genera into mutually exclusive species, just as it is to find a rela- tion between subject and predicate in virtue of which we can say not only " All S is P " but " All P is S," i.e. to attain to the predication of property. Now, though in many cases- when we assert that " All S is P " we know that " All P is S," no one maintains that we can infer from the form of the judgment that this is so. But, if logicians like Mr. Bradley consistently applied the principle they adopt in* interpreting the disjunctive judgment, they would have to assert that the universal affirmative, properly employed, is simply convertible. So much for the argument from consistency, but there are- other considerations which go to show how inexpedient it is to treat the disjunctive judgment as necessarily exclusive. It is generally admitted that the force of a disjunction can be partially rendered by hypotheticals. The hypothet- ical do not exhaust its content, for disjunctive judgment is- the union of hypotheticals upon a categoric basis. "A is- either B or C " means that A is positively related to X the underlying identity of both B and C. Though our alter- natives be B and not-B, the mere nomen indefinitum (in which case the disjunction is a priori, merely a particular instance of the law of excluded middle, and can be made, whatever the concept symbolised by B), there is still, I suppose, the underlying identity of Being, the X which pervades both: B and not-B. But commonly B and not-B are merely contradictories within a genus or limited " Universe of Discourse ". In such a case the alternatives are more properly symbolised by b x- and b' x as, for example, in this instance " triangles are either right-angled or not right-angled ". The categorical assump- tion at the basis of this disjunction is that the triangle has-