Page:Mind (New Series) Volume 6.djvu/364

 J. ELLIS MCTAGGART : the qualities of every A. A, of course, has other qualities. Let these other qualities be called X. Then it is at once clear that, if anything is X, it is B. Here we have the Hypothetical Judgment. The advance, such as it is, con- sists in eliminating the slight suggestion of Subsumption, which remains even in the Categorical Judgment, and so bringing out more clearly the necessary connexion between Universals which is the essence of the Judgment of Neces- sity. Disjunctive Judgment. It is clear that Categorical and Hypothetical Judgments do not admit of simple conversion. It does not follow because all A is B, that all B will be A. It may be so in some cases, but we can never logically advance from the one statement to the other. And we know that in all cases it cannot be so. For if all Judgments were simply convertible a Universal could never be connected by them with any Universal wider than itself. And thus we could never express by Universals the relation between two Individuals which resembled one another in some points but not in others. And since we saw that the nature of Individuals could only be expressed by Universals, this involves that such a relation could not be expressed at all. And, as it has already been shown that every Individual must be like and unlike every other, it follows that it would be impossible by such Judgments to express the nature of Individuals at all. We know, therefore, that in some of our Judgments of Necessity the Predicate will be wider than the Subject. All A are B, but there are some B which are not A. Now these Individuals which are not A cannot be B as simply isolated Individuals, as was proved above. Each of them must have some Universal, with which B is invariably connected by another Categorical Judgment. How many of these there may be we do not know, but we know that every case of B must have one of them. Thus we arrive at the conclusion, all B is either A, or C, or D, where C and D represent an unknown number of Universals. This is the Disjunctive Judgment. The view of the universe which results from the estab- lishment of the validity of this category can be stated as follows : The similarities and dissimilarities of Individuals may be expressed by general propositions concerning the relations of Universals of different extent, which are such that the presence of the narrower Universal implies the