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356 J. ELLIS MCTAGGAET : to unite and to differentiate everything in the universe, their ultimate connexions must, in some cases at least, be between Universals of different extent. It will happen then with Categorical Laws, as it did with Categorical Judgments, that in some cases the Predicate-Universal will be wider than the Subject-Universal. The Individuals included under this further extent of the Predicate, must be connected with it by one or more other Subject- Universals. And so, by enume- rating all the narrower Universals which come under a wider one, we get the Disjunctive Law the final form of the Subjective Notion. Here we have the essentially Hegelian idea of the self- differentiating Notion. The phrase is a rather alarming one, and seems to suggest mysterious and recondite activity. But the reality is simple. It means nothing but a Universal, which is always accompanied by one of a certain number of subordinate Universals which are not deducible from it, but which are peculiar to it. Thus, if we take the co-existence of the chief characteristics of animals as an ultimate truth, we may get the Law All vertebrates are either mammals or fish (leaving out the other sub -classes for the sake of brevity). Every vertebrate will have one of these additional qualifications. They are not deducible from the mere idea of a vertebrate animal, in which there is nothing which would prevent all vertebrates from being mammals, or some of them from belonging to some sub- class which does not in fact exist. And the sub-classes are peculiar to the class, for there are no mammals or fish which are not verte- brate. This is the connexion of Universals which has been rendered necessary by the conception of Individuals as simi- lar and dissimilar with which the Subjective Notion started. The conception of a self-differentiating Notion has been rather misunderstood. It is sometimes supposed to mean that a Universal when it is one of the ultimate Universals which enter into Laws of Nature splits itself up by pure thought in the same way that the dialectic advances by pure thought. You have only to take the idea of a class and examine it with sufficient care, and it will proceed to develop the ideas of its sub-classes. In fact, the old story of the German who conducted his zoological studies by endeavour- ing to evolve the idea of a camel out of his inner conscious- ness, is scarcely a parody of what is supposed by some people to be Hegel's theory on this subject. Such a theory is obviously incorrect, nor do I believe that there is the slightest evidence for the view that it was Hegel's. The only case in which Hegel professes to evolve