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HEGEL'S TREATMENT OF THE SUBJECTIVE NOTION. 345 there are no valid and objective laws to be found, that the objective truth lies only in the particular Individuals, that the uniformities we have found, when true, are merely accidental, and that we have no right to assume that they do exist in cases where they have not yet been found. It may be worth while, therefore, to recapitulate the steps which have led us to our present conclusion. The Indi- viduals of which a certain Universal can be predicated must be either isolated or connected. If they are connected it can only be by a second Universal introduced into the Subject. Now this Subject-Universal may either include other Individuals of which the Predicate-Universal is not true, or it may include only those to which the Predicate-Universal does apply. We have thus three cases. The first gives the Singular Judgment, and that we have seen, in the Judgment of Inherence, to lead to contradictions if we try to take it as an independent and adequate form. The second gives the Particular Judgment, which we have also seen to be inadequate as an independent form, since it only predicates the same uncertainty about all the members of a class, al- though the truth is that some of them are certainly one thing, and some of them certainly the other. There remains only the third alternative, and this gives what Hegel calls the Judgment of Allness All things which have the Subject- Universal have the Predicate-Universal. That it is by the Judgment of Allness we are to escape from our difficulty, if we are to escape from it at all, seems clear, since it is the only alternative left. But can we escape in this way ? Does the Judgment of Allness avoid the diffi- culties which made us surrender successively the Singular and the Particular Judgments? The defect of the Particular Judgment is obviously re- moved by it. That defect was that it did not enable us to say definitely of each Individual included in the Subject, whether it did or did not possess the Predicate. But with the Judgment of Allness we can say definitely of each of those Individuals that it does possess the Predicate. The defect of the Singular Judgment lay, as we have seen, in the fact that the Subject and the Predicate could not be regarded as identical. Nor are they identical in the Judg- ment of Allness. If we say All lions are mammals, it is true that there are many mammals which are not lions, and that lions have many qualities not shared by the rest of the mammalia. But we have now risen to a point at which it is no longer necessary to identify the Subject and the Predicate. We do not require to say here that the