This negative character of the universal judgments holds true of them, as we have just said, just in so far as you sunder the external and internal meaning, and just in so far as you view the real as the beyond, and as the merely beyond. If you turn your attention once more to the realm of ideas, viewed as internal meaning, you see, indeed, that they are constantly becoming enriched in their inner life by all this process. To know by inner demonstration that 2+2=4 and that this is necessarily so, is not yet to know that the external world, taken merely as the Beyond, contains any true or finally valid variety of objects at all, any two or four objects that can be counted.... On the other hand, so far as your internal meaning goes, to have experienced within that which makes you call this judgment necessary, is indeed to have observed a character about your own ideas which rightly seems to you very positive.[183] This passage deserves especial attention. In the light of Kant, and in view of Mr. Royce's general definition of the judgment as the reference of internal to external meanings, one is puzzled to find that for the mathematician the positive value of the judgment "two and two are four" is confined to the realm of internal meaning. To be sure, Mr. Royce says that this limitation of the positive value of the universal judgment to the world of internal meaning occurs only when the external and internal meaning are sundered. But the point is: Does the mathematician or anyone else ever so sunder as to regard the judgment "two and two are four" as of positive value only as internal meaning? Indeed, in another connection Mr. Royce himself shows most clearly that mathematical results are as objective and as empirical as the astronomer's star.[184] Nor would it appear competent for anyone to say here: "Of course, they are not internal meanings _after_ we come to see, through the kind offices of the epistemologist, that the internal meanings are valid of the external world." We are insisting that they are never taken by the mathematician and scientists at first as merely internal meaning whose external meaning is then to be established. Surely the mathematical judgment, or any other, does not require an epistemological midwife to effect the passage from internal to external meaning. The external meaning is there all the while in the form of the diagrams and motor tensions and images with which the mathematician works. The difficulty here again seems to be that the distinction above discussed between the idea in the logical sense, as purpose, and the immediate fulfilling experience is lost sight of. The relation between two and four is not first discovered as a merely internal meaning. It is discovered in the process of fulfilling some purpose involving the working out of this relation. So the sum of the angles of a triangle is not discovered as a