The universal judgment.—The problem is, then, to discover just the nature and ground of this relation between the internal and external meaning, between the idea and its object. This relation is established in the act of judgment. Taking first the universal judgment, we find here that the internal meaning has at best only a negative relation to the external meaning.
To say that all A is B is in fact merely to assert that the real world contains no objects that are A, but that fail to be of the class B. To say that no A is B is to assert that the real world contains no objects that are at once A and B.[181]
The universal judgments then "tell us indirectly what is in the realm of external meaning; but only by first telling us what is not."[182]
However, these universal judgments have after all a positive value in the realm of internal meaning; that is, as mere thought.
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 mere internal meaning whose external meaning is then to be found. It is found in working with the triangle. It is discovered in the triangle. And, once more, it matters not if the triangle here is a mere memory image. In relation to the purpose, to the logical idea, it is as truly external and objective as pine sticks or chalk marks. The streams of motor, etc., images that flow spontaneously under the stimulus of the purpose are just as immediate fulfilling experiences as the manipulation of sticks or chalk lines.
The difficulty in keeping the universal judgment, as a judgment, in terms of merely internal meaning may be seen from the following:
As to these two types of judgments, the universal and the particular, they both, as we have seen, make use of experience. The universal judgments arise in the realm where experience and idea have already fused into one whole; and this is precisely the realm of internal meanings. Here one constructs and observes the consequences of one's construction. But the construction is at once an experience of fact and an idea.... Upon the basis of such ideal constructions one makes universal judgments. These in a fashion still to us, at this stage, mysterious, undertake to be valid of that other world—the world of external meaning.[185]
One is somewhat puzzled to know just what is meant by the fusion "of experience and idea." We must infer that it means the fusion of some aspect of experience which can be set over against idea, and this has always meant the external meaning, and this interpretation seems further warranted by the statement immediately following which describes the fusion as one "of fact and idea." The situation then seems to be this: An internal and an external meaning, a fact and an idea, "fuse into one whole" and thus constitute that which is yet "precisely the realm of internal meanings," which aims to be valid of still another world of external meanings. And this waives the question of how experience fused into one whole can be an internal meaning, since as such it must be in opposition and reference to an external meaning; or conversely, how experience can be at once fact and idea and still be "fused into one whole."
Nor does the difficulty disappear when we turn to the aspects of universality and necessity. What is the significance and basis of universality and necessity as confined merely to the realm of internal meaning?