Now "the only possible justification of any theory is that it makes things clear and reasonable." In this theory the central and controlling position is that the objectively real relations invade the mind in person and there obtain as the concept.—This doctrine is so far as we can see the original idea of Dr. Abbott and must be considered as his contribution to philosophy. It is by this that his work is to be tested. Does the addition of this new postulate clear up any obscurity?—Is this new postulate one of the assumptions of Science? The truth about this whole matter of universals seems to be that it belongs to the theory of notation primarily, and then to psychology and ontology. The mind proceeds to obtain correspondence with its alternative by analysis and synthesis. The recognition of difference or otherness is an indispensable condition of consciousness itself. One phase of the recognition of difference is that activity called abstraction. But along with difference comes the recognition of what is different from difference, or likeness in all its grades and involutions. The sense of relation, and the impulse of generalisation also arise, and altogether these mentalities become effectual in virtue of some system or some plexus of systems of notation. Long before man ever began to reflect upon his mental operations and the means or tools employed on that behalf, his mental manners and customs had become a second mental nature. What warrant have we for taking these mental manners and customs as the same are reflected in ordinary language as adequate criteria for the world-problems, or even as representative of the very constitutional laws of thought itself? Just as philosophy found it profitable to postpone ontology to psychology, so it is submitted may it again find it profitable to postpone psychology to a study not merely of language but of notation generally, of which the notation of mathematics will undoubtedly be found the most significant. Here we have distinction, abstraction, assimilation, relation, and generalisation carried on and carried out with unchecked thoroughness, and systems of universals ascertained that not only correspond exactly with every acquired and incoming item of our experience, but are also in respect to one another continuous throughout the whole of their range. It will be impossible for any one who once appreciates the nature and competence of mathematical notation to regard any theory of universals relating to ordinary language as a solution of its problem that does not conform to the perfect models set in mathematics.