duration, and begin and cease to exist—can be objects of perception. But the most prominent members of this class are perhaps numbers. It is quite certain that two natural objects may exist; but it is equally certain that two itself does not exist and never can. Two and two are four. But that does not mean that either two or four exists. Yet it certainly means something. Two is somehow, although it does not exist. And it is not only simple terms of propositions—the objects about which we know truths—that belong to this class. The truths which we know about them form, perhaps, a still more important subdivision. No truth does, in fact, exist; but this is peculiarly obvious with regard to truths like ‘Two and two are four,’ in which the objects, about which they are truths, do not exist either. It is with the recognition of such truths as these—truths which have been called ‘universal’—and of their essential unlikeness to what we can touch and see and feel, that metaphysics proper begins. Such ‘universal’ truths have always played a large part in the reasonings of metaphysicians from Plato’s time till now; and that they have directed attention to the difference between these truths and what I have called ‘natural objects’ is the chief contribution to knowledge which distinguishes them from that other class of philosophers—‘empirical’ philosophers—to which most Englishmen have belonged.
But though, if we are to define ‘metaphysics’ by the contribution which it has actually made to knowledge, we should have to say that it has emphasized the importance of objects which do not exist at all, metaphysicians themselves have not recognised this. They have indeed recognised and insisted that there are, or may be, objects of knowledge which do not exist in time, or at least which we cannot perceive; and in recognising the possibility of these, as an object of investigation, they have, it may be admitted, done a service to mankind. But they have in general supposed that whatever does not exist in time, must at least exist elsewhere, if it is to be at all—that, whatever does not exist in Nature, must exist in some supersensible reality, whether timeless or not. Consequently they have held that the truths with which they have been occupied, over and above
