a numerical or geometrical subject-matter. Their usefulness in enabling us to co-ordinate and predict facts of direct experience need no more guarantee their own reality, than the usefulness of such a calculus guarantees our ability to find an intelligible interpretation for all the symbolic operations it involves.[24] In a pure or completed experience, at once all-comprehending and systematic, where existence and content, fact and construction, were no longer separated, there could of course be no place for such ultimately uninterpretable symbolism. Our fundamental metaphysical problem, then, is that of discovering, if we can, the general or formal characteristics of such a complete or “pure” experience, _i.e._ those characteristics which belong to it simply in virtue of its all-containing and completely systematic nature. Further, it would be the work of a completed Metaphysic to ascertain which among the universal characteristics of our own human experience of the world are such as must belong to any coherent experience in virtue of its nature, and are thus identifiable with the formal characteristics of a “pure” experience. Also, our science would have to decide what features of human experience, among those which do not possess this character, approximate most nearly to it, and would thus require least modification in order to enable them to take their place in an absolutely complete and harmonious experience of reality. If we could completely carry out our programme, we should, in the first place, have a general conception of what in outline the constitution of experienced reality as a systematic whole is; and, in the second, we should be able to arrange the various concepts and categories by which we seek, alike in everyday thinking and in the various sciences, to interpret the world of our experience, in an ascending order of degrees of truth and reality, according to the extent to which they would require to be modified before they could become adequate to express the nature of a systematic experienced reality. The knowledge conveyed by such a science would, of course, not be itself the pure or all-embracing experience of Reality, but merely mediate knowledge about the general nature of such an experience, and would therefore, so far, be like all mere knowledge about an object, abstract and imperfect. It would still refer to something beyond itself, and thus have a meaning other than its own existence. But, unlike all other knowledge, our metaphysical knowledge of the formal character of an all-inclusive experienced whole would be _final_, in the sense that no addition of fresh knowledge could modify it in principle. Fresh knowledge, which in all other cases involves at least the possibility of a transformation of existing theories, would here do no more than fill in and make more concrete our conception of the system of Reality, without affecting our insight into its general structure.