or that object exists in his new world at all. And meanwhile, despite this eternity and this relative independence of private ideas which characterize the mathematical objects, and give the world of Forms unity, the objects and the forms exist, if at all, not as the atoms and monads of realism exist, nor as the things in themselves of Kant. For nobody, according to Realism, is able to discover the things in themselves, the supposed entities of Realism, by any process of consciously free ideal construction, such as in fact produces the mathematician’s ideas. On the other hand, the mathematical beings undertake to be real just as objects of possible thought, as valid truths, and not as independent of all thinking processes, whether actual or possible.
These contrasts and problems may weary. But it is necessary to face them. The world of validity is indeed, in its ultimate constitution, the eternal world. It seems to us so far a very impersonal world and a very cold and unemotional realm, — the very opposite of that of the mystic. Before we are done with it we shall find it in fact the most personal and living of worlds. Just now it appears to us a realm of bodiless universal meanings. Erelong we shall discover that it is a realm of individuals, whose unity is in One Individual, and that theory means, in this eternal world, not mere theory, but Will and Life.
