Someone, however, might think this over, and after becoming a Mathematist he might say to himself: “It cannot be a superstition that the color blue has so and so many vibrations. The world is ordered mathematically. If mathematical ideas are found to be real in the world, why should not other ideas have equal reality?‿ Such a person accepts this—that ideas are active in the world. But he grants validity only to those ideas that he discovers outside himself—not to any ideas that he might grasp from his inner self by some sort of intuition or inspiration, but only to those he reads from external things that are real to the senses. Such a person becomes a Rationalist, and his outlook on the world is that of Rationalism. If, in addition to the ideas that are found in this way, someone grants validity also to those gained from the moral and the intellectual realms, then he is already an Idealist. Thus a path leads from crude Materialism, by way of Mathematism and Rationalism, to Idealism.