Take another line and divide it into two parts, one representing our ideas, the ordinary occupants of our minds, such as whiteness, equality, and the other representing our true knowledge, which is of eternal principles, such as beauty, goodness. A^1 B^1 ——————————————————————————————|————————————————————————————————- Eternal principles, Appearances in the mind, as beauty as whiteness, equality Then as A is to B, so is A^1 to B^1 That is, the soul can proceed, going away from real things to a region of perfect certainty, where it beholds what is, not the scattered reflections; beholds the sun, not the glitter on the sands; true being, not chance opinion. Now, this is to us, as it was to Aristotle, absolutely inconceivable from a scientific point of view. We can understand that a being is known in the fulness of his relations; it is in his relations to his circumstances that a man’s character is known; it is in his acts under his conditions that his character exists. We cannot grasp or conceive any principle of individuation apart from the fulness of the relations to the surroundings. But suppose now that Plato is talking about the higher man—the four-dimensional being that is limited in our external experience to a three-dimensional world. Do not his words begin to have a meaning? Such a being would have a consciousness of motion which is not as the motion he can see with the eyes of the body. He, in his own being, knows a reality to which the outward matter of this too solid earth is flimsy superficiality. He too knows a mode of being, the fulness of relations, in which can only be represented in the limited world of sense, as the painter unsubstantially portrays the depths of woodland, plains, and air. Thinking of such a being in man, was not Plato’s line well divided? It is noteworthy that, if Plato omitted his doctrine of the independent origin of ideas, he would present exactly the four-dimensional argument; a real thing as we think it is an idea. A plane being’s idea of a square object is the idea of an abstraction, namely, a geometrical square. Similarly our idea of a solid thing is an abstraction, for in our idea there is not the four-dimensional thickness which is necessary, however slight, to give reality. The argument would then run, as a shadow is to a solid object, so is the solid object to the reality. Thus A and B´ would be identified. In the allegory which I have already alluded to, Plato in almost as many words shows forth the relation between existence in a superficies and in solid space. And he uses this relation to point to the conditions of a higher being.