acceptation of lineal diagrams, although sufficiently true for the conclusions of mathematics, does not cut deep enough for a fourth dimension, which, if diagrams are to facilitate our comprehension of it, needs the exact truth of what they postulate. Less than this will leave us where it finds us—"cabined, cribbed, confined" in three dimensions. Professor Zöllner will pardon a little rigor in the interpretation of figures employed to throw light on a theory so occult. For the purpose he has in hand, which lies considerably deeper than the lowest foundation of mathematical reasoning, we are bound to demand that his diagrams shall represent in reality exactly what they purport to represent; that, in plain words, they shall stand for real surfaces without thickness, and real lines without breadth or thickness. But these things do not exist for the human mind. They are incapable of representation in thought. If they were conceivable, they might then assist us to comprehend a fourth dimension, because, if we once cross the absolute limits of conceivability, there is no telling what we might or might not comprehend: presumably new heavens and a new earth would open on us, and certainly a new mind would open in us. But they are not conceivable, and the speculation is idle. For this reason, if no other, Professor Zöllner'sillustrations do not illustrate. They but offer one inconceivable thing to help us conceive another. They begin and end in nothing.
It turns out as was foreseen. Professor Zöllner understands himself even less than he understands Kant. It is very sad; yet the sadness has a silver lining. His merit is greater than he has dreamed. Although evidently a modest man, his modesty can not be spared. He is himself the author of his theory. He owes nothing to Kant. Let justice be done, though the blushes rise. But justice requires another word. Professor Zöllner can not imagine the possibility of the truth of his theory. He can not represent to his own mind the theory itself. It is unthinkable. Not to put too fine a point on it, his theory, in philosophical strictness, is pure nonsense. Let justice be done, though the blushes spread. We are now in a position to answer the question at the head of this paper, and the answer can hardly be put more aptly than in the terms of a definition of metaphysics familiar to every civilized country, and claimed as its own, I believe, by each in turn, if not simultaneously: When Zöllner tells the world what the world can't understand, and what Zöllner doesn't understand himself, that is transcendental physics.