to deny that he was ever a Zöllnerite at all; and, should he yield to the temptation, the recording angel might fitly blot with a tear the record of the lapse. At all events, Professor Zöllner does not understand Kant.
Does he understand himself? "If from our childhood," he says, "phenomena had been of daily occurrence, requiring a space of four dimensions for an explanation which should be free from contradictions, i. e., conformable to reason, we should be able to form a conception of space of four or more dimensions. It follows that the real existence of a four-dimensional space can only be decided by experience, i. e., by observation of facts." Yes, it all depends on experience, which, as every good Kantist will tell you, furnishes the matter of our cognitions, while the mind furnishes the form, the two elements uniting in the act of cognition; insomuch that the form without the matter is void, as the matter without the form is undetermined. Wherefore, we can have no conception the matter of which has not been furnished by experience, or, as a strict Kantist would say, by sensibility. But what experience, known or conceivable, can furnish the matter of the conception of a fourth dimension? Contradictions, which nothing but a fourth dimension will reconcile, answers Professor Zöllner—such as the tying of knots in endless cords, disappearance and reappearance of solid objects, passage of a shell through a table, impressions of feet on the inner sides of a closed book-slate, and other "contradictions" emerging or appearing to emerge in the presence of Dr. Slade. But contradictions are objects not of the sensitive faculty but of the understanding, and, however amazing, do not furnish new matter of conception; they merely call for new applications or new combinations of the conceptions we have. A knot tied in an endless cord is, so far as presented to us, a phenomenon within three dimensions, and, though we may not know how the knot was tied, our ignorance of the way of tying it can give us no new matter of thought. It is an appeal to our sense, not to our senses; and the office of our sense is to receive and organize the matter of thought, not give it. The mind has no portal through which a fourth dimension can enter, no chamber in which it may lodge. To assume that, because the contradictions in question are irreconcilable, they ipso facto present to our mind a new dimension of space, in the perception of which only they become reconcilable, is to make the simple inexplicability of a problem not only the verification of a given solution of it, but the occasion of a new experience in sense, and a new form in thought—a change, that is, in the constitution of our faculties. If a theory explains a phenomenon, the theory is so far confirmed; but, if the phenomenon is comprehensible only by a theory which is incomprehensible, the phenomenon itself is incomprehensible, and, a sensible person would say, there is an end of it. With Professor Zöllner, however, there is only the beginning of it, the incomprehensibility of the phenomenon,
