paradoxical and abstruse. "What is said to exist," he argues, "is so spoken of because it does exist; and, if so, there is nothing in the universe that does not exist. Similarly, what is said not to exist is so spoken of because it does not exist; and, if so, there is nothing in the universe which is not non-existent." This follows close upon the enunciation of a theory which is not without its bearing upon both speculative and practical mathematics. The argument is, briefly, as follows:—"Subtlety is the occult part of the minute. Be a thing subtle or gross, it seems to me that it must have a form. A formless or unsubstantial thing cannot be distinguished as gross or subtle, discriminate as minutely as you will. What can be spoken of is the gross or palpable part of an entity; what can be imagined only is its subtle part or essence; but I take it that what is neither gross nor subtle can neither be talked of nor imagined." Some time ago there died, at Peking, the greatest Chinese mathematician of the present century. His name was Li Shan-lan, and he was Professor of Mathematics at the T'ung Wen Kuan. But he differed from the mathematicians of Europe in this respect, that he denied the non-existence of a point. A point, said Professor Li, is an infinitesimally small cube; and in saying so he only reproduced the theories put into the mouth of the sophistical God of the Northern Sea, two thousand years ago, by Chuang-tzŭ.
