writing under the influence of this very confusion, has given wide popularity to the view that the best known of the pure sciences, that of mathematics, depends upon the admission of empirical premises in the form of an appeal to intuition of the kind just described. Fortunately the recent developments of arithmetic at the hands of such men as Weierstrass, Cantor, and Dedekind seem to have definitely refuted the Kantian view as far as general arithmetic, the pure science of number, is concerned, by proving that one and all of its propositions are _analytic_ in the strict sense of the word, that is, that they are capable of rigid deduction from self-evident premises, so that, in what regards arithmetic, we may say with Schröder that the famous Kantian question "how are synthetic judgments _a priori_ possible?" is now known to be meaningless. As regards geometry, the case appears to a non-mathematician like myself more doubtful. Those who hold with Schröder that geometry essentially involves, as Kant thought it did, an appeal to principles not self-evident and dependent upon an appeal to sensuous "intuition," are logically bound to conclude with him that geometry is an "empirical," or as W. K. Clifford called it, a "physical" science, different in no way from mechanics except in the relative paucity of the empirical premises presupposed, and to class it with the applied sciences. On the other hand, if Mr. Bertrand Russell should be successful in his promised demonstration that all the principles of geometry are deducible from a few premises which include nothing of the nature of an appeal to sensuous diagrams, geometry too would take its place among the pure sciences, but only on condition of our recognizing that its truths, like those of arithmetic, are one and all, as Leibniz held, strictly analytical. Thus we obtain as a first distinction between the pure and the empirical sciences the principle that the propositions of the former class are all analytical, those of the latter all synthetic. It is not the least of the services which France is now rendering to the study of philosophy that we are at last being placed by the labors of M. Couturat in a position to appreciate at their full worth the views of the first and greatest of German philosophers on this distinction, and to understand how marvelously they have been confirmed by the subsequent history of mathematics and of logic.