the same reason untrue of inference, though true of inductive inference, that it is essentially a passage from the known to the unknown. In dealing with the relation of metaphysics to the formal sciences generally, the great difficulty which confronts us is that of determining exactly the boundaries which separate one from another. Among such pure sciences we have by universal admission to include at least two, pure formal logic and pure mathematics, as distinguished from the special applications of logic and mathematics to an empirical material. Whether we ought also to recognize ethics and æsthetics, in the sense of the general determination of the nature of the good and the beautiful, as non-empirical sciences, seems to be a more difficult question. It seems clear, for instance, that ethical discussions, such as bulk so largely in our contemporary literature, as to what is the right course of conduct under various conditions, are concerned throughout with an empirical material, namely, the existing peculiarities of human nature as we find it, and must therefore be regarded as capable only of an empirical and therefore problematic solution. Accordingly I was at one time myself tempted to regard ethics as a purely empirical science, and even published a lengthy treatise in defense of that point of view and in opposition to the whole Kantian conception of the possibility of a constructive _Metaphysik der Sitten_. It seems, however, possible to hold that in the question "What do we mean by good?" as distinguished from the question "What in particular is it right to do?" there is no more of a reference to the empirical facts of human psychology than in the question "What do we mean by truth?" and that there must therefore be a non-empirical answer to the problem. The same would of course hold equally true of the question "What _is_ beauty?" If there are, however, such a pure science of ethics and again of æsthetics, it must at least be allowed that for the most part these sciences are still undiscovered, and that the ethical and æsthetical results hitherto established are in the main of an empirical nature, and this must be my excuse for confining the remarks of the next two paragraphs to the two great pure sciences of which the general principles may be taken to be now in large measure known.