In passing on to discuss in brief the nature of the boundary lines which divide metaphysics from other branches of study, it seems necessary to start with a clear distinction between the "pure" or "formal" and the "applied" or "empirical" sciences, the more so as in the loose current employment of language the name "science" is frequently given exclusively to the latter. In every-day life, when we are told that a certain person is a "man of science," or as the detestable jargon of our time likes to say, a "scientist," we expect to find that he is, _e. g._, a geologist, a chemist, a biologist, or an electrician. We should be a little surprised to find on inquiry that our "man of science" was a pure mathematician, and probably more than a little to learn that he was a formal logician. The distinction between the pure and the empirical sciences may be roughly indicated by saying that the latter class comprises all those sciences which yield information about the particular details of the temporal order of events physical and psychical, whereas the pure sciences deal solely with the general characteristics either of all truths, or of all truths of some well-defined class. More exactly we may say that the marks by which an empirical is distinguished from a pure science are two. (1) The empirical sciences one and all imply the presence among their premises of empirical propositions, that is, propositions which assert the actual occurrence of some temporal fact, and depend upon the witness of immediate apprehension, either in the form of sense perception or in that of what is commonly called self-consciousness. In the vague language made current by Kant, they involve an appeal to some form of unanalyzed "intuition." The pure sciences, on the other hand, contain no empirical propositions either among their premises or their conclusions. The principles which form their premises are self-evidently true propositions, containing no reference to the actual occurrence of any event in the temporal order, and thus involving no appeal to any form of "intuition." And the conclusions established in a pure science are all rigidly logical deductions from such self-evident premises. That the universality of this distinction is still often overlooked even by professed writers on scientific method seems explicable by two simple considerations. On the one hand, it is easy to overlook the important distinction between a principle which is self-evident, that is, which cannot be denied without explicit falsehood, and a proposition affirmed on the warrant of the senses, because, though its denial cannot be seen to be obviously false, the senses appear on each fresh appeal to substantiate the assertion. Thus the Euclidean postulate about parallels was long falsely supposed to possess exactly the same kind of self-evidence as the _dictum de omni_ and the principle of identity which are part of the foundations of all logic. And further Kant,