[Alfred Edward Taylor, Frothingham Professor of Philosophy, McGill University, Montreal, Canada. b. Oundle, England, December 22, 1869. M.A. Oxford. Fellow, Merton College, Oxford, 1891-98, 1902-; Lecturer in Greek and Philosophy, Owens College, Manchester, 1896-1903; Assistant Examiner to University of Wales, 1899-1903; Green Moral Philosophy Prizeman, Oxford, 1899; Frothingham Professor of Philosophy, McGill University, 1903-; Member Philosophical Society, Owens College, American Philosophical Association. Author of _The Problem of Conduct_; _Elements of Metaphysics_.] When we seek to determine the place of metaphysics in the general scheme of human knowledge, we are at once confronted by an initial difficulty of some magnitude. There seems, in fact, to be no one universally accepted definition of our study, and even no very general consensus among its votaries as to the problems with which the metaphysician ought to concern himself. This difficulty, serious as it is, does not, however, justify the suspicion that our science is, like alchemy or astrology, an illusion, and its high-sounding title a mere "idol of the market-place," one of those _nomina rerum quae non sunt_ against which the Chancellor Bacon has so eloquently warned mankind. If it is hard to determine precisely the scope of metaphysics, it is no less difficult to do the same thing for the undoubtedly legitimate sciences of logic and mathematics. And in all three cases the absence of definition merely shows that we are dealing with branches of knowledge which are, so to say, still in the making. It is not until the first principles of science are already firmly laid beyond the possibility of cavil that we must look for general agreement as to its boundary lines, though excellent work may be done, long before this point has been reached, in the establishment of individual principles and deduction of consequences from them. To revert to the parallel cases I have just cited, many mathematical principles of the highest importance are formulated in the _Elements_ of Euclid, and many logical principles in the _Organon_ of Aristotle; yet it is only in our own time that it has become possible to offer a general definition either of logic or of mathematics, and even now it would probably be true to say that the majority of logicians and mathematicians trouble themselves very little about the precise definition of their respective studies.