falsity of which is a proper subject for metaphysical investigation. Thus the arguments by which it has been sought to demonstrate the impossibility of Metaphysics themselves afford unimpeachable evidence of the necessity for the scientific examination of the metaphysical problem.[6] § 7. With the other two anti-metaphysical contentions referred to at the beginning of the last section we may deal much more briefly. (2) To the objector who maintains that Metaphysics, if possible, still is useless, because the sciences and the practical experience of life between them already supply us with a coherent theory of the world, devoid of contradictions, we may reply: (_a_) The fact is doubtful. For, whatever may be said by the popularisers of science when they are engaged in composing metaphysical theories for the multitude, the best representatives of every special branch of mathematical and experimental science seem absolutely agreed that ultimate questions as to first principles are outside the scope of their sciences. The scope of every science, they are careful to remind us, is defined by certain initial assumptions, and what does not fall under those assumptions must be treated by the science in question as non-existent. Thus Mathematics is in principle restricted to dealing with the problems of number and quantity; whether there are realities which are in their own nature non-numerical and non-quantitative[7] or not, the mathematician, as mathematician, is not called upon to pronounce; if there are such realities, his science is by its initial assumptions debarred from knowing anything of them. So again with Physics; even if reduced to pure Kinematics, it deals only with displacements involving the dimensions of length and time, and has no means of ascertaining whether or not these dimensions are exhibited by all realities. The notion that the various sciences of themselves supply us with a body of information about ultimate reality is thus, for good reasons, rejected by their soundest exponents, who indeed are usually so impressed with the opposite conviction as to be prejudiced in favour of the belief that the ultimately real is unknowable. (_b_) Again, as we have already seen, the results of physical science, and the beliefs and aspirations which arise in the course of practical experience and take shape in the teachings of poetry and religion, often appear to be in sharp antagonism. “Science” frequently seems to point in one direction, our deepest ethical and religious experience in another. We cannot avoid asking whether the contradiction is only apparent or, supposing it real, what degree of authority belongs to each of the conflicting influences. And, apart from a serious study of Metaphysics, this question cannot be answered. (_c_) Even on the most favourable supposition, that there is no such contradiction, but that science and practical experience together afford a single ultimately coherent theory of the world, it is only after we