Experience has shown where the dream of universal mathematics leads us. Number is driven to the heart of phenomena and nature dissected with this delicate scalpel. Speaking in more general terms, we adopt spatial relation as the perfect example of intelligible relation. I do not wish to deny the use of such a method now and again, the services it may render, or the beauty of construction peculiar to the systems it inspires. But we must see what price we pay for these advantages. Do we choose geometry for an informing and regulating science? The more we advance towards the concrete and the living, the more we feel the necessity of altering the pure mathematical type. The sciences, as they get further from inert matter, unless they agree to reform, pale and weaken; they become vague, impotent, anaemic; they touch little but the trite surface of their object, the body, not the soul; in them symbolism, artifice, and relativity become increasingly evident; at length, arbitrary and conventional elements crop up and devour them. In a word, the claim to treat the living as inert matter conduces to the misconception in life of life itself, and the retention of nothing but the material waste. This experience furnishes us with a lesson. There is not so much one science as several sciences, each distinguished by an autonomous method, and divided into two great kingdoms. Let us therefore from the outset follow Mr Bergson in tracing a very sharp line of demarcation between the inert and the living. Two orders of knowledge will thereby become separate, one in which the frames of geometrical understanding are in place, the other where new means and a new attitude are required. The essential task of the present hour will now appear to us in a precise light; it will henceforward consist, without any disregard of a glorious past, in an effort to found as specifically distinct methods of instruction those sciences which take for objects the successive moments of life in its different degrees, biology, psychology, sociology;--then in an effort to reconstruct, setting out from these new sciences and according to their spirit, the like of what ancient philosophy had attempted, setting out from geometry and mechanics. By so doing we shall succeed in throwing knowledge open to receive all the wealth of reality, while at the same time we shall reinstate the sense of mystery and the thrill of higher anxieties. A further result will be that the phantom of the Unknowable will be exorcised, since it no longer represents anything but the relative and momentary limit of each method, the portion of being which escapes its partial grip.