What remains of the visible world after deducting its ideal elements is pure space. This, which to some seems the clearest of all conceptions, was to Plato one of the obscurest. He can only describe it as the formless substance out of which the four elements, fire, air, water, and earth, are differentiated. It closes the scale of existence and even lies half outside it, just as the Idea of Good in the _Republic_ transcends the same scale at the other end. We may conjecture that the two principles are opposed as absolute self-identity and absolute self-separation; the whole intermediate series of forms serving to bridge over the interval between them. It will then be easy to understand how, as Aristotle tells us, Plato finally came to adopt the Pythagorean nomenclature and designated his two generating principles as the monad and the indefinite dyad. Number was formed by their combination, and all other things were made out of number. Aristotle complains that the Platonists had turned philosophy into mathematics; and perhaps in the interests of science it was fortunate that the transformation occurred. To suppose that matter could be built up out of geometrical triangles, as Plato teaches in the _Timaeus_, was, no doubt, a highly reprehensible confusion; but that the systematic study of science should be based on mathematics was an equally new and important aperçu. The impulse given to knowledge followed unforeseen directions; and at a later period Plato’s true spirit was better represented by Archimedes and Hipparchus than by Arcesilaus and Carneades. It is remarkable that the spontaneous development of Greek thought should have led to a form of Theism not unlike that which some persons still imagine was supernaturally revealed to the Hebrew race; for the absence of any connexion between the two is now almost universally admitted. Modern science has taken up the attitude of Laplace towards the hypothesis in question; and those critics who, like Lange, are most imbued with the scientific spirit, feel inclined to regard its adoption by Plato as a retrograde movement. We may to a certain extent agree with them, without admitting that philosophy, as a whole, was injured by departing from the principles of Democritus. An intellectual like an animal organism may sometimes have to choose between retrograde metamorphosis and total extinction. The course of events drove speculation to Athens, where it could only exist on the condition of assuming a theological form. Moreover, action and reaction were equal and contrary. Mythology gained as much as philosophy lost. It was purified from immoral ingredients, and raised to the highest level which supernaturalism is capable of attaining. If the _Republic_ was the forerunner of the Catholic Church, the _Timaeus_ was the forerunner of the Catholic faith. IX.