Leibniz has, however, a complete philosophy of nature. In his other writing, he explains the ideas of matter and force in their dependence upon his metaphysic, or doctrine of spiritual entelechies. The task does not at first sight appear an easy one. The reality, according to Leibniz, is purely spiritual, does not exist in space nor time, and is a principle of activity following its own law,--that of reflecting the universe of spiritual relations. How from this world of ideal, unextended, and non-temporal dynamic realities we are to pass over to a material world of extension, with its static existence in space, and transitory passage in time, is a question challenging the whole Leibnizian system. It is a question, however, for which Leibniz himself has provided an answer. We may not regard it as adequate; we may think that he has not truly derived the material world from his spiritual principles: but at all events he asked himself the question, and gave an answer. We shall investigate this answer by arranging what Leibniz has said under the heads of: matter as a metaphysical principle; matter as a physical phenomenon; and the relation of phenomena to absolute reality, or of the physical to the metaphysical. In connection with the second head, particularly, we shall find it necessary to discuss what Leibniz has said about space, time, and motion. Wolff, who put the ideas of Leibniz into systematic shape, did it at the expense of almost all their significance. He took away the air of paradox, of remoteness, that characterized Leibniz's thought, and gave it a popular form. But its depth and suggestiveness vanished in the process. Unfortunately, Wolff's presentations of the philosophy of Leibniz have been followed by others, to whom it seemed a dull task to follow out the intricacies of a thought nowhere systematically expressed. This has been especially the case as concerns the Leibnizian doctrine of matter. A superficial interpretation of certain passages in Leibniz has led to an almost universal misunderstanding about it. Leibniz frequently says that since matter is composite or complex, it follows that there must be something simple as its basis, and this simple something is the monad. The misinterpretation just spoken of consists in supposing that Leibniz meant that matter as composite is made up of monads as simple; that the monad and matter are facts of the same order, the latter being only an aggregate, or continued collection of the former. It interpreted the conception of Leibniz in strict analogy with the atomic theory of Lucretius, excepting that it granted that the former taught that the ultimate atom, the component of all complex forms of matter, has position only, not extension, its essence consisting in its exercise of force, not in its mere space occupancy. The monad was thus considered to be _in_ space, or at least conditioned by space relations, as is a mathematical point, although