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324 LEIBNITZ suggesting new methods of manufacturing len- ses; to Magliabecchi at Florence, urging him in elegant Latin verses to publish his bibli- ographical discoveries; to the elector of Sax- ony, on the culture of the silkworm ; to Gri- maldi, the Jesuit missionary in China, to im- part his researches in Chinese philosophy, and to prevail on the emperor to introduce his new binary arithmetic, suggesting that the latter may be a key to the book Ye-kim, supposed to contain the mysteries of Fo; to Bossuet and Mme. Brinon concerning the union of the Protestant and Catholic churches, and to Span- heim on the union of the Lutheran and Ke- f ormed ; to Pere des Bosses on transubstantia- tion, and to Dr. Samuel Clarke on time and space ; to Kemond de Montmort on Plato, and to Francke on popular education ; to the queen of Prussia, his pupil, on free will and pre- destination ; to the electress Sophia, her mother, on English politics ; and to the cabinet of Peter the Great on the Slavic and oriental languages. A controversy with Newton concerning the dis- covery of the differential calculus embittered the latter years of his life. There js little doubt that Newton's method of fluxions and Leibnitz's method of infinitesimals were both independent and original discoveries ; but the priority of publication belongs to Leibnitz, who gave a summary of the principles of the dif- ferential calculus in the Acta Eruditorum in 1684. Sir David Brewster's account of this matter, in his "Life of Newton," is, according to the German authorities Gerhart and Guh- rauer, very incomplete, ignoring some impor- tant documents, particularly a letter of Leib- nitz to Oldenburg dated Aug. 27, 1676. The royal society of London appointed a commis- sion to examine the question, whose report, Commercium Epistolicum (1712), was in fa- vor of Newton. This is admitted not to have been impartial, and its deficiencies are shown in a revised edition by Biot and Lefort (1856). The principal metaphysical speculations of Leibnitz are contained in his Theodicee, Nou- veaux essais, Systeme nowveau de la nature (1695), De Ipsa Natura (1698), the fragment on Monadologie (1714), and in portions of his correspondence. He was too much occupied with all the learning of Europe to give a com- plete and systematic development of his opin- ions either in this or any other department. His mind was nurtured in the controversy be- tween the principles of Descartes and Locke, the ultimate tendencies of each of which he was able to perceive, and between which he wished to establish a position. He contro- verted Locke's rejection of innate ideas, by maintaining that, though no ideas be innate, there is yet an innate faculty for forming ideas independent of and superior to sensation. To the old axiom of sensualism, Nihil est in intel- lectu, quod non fuerit prius in sensu, he made the revolutionary addition, nisi ipse intellectus. The mind he compares not to a tabula rasa, a blank tablet, but to a block of marble that has certain characteristic veins in it ; affirms it to contain potentially in itself the general notions of things, which are unfolded as occasions in- vite, the germs of our ideas and of the eternal truths which are derived from them. Those necessary truths, which take their origin not from experience, but primarily from the think- ing soul, are the elements of all knowledge. Thus, unlike that of Locke, the starting point of his philosophy is not the products of sensa- tion, but the laws of the understanding ; and he creates not a system of empiricism, but a system of rationalism. He departs almost equally from the results of Cartesianism as developed by Malebranche and Spinoza. In Descartes the prominence of the idea of the infinite or absolute tends to cast finite nature into the shade. This tendency appears more decidedly in Malebranche, who denied second causes, and limited all real agency to the Su- preme Being, and in Spinoza, who affirmed all thought and substance to be alike parts and modifications of the one sole Existence. Thus the idea of cause was banished from the uni- verse of created things, and all phenomena were regarded only as modes of the divine ac- tion. To avoid this result, to vindicate the notion of causality, was the object which Leib- nitz had in view in declaring all matter to be necessarily active. He affirmed that one body cannot receive the power of acting from any other, but that the whole force is preexistent in itself. He thus substituted in the study of nature the notion of force for that of mode, the form of dynamics for the form of abstract geometry. This principle is the key to his peculiar system. He begins with maintaining that the pure d priori conceptions of the rea- son are full and adequate expressions of ob- jective realities. Logical truth is equivalent to actual truth ; rational possibility is necessarily reality; ideas are identical with things. He introduces the two test principles of contra- diction and sufficient reason, the former ap- plying to the realm of necessary ideas, the latter to that of contingent facts. "Whatso- ever abstract conception involves no con- tradiction with the reason itself is absolutely true. But to determine what ideas are valid in any world of contingent phenomena, in any particular circumstances, there is needed the second principle. For every actual truth a sufficient reason must be rendered, show- ing that it is that which is best adapted to bring about the intended result. Thus every- thing must be judged by its final cause. The Cartesian doctrine, that substance consists essentially in extension, does not explain the constant movements and developments of na- ture. Unless, therefore, every phenomenon be regarded as a direct product of the divine mind, Leibnitz maintains that some inherent, causative, initiative power must be attributed to matter. This power cannot reside in mass- es as such, since they are infinitely divisible, and may therefore be reduced to a zero of ex-