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334 ROBERT LATTA: exception of his own Monadology. 1 " Spinoza would be right," he says, "if there were no Monads." 2 And it is interesting further to notice that the doctrine of Spinoza which most repelled Leibniz was his denial of final causes, and that in almost every philosophical letter written by Leibniz from 1679 onwards the idea of final cause appears. My purpose in this paper is to consider what light may be thrown upon the two systems and their relation to one another by taking account of the general scientific thought of the time. The dominating science of the seventeenth century was Mathematics, so that for a seventeenth century writer exact scientific method was synonymous with mathematical method. The endeavour to make an exact study of external nature, which was one of the first fruits of the revulsion from Scholasticism, led inevitably to the development of Mathematics as a science of calculation or measurement. Problems which formerly had merely a speculative interest now pressed for immediate solution, and the practical neces- sities of physical science led gradually to the development of new mathematical methods, such as the introduction of the notion of " infinity " by Kepler, the Analytical Geometry of Descartes and the Infinitesimal Calculus of Newton and Leibniz. Both Spinoza and Leibniz were mathematicians and as mathematicians they shared the ideal of their time, that of a mathematically exact and certain system of know- ledge, a comprehensive " scientific " philosophy. They were both interested in mathematical problems, but from some- what different points of view. Spinoza was chiefly impressed with the certainty and necessity of such geometrical demon- stration as that of Euclid, which proceeded from self-evident axioms and unfolded with rigorous truth the attributes of certain objects from precise definitions of them. Leibniz, on the other hand, was more interested in the progress of Mathematics than in the security of its established methods. He sought to grasp the real nature of matter and he found the current Mathematics too abstract to be sufficiently service- able. Atomism (as in Cordemoi, Gassendi and others) ha<f charmed him for a time, and the metaphysical problems of the Eucharist (in connexion with the question of the re- union of Christendom) impelled him from another side to the study of matter. But Atomism represented matter as toe absolutely discrete while Cartesianism made it too smoothly continuous, and some advance in mathematical method was necessary in order to reconcile the discrete and the P. 252. z Lettre a Bourquet (1714), Erdinann, 720 ; Gerhardt, iii., 575.