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of unpublished manuscripts, to which was brought, what is abso- lutely essential, a wide and thorough knowledge of modern mathe- matics Symbolic Logic, Arithmetic and Geometry. Without such knowledge, it is impossible to appreciate the merit of attempts which have not succeeded, to know why they failed, or to realise that success was possible and of the highest moment. Three objects are served by M. Couturat's work. The first, which he mentions as the chief, is to show that " Leibniz's metaphysic rests solely upon the principles of his Logic, and proceeds entirely from them " (p. x.). The second is to set forth precisely what his Logic was, and the third is to show its connexion with the various projects of a universal characteristic, a universal language, a universal mathematics, etc., which Leibniz cherished throughout his life. In all three objects, as it seems to me, although some of the principal conclusions absolutely contradict received opinions, the work is completely successful. Perhaps the most revolution- ary conclusion in the whole book is, that the principle of reason, for all its trappings of teleology and Divine goodness, means, no more than that, in every true proposition, the predicate is con- tained in the subject, i.e., that all truths are analytic (p. x.). In face of the evidence adduced, this conclusion, startling as it is, appears to be quite irrefutable. 1 The work is divided into nine chapters, dealing respectively with Syllogistic, the Ars Combinatoria, the Universal Language, the Universal Characteristic, the Encyclopaedia, the Scientia Generalis, the Universal Mathematics, the Logical Calculus, and the Geometrical Calculus. All these projects are shown to be interconnected, and to spring from a common logical root. Some have been proved by time to be chimerical, while others notably the three last are now actually constituted, two of them very much as Leibniz endeavoured to constitute them. The common logical source of his doctrines consists, as M. Couturat points out, of two postulates : (1) All ideas are compounded of a very small number of simple ones, forming the Alphabet of human thoughts ; (2) complex ideas proceed from these simple ones by a uniform and symmetrical method of combination analogous to arithmetical multiplication (p. 431). Both these postulates are of course false ; but while in some regions their falsity is disastrous, in others it is only unfortunate. Two other errors, less fundamental, but perpetually recurring, are pointed out by M. Couturat, and are attributed by him (p. 438) to an almost unconscious respect for Aristotle. The first of these, which was only a defect of method, consisted in a preference for taking syllogisms in intension rather than extension ; the second, which rendered Leibniz's attempts to found the logical calculus abortive, was the failure to realise the fallacy in such moods as Darapti and in the scholastic doctrine of 1 In my Philosophy of Leibniz, chap, iii., I gave a different interpre- tation, which M. Couturat's work has persuaded me to abandon.