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RECENT WORK ON THE PHILOSOPHY OF LEIBNIZ. 179 conversion and subalternation, which results from wrongly assign- ing existential import to universal terms (pp. 32, 348 ff.). These errors are already set forth in the first chapter, together with certain technical improvinents which Leibniz suggested in the treatment of syllogisms. The second chapter deals with the De Arte Combinatoria, which Leibniz published at the age of twenty. The art suggested consists in analysing all concepts by reducing them to simpler concepts, until at last we reach certain simple indefinable concepts: these will be the terms of the first order. Every composite term will then be represented by the symbolic product of its constituent simple terms, which will constitute its definition. The predicates of a term are its factors, and the subjects of which it can be affirmed are its multiples. Here already, as M. Couturat remarks (pp. 48-49), we find Leibniz's leading ideas. The third chapter points out that the characteristic was at first conceived by Leibniz as a universal language, not as an Algebra. This language was to be simple, because it was to be based on a logical foundation, i.e. on a complete analysis of concepts : for every simple concept there was to be a symbol. "When he first hoped for an Algebra of thought, he identified this with his universal language. This was his view in 1676 ; but four years later he distinguishes his language from every kind of Calculus (pp. 61, 78). He had a device by which the syllables of a word could be permuted without change of meaning; this, he says (p. 63), would give great facility for verse or music, enabling very beautiful songs and poems to be composed by an infallible and quasi-demonstrative method ! For the purpose of his universal language, he undertook a grammatical analysis. He rightly de- cided that inflexions are to be avoided as far as possible, and that the philosophic language should be analytic. Nouns, he says, express ideas, while verbs express propositions, and particles (though this is not so clearly said) express relations (pp. 69, 71, 72). Besides adjectives and particles, he says, we require only one noun, ens, and one verb. est. He has great difficulty in the treatment of the genitive, and in other forms involving relations not reducible to predication. In all his grammatical analysis, he has a logical purpose, namely the justification of the asyllogistic inferences which he had learnt to study from Jungius. Two types of these occupied him, namely the inversion of relations (David was the father of Solomon, therefore Solomon was the son of David), and inferences from the direct to the oblique, such as : A horse is an animal, therefore the head of a horse is the head of an animal (this is not Leibniz's instance, but, I think, Jevons's). His grammatical analysis, as M. Couturat remarks (p. 437), gave him the materials for a logic of relations ; but out of respect for scholastic tradition, he regarded these materials as merely grammatical, and made no logical use of them. Thus he was una ^e to symbolise the above two types of inference, of