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 180 B. EUSSELL: which, we may observe, the true statement is the following : (1) If x has to y the relation E, y has to x the converse relation ; (2) if all a is b, every term having the relation K to an a has this relation to a b. Leibniz's grammatical studies suggest the reflexion, recommended also by many more general considerations, that philo- sophical theories of Logic have far too much neglected grammar, and that the endeavour to represent actual sentences in accordance with received doctrine would long ago have revealed the importance of many neglected points. Leibniz appears to me to be right in holding that the verb conceals the inmost essence of the proposition, and even of truth itself; but the necessity for particles in his language ought to have shown him the falsity of the subject- predicate logic. Philosophical grammar appears to be a subject of the highest importance ; but, like all other subjects, it has been most shamefully neglected. The construction of a universal language, we saw, was to be based upon the " Alphabet of human thoughts " ; but this required an analysis of all concepts and an inventory of human knowledge. The latter was to be the Encyclopaedia ; the former would give the materials for the universal characteristic. These two projects thus developed out of the attempt to construct a truly philosophic language (p. 79) ; and neither could be carried far without the other, since the characteristic requires the reduction of all scien- tific notions to a logical system, which is the work of the Encyclo- paedia, while this in turn presupposes a determination of the order of scientific truths, which depends upon the characteristic. For this reason, both must be developed and perfected together (p. 80). Chapter iv. explains what the characteristic was to be. It was to consist of a collection of signs which not merely represented ideas, but were to be positive aids to reasoning, like the symbols of Arithmetic and Algebra. Indeed, the characteristic was actually to replace the necessity of reasoning by rules for the manipulation of signs (p. 101). Leibniz attached so much importance to the in- vention of proper symbols that he attributed to this alone the whole of his discoveries in mathematics (pp. 83-4). In this high estimate of symbolism, those who have profited by modern Sym- bolic Logic will be inclined to agree with him ; while the bulk of the learned world will probably continue to agree -with Tschirn- haus, who wrote that he saw no utility in the invention of the Infinitesimal Calculus, and that the introduction of new notations made the sciences difficult (p. 86). The Characteristic was to apply to all strict reasoning, and was to be especially useful in philosophy, where (as Leibniz most justly observes) rigour is more essential than in geometry, because errors are less easily detected (p. 93, note). Leibniz allowed several parallel symbolisms for his logic arithmetical, algebraical, geometrical, and even mechanical for all rational sciences must "symbolise" with each other (p. 116). This rather difficult expression means, I fancy, that, by