RECENT WORK ON THE PHILOSOPHY OF LEIBNIZ. 183 of the analytic theory of truth and of the whole subject-predicate logic. That Leibniz held all truths, not only the necessary ones, to be analytic, is proved by many passages which M. Couturat quotes (see p. 208 ff.). This principle, that the predicate is always con- tained in the subject, is held to be the foundation of Leibniz's metaphysic (p. 209, note) a thesis which is amply demonstrated in a separate article. 1 Every truth is either formally or virtually identical, and consequently has its a priori proof ; but in the case of truths of fact, this proof requires an infinite analysis, which God alone can accomplish. Contingent truths, as Leibniz is fond of remarking, resemble incommensurables ; the exact point of re- semblance is that both involve an infinite series. The view that propositions which are analytic may i not be necessary is strangly paradoxical, and brings out with startling clearness the hopeless inconsequence involved in Leibniz's doctrine of contingency, with its tiresome progeny of final causes, liberty, and optimism. Nevertheless the following passage, quoted by M. Couturat from an unpublished MS. (EMM, p. 11, note), leaves it beyond doubt that the above was really his view : " Ita arcanum aliquod a me evolutum puto, quod me diu perplexum habuit, non intelligentem, quomodo praedicatum subjecto inesse posset, nee tamen propositio fieret necessaria. Sed cognitio rerum geometricarum atque analysis mnnitorum hanc mihi lucem accendere, ut intelligerem, etiam notiones in infinitum resolubiles esse." 2 The view which Leibniz held in youth, namely that the number of simple concepts is finite, and that there is only one kind of synthesis of concepts, involves the consequence that the total number of concepts is finite. For, owing to the law of tautology, nothing is gained by the repetition of a concept in a complex in which it already occurs ; hence if n be the number of simple concepts, 2 n - 1 will be the total number of concepts, both simple and complex. This con- sideration alone should have led Leibniz to reflect either that there is more than one kind of synthesis, or that the number of 1 " Sur la me'taphysique de Leibniz (avec un opuscule inedit)," Revue de Metaphysique et de Morale, January, 1902. I shall refer to this article in future as EMM. 2 The view that infinite complexity is the defining property of the contingent has the curious consequence that truths about possible sub- stances are contingent. For any substance that might have existed in a possible world (since all possible worlds involve time) would have had the same infinite complexity as actual substances have. I imagine Leibniz would have replied that individual substances as opposed to generic and specific notions are known to us only by experience, which requires actual existence ; what we can know a priori never has infinite complexity, and hence we cannot have the notion of any one particular possible substance in a possible world, unless this substance actually exists. The infinite complexity required for particularising a substance exists confusedly in perception, but does not exist at all in our knowledge of possible non-existent substances.
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