History of Western Philosophy - Bertrand Russell [336]
Leibniz was a firm believer in the importance of logic, not only in its own sphere, but as the basis of metaphysics. He did work on mathematical logic which would have been enormously important if he had published it; he would, in that case, have been the founder of mathematical logic, which would have become known a century and a half sooner than it did in fact. He abstained from publishing, because he kept on finding evidence that Aristotle's doctrine of the syllogism was wrong on some points; respect for Aristotle made it impossible for him to believe this, so he mistakenly supposed that the errors must be his own. Nevertheless he cherished throughout his life the hope of discovering a kind of generalized mathematics, which he called Characteristica Universalis, by means of which thinking could be replaced by calculation. 'If we had it,' he says, 'we should be able to reason in metaphysics and morals in much the same way as in geometry and analysis.' 'If controversies were to arise, there would be no more need of disputation between two philosophers than between two accountants. For it would suffice to take their pencils in their hands, to sit down to their slates, and to say to each other (with a friend as witness, if they liked): Let us calculate.'
Leibniz based his philosophy upon two logical premisses, the law of contradiction and the law of sufficient reason. Both depend upon the notion of an 'analytic' proposition, which is one in which the predicate is contained in the subject—for instance, 'all white men are men'. The law of contradiction states that all analytic propositions are true. The law of sufficient reason (in the esoteric system only) states that all true propositions are analytic. This applies even to what we should regard as empirical statements about matters of fact. If I make a journey, the notion of me must from all eternity have included the notion of this journey, which is a predicate of me. 'We may say that the nature of an individual substance, or complete being, is to have a notion so completed that it suffices to comprehend, and to render deducible from it, all the predicates of the subject to which this notion is attributed. Thus the quality of king, which belongs to Alexander the Great, abstracting from the subject, is not sufficiently determined for an individual, and does not involve other qualities of the same subject, nor all that the notion of this prince contains, whereas God, seeing the individual notion or haecceity of Alexander, sees in it at the same time the foundation and the reason of all the predicates which can be truly attributed to him, as e.g. whether he would conquer Darius and Porus, even to knowing a priori (and not by experience) whether he died a natural death or by poison, which we can only know by history.'
One of the most definite statements of the basis of his metaphysic occurs in a letter to Arnauld:
'In consulting the notion which I have of every true proposition, I find that every predicate, necessary or contingent, past, present, or future, is comprised in the notion of the subject, and I ask no more.... The proposition in question is of great importance, and deserves to be well established, for it follows that every soul is as a world apart, independent of everything else except God;