Page:Mind (New Series) Volume 12.djvu/200

186 B. RUSSELL : reason is quite plain from the discussion in Gerh., vii., p. 194, where it is laid down that " the first truth of fact, from which all experi- ences can be proved a priori, is this, namely : Everything possible demands that it should exist ". And this principle is proved by observing that, unless there were some inclination to exist involved in essence itself, nothing would exist, since no reason can be given vwhy some essences should demand existence rather than others. Thus essences range themselves in the conflict on the side of those with which they are compossible, and a tug of war results, in which the majority are victorious. An interesting conflict of ghosts all hoping to become real ! But it is hard to see what God has to do in that galere. Sciences dealing with actual existents, as appears from the above theory, were for Leibniz just as a priori as other sciences. Immediate internal experiences are first truths for us, but not .absolutely ; experience is only confused reason (pp. 256, 259). Induction, as understood by empiricists, is absolutely condemned by Leibniz, as insufficient and even misleading (p. 261). Deduc- tion is for him the only method, and abstract mathematics is the true logic of the natural sciences (p. 271). These views are not in harmony with those of most modern logicians, but I cannot help thinking, with M. Couturat (p. 271 note), that there is no valid inference which is not deduction, and that induction, in so far as it is not disguised deduction, is merely a method of making more or less plausible guesses. Where Leibniz erred was, not in in- sisting that deduction is the only method of inference, but in failing to realise that the number of independent premisses, obtainable only, if at all, by immediate inspection, instead of being two, is strictly infinite. Chapter vii. deals with Universal Mathematics a subject which appears to be precisely identical with what Mr. Whitehead has called Universal Algebra. Although M. Couturat deals with this subject in a different chapter from that devoted to the Logical Calculus, he does not clearly state, any more than Leibniz does, regarded " truths of fact " as analytic in 1686, when his system was new and he had not yet forgotten his reasons for it. In later years, however, expressions occur which are difficult to reconcile with this view, such as : "Truths of fact are contingent and their opposite is possible" (1714; Gerh., vi., 612) ; " A truth is necessary when the opposite implies contra- diction ; and when it is not necessary, it is called contingent " ( 1 707 ; Gerh., iii., 400) ; " when any one has chosen in one way, it would not imply a contradiction if he had chosen otherwise" (1711 ; Gerh., ii., 423). Such passages can only be reconciled with M. Couturat's view by the distinction between explicitly and implicitly analytic propositions ; where an infinite analysis, which only God can perform, is required to exhibit the contradiction, the opposite will seem to be not contradictory. The only other escape I can imagine, which appears to be that favoured by M. Couturat, would be to suggest that the denial of an analytic truth might be not self -contradictory ; this mode of escape, however, would not, I think, commend itself to Leibniz.