Page:Mind (New Series) Volume 12.djvu/198

184 B. RUSSELL : simple concepts is infinite. One or other of these (both of which are true) is involved in the possibility of infinite complexity. I do not know whether Leibniz perceived this, nor, if he did, which of the two he adopted. It is certain that the doctrine of the infinite complexity of contingents belongs to his mature philosophy rather than to his earlier attempts; and M. Couturat's chapter on the Logical Calculus seems to show that his views on the kinds of synthesis did not change sufficiently to allow of infinite complexity resulting from a finite number of concepts. If, then, Leibnix perceived this difficulty at all, he must have abandoned the view which seems to have been rather an unconscious prejudice than a definite opinion that the number of simple concepts is finite. The principle that all truths are analytic is Leibniz's " principle of reason ". This principle is first stated in 1670, in the " Theoria Motus Abstracti " ; it is not, M. Couturat says, a consequence of the law of contradiction, but its complement, for while the one affirms that every identical proposition is true, the other affirms- that every true proposition is analytic, i.e., virtually identical (pp. 214-215). The mutual independence of these two principles which seems to be true in fact, and is suggested, though not explicitly stated, in Leibniz's language has a very curious consequence, not pointed out by M. Couturat. If the principle of reason does not follow from the law of contradiction, it cannot, according to Leibniz's logic, be itself analytic, and is therefore an instance of its own falsity. This proves that, unless we can deduce from the law of contradiction itself that all truths are analytic, there must be at least one truth which is synthetic. The principle of reason, therefore, is either false or a mere consequence of the law of con- tradiction an alternative which we can have no hesitation in deciding. 1 Leibniz speaks sometimes as though the principle of reason were only applicable to contingents. This, M. Couturat rightly remarks, is due to the fact that elsewhere, though applicable, it is not required for demonstration (p. 216). Its universality results from Leibniz's dictum : " We may say, in some sort, that these two principles are contained in the definition of the true and the false " (p. 217). The contingency of all temporal existents results from the definition by infinite complexity through the principle that the cause is the ground of the effect, whence an infinite analysis is required for the a priori proof of temporal propositions (p. 222). The use of the principle of reason in deducing the nature of what actually exists is interesting, but very confused. M. Couturat proves from an unpublished MS. that already in December 1676 Leibniz held that not all possibles exist (p. 219, note) a fact 1 M. Coutnrat tells me that he regards as analytic every proposition which follows from the principles of logic, of which the law of contra- diction is only one. I do not know whether he attributes this position, which solves the above difficulty as well as many others, to Leibniz.