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 KANT'S ANTITHESIS OF DOGMATISM AND CRITICISM. 197 of metaphysics. Demonstration consists in just the process of conceptual analysis whereby the implied content or mean- ing of two concepts is thus brought out with such definite- ness as to make clear to the mind the impossibility of thinking them together, and therefore the necessity of thinking each of them and the opposite of the other together. " Virtually identical " judgments, to be sure, always bring us back ad identical* formales sive expressas, that is, to propositions in- volving two "simple" concepts, the necessary coinherence of which, in the given proposition, is manifest because the opposite of that proposition involves an explicit and literal contradiction : " Manifestum est omnes propositiones neces- sarias ... ad primas veritates revocari possunt, ita ut ap- pareat oppositum implicare contradictionem et cum identica aliqua sive prima veritate pugnare " (Gerhardt vii., p. 300). There is still, it is true, in all this a singular inconsistency, or failure in clear thinking, on the part of Leibniz, which Mr. Bertrand Kussell has already noted (Philosophy of Leibniz, p. 18). If theprimce veritates are literally " identical " propo- sitions A is A, B is not non-B and if other necessary pro- positions are demonstrable only in so far as they are reducible (by the process of definition of the concepts involved) to such primes veritates, then nothing but identical propositions can be really demonstrable at all the principle of contradiction can never help us to prove anything more than that a thing is itself and is not anything not-itself. And again, to note another aspect of Leibniz's confusion if all demonstration consists in definition, and if definition is the analysis of complex concepts into truly simple ones then, once more, between these simple concepts there can be no relations except those of identity and (mere) difference, and therefore no possibility of demonstrating any synthetic truths. For it is not clear how a genuinely simple concept can contain within itself the necessity for the coinherence with itself of other and distinct concepts, or even any special or preferential repugnancies towards any particular other concepts. If the fundamental concepts were really simple in their connota- tive content, they would be a sort of logical atoms, or window- less monads, capable, perhaps, of entering casually and con- tingently into any kind of intellectual combination, but not necessitated by their own nature to enter into (or to refuse) any. And so we could discover no really instructive logical relations between distinct ideas, could find in a given subject no necessary coinherence with any predicate except its own simple and unanalysable self. And so, once more, no truly synthetic judgments a priori would be possible anywhere, 14