Leibniz takes a middle position, he says, between those who consider this a demonstrative argument, and those who regard it as a mere paralogism. It is pre-supposed by this argument that the notion of a Supreme Being is possible, or that it does not involve contradiction. This pre-supposition is to be proved. First, it is well to simplify the argument itself. The Cartesian definition may be reduced to this: "God is a being in whom existence and essence are one. From this definition it follows as a corollary that such a being, if possible, exists. For the essence of a thing being just that which constitutes its possibility, it is evident that to exist by its essence is the same as to exist by its possibility. Being in itself, then, or God, may be most simply defined as the Being who must exist if he is possible." There are two ways of proving this last clause (namely, that he is possible) the direct and the indirect. The indirect is employed against those who assert that from mere notions, ideas, definitions or possible essences, it is not possible to infer actual existence. Such persons simply deny the possibility of being in itself. But if being-in-itself, or absolute being, is impossible, being-by-another, or relative, is also impossible; for there is no "other" upon which it may depend. Nothing, in this case, could exist. Or if necessary being is not possible, there is no being possible. Put in another way, God is as necessary for possibility as for actual existence. If there is possibility of anything, there is God. This leads up to the direct proof; for it follows that, if there be a possibility of God,--the Being in whom existence and essence are one,--he exists. "God alone has such a position that existence is necessary, if possible. But since there can be nothing opposed to the possibility of a being without limit,--a being therefore without negations and without contradiction,--this is sufficient to prove _a priori_ the existence of God." In short, God being pure affirmation, pure self-identity, the idea of his Being cannot include contradiction, and hence is possible,--and since possible, necessary. Of this conception of God as the purely self-identical, without negation, we shall have something to say in the next chapter.