fourfold necessity corresponding to the four forms of the principle of sufficient reason: – (1.) The logical form, according to the principle of the ground of knowledge; on account of which, if the premisses are given, the conclusion follows. (2.) The physical form, according to the law of causality; on account of which, if the cause is given, the effect must follow. (3.) The mathematical form, according to the law of being; on account of which every relation expressed by a true geometrical proposition is what it is affirmed to be, and every correct calculation is irrefutable. (4.) The moral form, on account of which every human being and every brute must, when the motive appears, perform the only act which accords with the inborn and unalterable character. A consequence of this is, that every department of science has one or other of the forms of the principle of sufficient reason as its basis. In conclusion, Schopenhauer points out that just because the principle of sufficient reason belongs to the a priori element in intelligence, it cannot be applied to the entirety of things, to the universe as inclusive of intelligence. Such a universe is mere phenomenon, and what is only true because it belongs to the form of intelligence can have no application to intelligence itself. Thus it is that it cannot be said that the universe and all things in it exist because of something else. In other words, the cosmological proof of the existence of God is inadmissible.
