He tells us further that all clear ideas are true—that whatever is clearly and distinctly conceived is true—and in these lie the vitality of his system, the cause of the truth or error of his thinkings.
The following are the rules he gave us for the detection and separation of true ideas from false, (i.e., imperfect or complex):—
"1. Never to accept anything as true but what is evidently so; to admit nothing but what so clearly and distinctly presents itself as true, that there can be no reason to doubt it.
"2. To divide every question into as many separate parts as possible, that each part being more easily conceived, the whole may be more intelligible.
"3. To conduct the examination with order, beginning by that of objects the most simple, and therefore the easiest to be known, and ascending little by little up to knowledge of the most complex.
"4. To make such exact calculations, and such circumspections as to be confident that nothing essential has been omitted. Consciousness being the basis of all certitude, everything of which you are clearly and distinctly conscious must be true: everything which you clearly and distinctly conceive, exists, if the idea of it involve existence."
In these four rules we have the essential part of one half of Des Cartes's system, the other, which is equally important, is the attempt to solve metaphysical problems by mathematical aid. To mathematics he had devoted much of his time. He it was who, at the age of twenty three, made the grand discovery of the applicability of algebra to geometry. While deeply engaged in mathematical studies and investigations, he came to the conclusion that mathematics were capable of a still further simplification, and of much more extended application. Impressed with the certainty of the conclusions arrived at by the aid of mathematical reasoning, he began to apply mathematics to metaphysics.
His ambition was to found a system which should be solid and convincing. Having searched for certitude, he had found its basis in consciousness; he next wanted a method, and hoped he had found it in mathematics.
He tells us that "those long chains of reasoning, all simple and easy, by which geometers used to arrive at their most difficult demonstrations, suggested to him that all things which came within human knowledge, must follow each other in a similar chain; and that provided we abstain from admitting anything as true which is not so, and that we always preserve in them the order necessary to deduce one from the other, there can be none so remote to which we cannot finally attain, nor so obscure but that we may discover them."
Acting out this, he dealt with metaphysics as we should with a problem from Euclid, and expected by rigorous reasoning to discover the truth. He, like Archimedes, had wished for a standing place from which to use the lever, that should overturn the world; but, having a sure standing place in the indubitable fact of his own existence, he did not possess sufficient courage to put forth the mighty power—it was left for one who came after him to fairly attempt the over-throw of the world of error so long existent.