In the four rules, and in this view of consciousness, we have only half of Descartes' system; the psychological half. It was owing to the exclusive consideration of this half that Dugald Stewart was led--in controverting Condorcet's assertion that Descartes had done more than either Galileo or Bacon toward experimental philosophy--to say that Condorcet would have been nearer the truth if he had pointed him out as the "Father of the Experimental Philosophy of the Mind." Perhaps the title is just; but Condorcet's praise, though exaggerated, was not without good foundation. There is, in truth, another half of Descartes' system, equally important, or nearly so: we mean the deductive method. His eminence as a mathematician is universally recognized. He was the first to make the grand discovery of the application of algebra to geometry; and he made this at the age of twenty-three. The discovery that geometrical curves might be expressed by algebraical numbers, though highly important in the history of mathematics, only interests us here by leading us to trace his philosophical development. He was deeply engrossed in mathematics; he saw that mathematics were capable of a still further simplification and a far more extended application. Struck as he was with the certitude of mathematical reasoning, he began applying the principles of mathematical reasoning to the subject of metaphysics. His great object was, amid the scepticism and anarchy of his contemporaries, to found a system which should be solid and convincing. He first wished to find a basis of certitude--a starting-point: this he found in consciousness. He next wished to find a method of certitude: this he found in mathematics. "Those long chains of reasoning," he tells us, "all simple and easy, which geometers use to arrive at their most difficult demonstrations, suggested to me 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." From these glimpses of the twofold nature of Descartes' method, it will be easy to see into his whole system: consciousness being the only ground of certitude, mathematics the only method of certitude.