Descartes, as is well known, had placed the ideal of perfect science in geometry, and endeavoured to reform philosophy and every other branch of knowledge upon this model. Now the geometrical method proceeds analytically till it reaches a self-evident truth, and thence by synthetic deduction it advances to more and more complex propositions. Accordingly, if philosophy were to adopt a rigorous scientific method, it also (thought Descartes) must look for a solid foundation in the shape of an elementary and self-evident truth from which to deduce all its subsequent statements, whether theological, metaphysical, physical, or ethical. Thus self-evidence--the "clear and distinct perception or idea"--was the supreme test: immediate inference--the intuitive connexion of thought with existence, _cogito_ with _sum--_ provided the elementary truth and the foundation of knowledge. By means of the clear and distinct perception, together with the systematic doubt which led him to the _cogito,_ Descartes persuaded himself that he had once and for all made an end of scepticism. But, by the same argument, all knowledge which had not been or could not be reduced to clear and distinct perception and geometrical deduction was bound to lose in his eyes all value and importance. This included history, as founded upon testimony; observation of nature, when not within the sphere of mathematics; practical wisdom and eloquence, which draw their validity from empirical knowledge of human character; and poetry, with its world of imaginary presentations. Such products of the mind were for Descartes illusions, chaotic visions, rather than knowledge: confused ideas, destined either to become clear and distinct and so no longer to exist in their original nature, or else to drag on a miserable existence unworthy of a philosopher's consideration. The daylight of the mathematical method rendered useless the lamps which, while they guide us in the darkness, throw deceptive shadows. Vico, unlike the other opponents of Descartes, did not confine himself to or waste time in scandalised outcries at the danger to religion entailed by the subjective method. He did not inquire, like the schoolmen, whether the _cogito_ was or was not a syllogism, and if so whether it was or was not defective. He did not join in the protest of outraged common-sense against the Cartesian contempt of history, rhetoric, and poetry. He went straight to the heart of the question, to Descartes' criterion of scientific truth itself, the principle of self-evidence. While the French philosopher believed himself to have satisfied all the demands of the strictest science, Vico saw that as a matter of fact, in view of the need which he set out to meet, his proposed method gave little or no assistance.