Rene Decartes

Meditations on First Philosophy

(1641) and

Principles of Philosophy

(1644), main works of French mathematician and scientist René Descartes, considered the father of analytic geometry and the founder of modern rationalism, include the famous dictum "I think, therefore I am."

A set of two perpendicular lines in a plane or three in space intersect at an origin in Cartesian coordinate system. Cartesian coordinate, a member of the set of numbers, distances, locates a point in this system. Cartesian coordinates describe all points of a Cartesian plane.

From given sets, {X} and {Y}, one can construct Cartesian product, a set of all pairs of elements (x, y), such that x belongs to {X} and y belongs to {Y}.

Cartesian philosophers include Antoine Arnauld.

René Descartes, a writer, highly influenced society. People continue to study closely his writings and subsequently responded in the west. He of the key figures in the revolution also apparently influenced the named coordinate system, used in planes and algebra.

Descartes frequently sets his views apart from those of his predecessors. In the opening section of the

Passions of the Soul

, a treatise on the early version of now commonly called emotions, he goes so far to assert that he writes on his topic "as if no one had written on these matters before." Many elements in late Aristotelianism, the revived Stoicism of the 16th century, or earlier like Saint Augustine of Hippo provide precedents. Naturally, he differs from the schools on two major points: He rejects corporeal substance into matter and form and any appeal to divine or natural ends in explaining natural phenomena. In his theology, he insists on the absolute freedom of act of creation of God.

Baruch Spinoza and Baron Gottfried Wilhelm von Leibniz later advocated Descartes, a major figure in 17th century Continent, and the empiricist school of thought, consisting of Thomas Hobbes, John Locke, George Berkeley, and David Hume, opposed him. Leibniz and Descartes, all well versed like Spinoza, contributed greatly. Descartes, the crucial bridge with algebra, invented the coordinate system and calculus. Reflections of Descartes on mind and mechanism began the strain of western thought; much later, the invention of the electronic computer and the possibility of machine intelligence impelled this thought, which blossomed into the Turing test and related thought. His stated most in §7 of part I and in part IV of

Discourse on the Method

.