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'''Rene Descartes''' (1596-1650) was a French mathematician and philosopher. Descartes rejected the Aristotelian-scholastic world view accepted for most of the previous two thousand years, and laid down new foundations for knowledge.[[CiteRef::Russell (1945)|p. 524]][[CiteRef::Newman (2014)]][[CiteRef::Garber (1993)]] Aristotelians had maintained that intuition schooled by experience was the route to knowledge. Descartes, in his ''Discourse on the Method of Rightly Conducting One’s Reason and of Seeking Truth in the Sciences'' (''Discourse on Method''), first published in 1637,[[CiteRef::Descartes (2007)]] put forward a rationalist scientific methodology in which a proposition is acceptable only if it can be clearly and distinctly perceived by the intellect beyond all reasonable doubt or follows deductively from such propositions.[[CiteRef::Newman (2014)]] This allowed him to advance a mathematical a priorist approach to scientific knowledge and inquiry.[[CiteRef::Garber (1992)]][[CiteRef::Clarke (1992)]] Rejecting the Aristotelian world of forms, substances, and teleology, he posited a mechanical world in which matter possessed only spatial extension and interacted only by contact. In mathematics he developed techniques that made possible analytic geometry. In natural philosophy, he was co-framer of the sine law of light refraction, developed a theory of the rainbow, and formulated a precursor of the nebular hypothesis of the origin of the solar system.[[CiteRef::Hatfield (2016)]]

|Historical Context=The [[Scientific Mosaic|scientific mosaic]]of the late sixteenth and early seventeenth centuries was based primarily on the works of Aristotle and some later Hellenistic natural philosophers, reconciled in various ways with Christian theology by scholars in the High Middle Ages. This '''Aristotelian-scholastic mosaic''' included Christian theology, humoral physiology, astrology, Ptolemaic astronomy, and Christian (Catholic, in many but not all communities contemporaneous with Descartes) theology.[[CiteRef::Haldane (1905)]] Descartes was well educated in this tradition through his attendance at the prestigious Jesuit La Fleche College between the ages of ten and eighteen. He studied a traditional scholastic curriculum of logic, grammar, philosophy, mathematics, and theology. Natural philosophy was taught from the works of Aristotle as interpreted by Christian scholars. Descartes also received an education in mathematics that was unusual for the Aristotelian tradition, and excelled at math. [[CiteRef::Gaukroger (1995)|pp. 38-61]][[CiteRef::Rodis-Lewis (1992)]][[CiteRef::Garber (1992)]]