Newtonian motion versus Cartesian motion
Main article: History of classical mechanics

Sir Isaac Newton (1643–1727)

In the late 17th and early 18th centuries, the Cartesian mechanical tradition was challenged by another philosophical tradition established by the Cambridge UniversityPhysicist and mathematician Isaac Newton. Where Descartes held that all motions should be explained with respect to the immediate force exerted by corpuscles, Newton chose to describe universal motion with reference to a set of fundamental mathematical principles: his three laws of motion and the law of gravitation, which he introduced in his 1687 work Mathematical Principles of Natural Philosophy. Using these principles, Newton removed the idea that objects followed paths determined by natural shapes (such as Kepler’s idea that planets moved naturally in ellipses), and instead demonstrated that not only regularly observed paths, but all the future motions of any body could be deduced mathematically based on knowledge of their existing motion, their mass, and the forces acting upon them. However, observed celestial motions did not precisely conform to a Newtonian treatment, and Newton, who was also deeply interested in theology, imagined that God intervened to ensure the continued stability of the solar system.

Gottfried Leibniz (1646–1716)

Newton’s principles (but not his mathematical treatments) proved controversial with Continental philosophers, who found his lack ofmetaphysical explanation for movement and gravitation philosophically unacceptable. Beginning around 1700, a bitter rift opened between the Continental and British philosophical traditions, which were stoked by heated, ongoing, and viciously personal disputes between the followers of Newton and Leibniz concerning priority over the analytical techniques of infinitesimal calculus, which each had developed independently. Initially, the Cartesian and Leibnizian traditions prevailed on the Continent (leading to the dominance of the Leibnizian calculus notation everywhere except Britain). Newton himself remained privately disturbed at the lack of a philosophical understanding of gravitation, while insisting in his writings that none was necessary to infer its reality. As the 18th century progressed, Continental natural philosophers increasingly accepted the Newtonians’ willingness to forgo ontological metaphysical explanations for mathematically described motions.[19][20][21]