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For Descartes, the ultimate justification of knowledge claims lie with human reason and the absence of doubt. He relied on classical methods of theorizing and conjectured hypotheses in order to construct scientific propositions.[[CiteRef::Janiak (2016)]] Such a '''rationalist''' approach to knowledge was also championed by Baruch Spinoza (1632-1677), Nicolas Malebranche (1638-1715), and Leibniz.[[CiteRef::Lennon and Dea (2014)]] But, by the early 17th century, experimental researchers like Galileo and Robert Boyle (1627-1691) had begun to elaborate and practice a very different approach to knowledge based on experimentation and extensive use of mathematics. Following the '''inductive methodology''' advocated by [[Francis Bacon]](1561-1626), they maintained that theoretical principles emerged from experimental data by a process of inductive generalization. However, there were also dissenters like Newton's contemporary Christiaan Huygens, who believed that most experimental work involved formulating hypotheses about unobservable entities, which were tested by their observable consequences. This was an early form of '''hypothetico-deductivism'''.

Newton's two most important works of natural philosophy were the ''Principia'', published in 1687 [[CiteRef::Newton (1687)]], which dealt with his theories of motion and universal gravitation, and ''Opticks: or, A Treatise of the Reflexions, Refractions, Inflexions, and Colours of Light'' [[CiteRef::Newton (1704)]] which was published in 1704 and dealt with his theories of light and color. [[CiteRef::Westfall (1999)]] Newton made mathematics much more central to the conduct of natural philosophy than Descartes, by producing a general mathematical theory of the motion of bodies. [[CiteRef::Janiak (2016)]] He posited three mathematical '''laws of motion''', together with a '''law of universal gravitation'''. Changes in the state of motion of objects were caused by '''forces''' acting on them. Quantities of force and amounts of matter were measurable. The laws specified the mathematical relationship between the acceleration experienced by an object, the quantity of matter composing it, and the magnitude of the forces acting on it. [[CiteRef::Smith (2009)]]

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