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Descartes was the most prominent member of a community of '''corpuscularist''' thinkers, who maintained that visible objects were made of unobservably tiny particles, whose relations and arrangement were responsible for the properties of visible bodies. In this '''mechanical natural philosophy''', particles influenced one another only by direct physical contact, which was the cause of all motion, and ultimately all change.[[CiteRef::Disalle (2004)]] One of the attractions of these ideas is that, unlike Aristotle's, they allowed for a movable planetary Earth, and celestial motions weren't different in kind from terrestrial motions. They explained gravity, in qualitative terms, as due to a swirling vortex of particles around the Earth, which pushed things towards its center. In accord with Copernican heliocentrism, Descartes posited that a larger vortex surrounded the sun, with the smaller planetary vorticies caught in a larger solar vortex.[[CiteRef::Garber (1992)]][[CiteRef::Disalle (2004)]] In Newton's time, major champions of the mechanical natural philosophy included Christiaan Huygens (1629-1695) and Gottfried Wilhelm Leibniz (1646-1716), who was to become a major rival of Newton's.
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'''.
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More than two centuries after Newton published the ''Principia'', a new theory of motion and gravitation was formulated by Albert Einstein (1879-1955), who was inspired by new developments in non-Euclidean geometry and by problems with James Clerk Maxwell's (1831-1879) theory of electromagnetic radiation. The new theory replaced Newton's theory as the accepted theory of motion and gravitation by about 1920. Einstein's '''General Theory of Relativity''' explained the success of its predecessor by showing that its equations reduce to those of Newton in the limit of weak gravitational fields and velocities that are an insignificant fraction of that of light. Einstein's theory eliminated the problem of action at a distance by postulating that the mass of an object warps space-time, and that the local manifestation of this curvature influences distant bodies. [[CiteRef::Barseghyan (2015)|p. 125]][[CiteRef::Isaacson (2007)]]
Newton's experimental philosophy shaped accepted claims about scientific methodology, influencing the methodological pronouncements of George Berkeley (1685-1753), David Hume, Thomas Reid (1710-1796), and Immanuel Kant (1724-1804). [[CiteRef::McMullin (2001)]] However, according to McMullin, Newton's methodology ran contrary to the consensus that had been emerging among natural philosophers of his time, in favor of what we now recognize as the '''hypothetico-deductive method'''. [[CiteRef::McMullin (2001)]] Historical research shows that the scientific community did not use Newton's own criteria in evaluating his work. His theories did not become accepted outside of England until after their prediction of the oblate spheroid shape of the Earth was confirmed by expeditions to Lapland and Peru. Newton's own theories became accepted via a '''hypothetico-deductive method''' based on confirmed novel predictions that distinguished them from the rival theory of Cartesian vortices, rather than by Newton's own '''inductive methodology'''. Further, Newton's theory, in fact, posited unobservable hypothetical entities, including gravitational attraction, absolute space, and absolute time.[[CiteRef::Barseghyan (2015)|p. 48-49]][[CiteRef::Terrall (1992)]][[CiteRef::McMullin (2001)]]
By the mid-eighteenth century natural philosophers were beginning to realize that many successful theories violated the strictures of Newton's inductive experimental philosophy. The eighteenth century saw the acceptance of a variety of other theories that posited unobservable entities, including Benjamin Franklin's (1706-1790) theory of electricity, which posited the existence of an unobservable electric fluid, the phlogiston theory of combustion and rust, which likewise posited an unobservable substance, and Augustin-Jean Fresnel's (1788-1827) wave theory of light which posited an unobservable fluid ether as the medium of light, and Herman Boerhaave's (1668-1738) vibratory theory of heat. [[CiteRef::Laudan (1984)|pp. 56-57]][[CiteRef::Barseghyan (2015)|p. 54]] The methodologists of the early nineteenth century, William Whewell (1794-1866)and John Hershel(1792-1871)recognized that the actual practice of science did not conform to the prescribed Newtonian methodology and openly advocated the '''hypothetico-deductive method'''. [[CiteRef::Laudan (1984)|pp. 56-60]]
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