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<blockquote>I have not as yet been able to deduce from phenomena the reason for these properties of gravity, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this experimental philosophy, propositions are deduced from the phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies and the laws of motion and law of gravity have been found by this method. And it is enough that gravity should really exist and should act according to the laws that we have set forth and should suffice for all the motions of the heavenly bodies and of our sea.[[CiteRef::Newton (1999)| p. 276]]</blockquote>
The generality of Newton's rejection of hypotheses in natural philosophy is unclear since, in the ''Opticks'' he did discuss hypotheses about light, and did raise the possibility of an invisible aether responsible for gravitational attraction. [[CiteRef::Janiak (2016) |pp. 25-26]] Newton called his methodology the '''experimental philosophy''', because theories about the behavior of empirical objects can only be refuted via experimental procedures.[[CiteRef::Smith (2002)]]
He expressed its core beliefs in a set of four “rules for the study of natural philosophy,” which he stated in book III of The ''Principia'' as follows:
Out of these four rules a new, engaged method for conducting science emerged that stood in stark contrast to the previous passive and theoretical Cartesian and Aristotelian-scholastic methods. Propositions formulated based on observations of the natural world and placed back into the natural world to be tested empirically.[[CiteRef::Smith (2002)]] The calculus became deeply incorporated into the experimental method, as it was used to mathematically calculate empirical predictions from natural laws, and then evaluate how exactly the prediction matched the observed reality. Newton claimed to have derived his law of universal gravitation using this method as applied to Kepler's laws of planetary motion. In the Cartesian natural philosophy, centripetal force had already been defined as the agent that pulled the moon towards the Earth, keeping its orbit circular rather than linear. Newton appealed to rules 1) and 2) to claim that the centripetal force, and the force that compelled objects to move downwards towards the Earth, were merely two different expressions of the same thing. Newton then went on to apply the third rule, and argue that this force, which he called gravity, must be a universal property of all material objects. From here, he went on to argue for the unification of superlunary and sublunary phenomena, which Aristotle had deemed to be distinct realms.[[CiteRef::Harper (2002)|pp. 183-184]]
|Criticism=Newton's theories provoked immediate and wide interest in Britain, and became accepted there by the first decade of the eighteenth century. [[CiteRef::Smith (2009)]][[CiteRef::Barseghyan (2015) |p. 210]] In continental Europe, acceptance came more slowly. To proponents of the mechanical philosophy, it was methodologically necessary that all motion be given a cause involving direct physical contact of bodies. Many of Newton's continental contemporaries, in particular Leibniz and Huygens, strongly objected to the idea that forces could act at a distance. Leibniz regarded the theory of gravitation as a regression in natural philosophy and accused Newton of treating gravity as an 'occult quality' beyond philosophical understanding. After an intense debate in the early eighteenth century. [[CiteRef::Janiak (2016)]] Newtonian gravitation theory became accepted through much of continental Europe by the middle of that century [[CiteRef::Barseghyan (2015) |pp. 211-212]][[CiteRef::Aiton (1958) |p. 172]][[CiteRef::Frangsmyr (1974) |p. 35]]
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 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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