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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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