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|Summary=Newton’s most notable contributions were made to the fields of physics, mathematics, and scientific method, which were so groundbreaking that he is currently considered to be one of the most important physicists in modern Western history.[[CiteRef::Janiak (2016)]] Philosophers of science credit Newton’s revolutionary theory of gravity and his experimental approach to conducting natural philosophy as outlined in his major work, ''Philosophiæ Naturalis Principia Mathematica'' (''Mathematical Principles of Natural Philosophy'' or simply the [[Newton (1687)|''The Principia'']]), whose principles became central to the mosaic of late 18th and 19th century science.[[CiteRef::Janiak (2016)]] Some consider The the ''Principia'' to be the work that initially created physics as its own scientific field separate from the umbrella of metaphysics and philosophy. [[CiteRef::Janiak (2016)]]|Historical Context=When Isaac Newton began his studies at Cambridge University's prestigious Trinity College in 1661, more than a century had passed since Nicolaus Copernicus (1473-1543) had proposed a '''heliocentric cosmology''' in his 1543 ''De Revolutionibus Orbium Coelestium'' (''On the Revolutions of Heavenly Spheres''). It had been fifty years since Galileo Galilei (1564-1642) had published his observations with the telescope in 1610, which uncovered dramatic evidence favoring for the Copernican system. His discovery of the phases of the planet Venus indicated that it revolved around the sun and was lit by reflected sunlight. His description of four moons circling Jupiter indicated that Earth, with its own moon, resembled this planet. Finally, his discovery of surface features on the moon indicated that it was another world, as expected under the Copernican system, but not by Aristotelianism. Around At about the same time, Johannes Kepler (1571-1630)published his laws of planetary motion, indicating that the planets revolved around the sun on elliptical paths, replacing the circular motion and complex epicycles of Copernicus and Claudius Ptolemy(c. 100-170).[[CiteRef::Westfall (1980)|pp. 1-7]] According to Westfall, "by 1661 the debate on the heliocentric universe had been settled; those who mattered had surrendered to the irresistible elegance of Kepler's unencumbered ellipses, supported by the striking testimony of the telescope, whatever the ambiguities might be. For Newton, the heliocentric universe was never a matter in question".[[CiteRef::Westfall (1980)|p. 6]] A planetary Earth that rotated on its axis and revolved around the sun was incompatible with the accepted Aristotelian physicsof [[Aristotle]] (384-322 BCE). The community of the time was engaged with the question of how it could be that the Earth itself was in motion through space, and with the question of how one could hope to gain reliable knowledge in the face of the failure of Aristotelian scholastic knowledge accepted for centuries.

Newton’s education at Cambridge was classical, focusing on Aristotelian rhetoric, logic, ethics, and physics. Bound to '''Aristotelian scholasticism ''' by statutory rules,the curriculum had changed little in decades.[[CiteRef::Christianson (1984)|p. 33]] the curriculum had changed little in decades.[[CiteRef::Westfall (1980)|pp. 81-90]][[CiteRef::Smith (2009)]] Like many of the more ambitious students, Newton distanced himself from classical metaphysics and instead studied the works of the French natural philosopher [[René Descartes]](1596-1650) on his own. By 1664, Newton is known to have read the 1656 Latin edition of Descartes' ''Opera Philosophica'', a one volume compilation of Descartes' major works.[[CiteRef::Smith (2009)]] Newton is known to have been profoundly influenced by Descartes views of space, matter, and God, and by commentaries on Descartes by Henry More (1614-1687). [[CiteRef::Janiak (2016)]] Descartes had died just over a decade priorearlier, and these his works had first been published within the preceding thirty years. They were gaining in popularity and by about 1680 would become the [[Theory Acceptance|accepted]] centerpiece of the Cambridge curriculum, as they also would in Paris by 1700.[[CiteRef::Barseghyan (2015)|p. 190]] When Newton is known to have been profoundly influenced by Descartes views of spacepublished his magnum opus, matterthe ''Principia'' in 1687, and God, and by commentaries on he was challenging a Cartesian orthodoxy. The full title of Newton's work suggests he intended it to be in dialog with Descartes by Henry More ' ''Principia Philosophiae'' (1614-1687''Principles of Philosophy'')published in 1644. [[CiteRef::Janiak (20142016)]]

While both Newton’s physics and philosophy were heavily influenced by Descartes’ ideas, they were also a challenge to what had, by then, become the new Cartesian orthodoxy. Descartes' '''mechanical natural philosophy''' was derived from ancient Greek atomism. He 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. Particles 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)]] Aristotle had explained the properties of visible bodies in terms of their form, rather than in terms One of the arrangement attractions of their constituent parts. He maintained these ideas is that heavy objects, composed of the element earth, tended towards their natural place; the center of the universe. The concept of a sphere of earth at rest in the center of the universe was central to unlike Aristotle's entire cosmology. Motion in the terrestrial , they allowed for a movable planetary Earth, and celestial realms were seen as fundamentally motions weren't differentin kind from terrestrial motions.[[CiteRef::Bodnar (2016)]] Descartes' theories They explained gravity , in qualitative terms, as due to a swirling vortex of particles around the Earth, which pushed things towards its center. Celestial motions were not different in kindcentre. 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. By the time Newton published his magnum opus, ''Philosophiae Naturalis Principia Mathematica'' (''Mathematical Principles of Natural Philosophy'')in 1687, Descartes' views had been accepted at Cambridge. The title of Newton's work suggests he intended it to be in dialog with Descartes' ''Principia Philosophiae'' (''Principles of Philosophy'') published in 1644.[[CiteRef::Janiak (2016)]] Newton contested Cartesianism as the orthodoxy he sought to overturn.

For Descartes saw , the ultimate justification of knowledge claims to 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 by Gottfried Wilhelm Leibniz.[[CiteRef::Lennon and Dea (2014)]] But, by the early 17th century, experimental researchers like Galileo Galilei 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 rejected Cartesian rationalism, and argued that the Cartesians did not sufficiently employ mathematics and experimentation in their work. He rejected the method of hypotheses outright. [[CiteRef::McMullin (2001)]][[CiteRef::Janiak (2016)]] He supported inductivism, and held epistemological views similar to those of his contemporary and friend [[John Locke]](1632-1704), who maintained that all knowledge came from experience.[[CiteRef::Rogers (1982)]]|Major Contributions={{#evt:service=youtube|id=ELbm5KUYMLM|alignment=right|description=Hakob Barseghyan's lecture on Newtonian Worldview|container=frame }}=== Newton on Mathematics and Natural Philosophy ===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'', or simply ''Opticks'', [[CiteRef::Newton (1704)]] which was published in 1704 and dealt with his theories of light and color. [[CiteRef::Westfall(1999)]] More than Descartes, Newton made mathematics much more central to the conduct of natural philosophythan 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)]]

In contrast with the Cartesian mechanical philosophy, in Newton’s physics, material objects were not required to be in direct contact in order to influence each other's motion. Instead,forces Forces could act at a distance. To explain both falling bodies on Earth and the motions of the moon and planets, Newton posited a '''gravitational force ''' that acted as the inverse square of the distance between objects. He claimed to have derived this relationship from Kepler's observational laws of planetary motion. ButThe works of Ptolemy, he was unable to supply a mechanical explanation for how gravity worked. Newton wrote that "I have not yet been able to deduce from phenomena the reason for these properties of gravityCopernicus, and I do not feign hypotheses". [[CiteRef::Smith (2009)|p. 7]] The Kepler used the mathematical language used of geometry in The their descriptive accounts of celestial motions. In the ''Principia'' was geometryNewton likewise presented his arguments geometrically. Unlike his predecessors, which was also the basis for prior major models Newton sought to do more than simply describe celestial motions. He sought to explain them in celestial mechanicsterms of gravitational forces acting between bodies. In order to do this, including the works Newton invented a new branch of Ptolemymathematics, Copernicus '''integral and Keplerdifferential calculus'''. None of these earlier works howeverCalculus deals with mathematical quantities that are continuously changing, offered any rigorously mathematical explanation such as the magnitude and direction of the motions they describedgravitational forces acting on an orbiting body. [[CiteRef::Friedman (2002)]][[CiteRef::Smith (2009)]] Even though Newton published his key work in developed the language basic concept of geometrycalculus during 1665-6, as while Cambridge University was closed due to a mathematician he is primarily role in inventing integral and differential calculusplague, but didn't publish it until the first decade of the eighteenth century. He is thus co-credited independently for the with inventing calculus alongside with his contemporary and rival natural philosopher, Gottfried Wilhelm Leibniz(1646-1716).[[CiteRef::Cohen and Smith (Eds.) (2002)|pp. 1310-14]] As a mathematical technique, calculus had been the first method that was capable of articulating the quantity of acceleration, unlocking a new world of calculations which geometry as a technique had been incapable of solving.[[CiteRef::Friedman (2002)]] Eventually, 18th century that mathematicians Jacob Hermann and Leonhard Euler expressed Newton’s laws of motion using Newton's own technique of calculus, but in the symbolic expression that Leibniz had developed.[[CiteRef::Smith (2009)|p. 2920]] In following years, calculus became indispensable tool for scientists in the Newtonian mosaic to solve problems in physics, and to predict the behaviour of material objects with an unprecedented degree of accuracy.[[CiteRef::Smith (2009)]] Although geometry is still taught in schools today, calculus is the primary mathematical technique learned and used in physics and engineering classrooms.

Prior to the publication of The ''Principia'', the philosophy of motion and change in the universe was largely a theoretical and non-mathematical enterprise. The dominating methodological approach both in the Aristotelian-scholastic and Cartesian natural philosophy, was one in which truths about the natural world were proposed as conjectural hypotheses. They were often deduced Cartesian '''rationalism'''sought to deduce such hypotheses from fundamental metaphysical principles that were deemed evidently true by human reason . [[CiteRef::Janiak (2016)]][[CiteRef::Lennon and Dea (2014)]]. Influenced by the more experimental and mathematically oriented methodologies of Bacon, Galileo, and Boyle, Newton drew a distinction between a conclusion drawn from observation or experimental evidence and one that was merely a speculative 'hypothesis'. He explicitly rejected this the method of hypotheses, and instead demanded that all propositions be deduced from the observed phenomena and then converted into general principles via '''induction''' . [[CiteRef::McMullin (2001)]][[CiteRef::Janiak (2016)]][[CiteRef::Smith (2002)]]. In the second edition of The the ''Principia'', Newton states:

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]] His epistemological beliefs were similar to those of his contemporary and friend, [[John Locke]] (1632-1704) who maintained that all knowledge came from experience. [[CiteRef::Rogers (1982)]] Newton called his method methodology the '''experimental philosophy''', because theories about the behavior of empirical objects can only be refuted via experimental procedures.[[CiteRef::Smith (2002)]] He expressed the its core beliefs from which he derived his method 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 in 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, the 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, Newtonian gravitation theory became accepted through much of continental Europe by the middle of the eighteenth century. [[CiteRef::Janiak (2016)]] [[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 what we now recognize as the '''hypothetico-deductive method'''. [[CiteRef::McMullin (2001)]] Historical research indicates shows that the scientific community did not use Newton's own criteria in evaluating his work. Newton's His theories did not become accepted outside of England until after its 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 it them from the rival theory of Cartesian vortices, rather than via 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)]] According  By the mid-eighteenth century natural philosophers were beginning to McMullin, realize that many successful theories violated the strictures of Newton's methodology ran contrary to inductive experimental philosophy. The eighteenth century saw the consensus acceptance of a variety of theories that had been emerging among natural philosophers 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 his timelight, in favor and Herman Boerhaave's (1668-1738) vibratory theory of hypothesisheat. [[CiteRef::McMullin Laudan (20011984a)|pp. 56-57]] Christiaan Huygens and John Locke are known to have taken the experimental philosophy, if not necessarily the full content of Newton’s theories, to heart.[[CiteRef::Janiak Barseghyan (20162015)|p. 54]]|Criticism=Although many natural philosophers in The methodologists of the 17th early nineteenth century were convinced by Newton’s views on the , William Whewell (1794-1866) and John Hershel (1792-1871) recognized that the proper method actual practice of conducting science, many were did not willing conform to abandon the Cartesian mechanical philosophy. Contemporary philosopher Leibniz in particular was concerned that prescribed Newtonian methodology and openly advocated the theory of gravity as a regression in natural philosophy, as Newton could not account for the source of gravity. To the Cartesians, it was more important that all motion in the universe could be given a direct cause, which was only possible under the mechanical philosophy, even if this amounted to a larger gap between theory and experimental evidencehypothetico-deductive method.[[CiteRef::Janiak Laudan (20161984a)|pp. 56-60]]

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