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|Summary='''Sir Isaac Newton''' (1642-1727) was a natural philosopher who lived and worked in England in the 17th and 18th century. 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, [[Newton (1687)|The Principia]] (''Philosophiæ Naturalis Principia Mathematica''), to be the foundation for the dominant Newtonian mosaic which influenced much of late 18th and 19th century science.[[CiteRef::Janiak (2016)]] Some consider 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. Galileo had discovered dramatic evidence favoring 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. His studies of sunspots indicated that the sun revolved on its axis, and finally, his discovery of surface features on the moon indicated that the moon was another world, as expected under the Copernican system, but not by Aristotelianism. Around the same time, Johannes Kepler had 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 Ptolemy.[[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 physics. 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 can gain reliable knowledge given the evident 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,[[CiteRef::Christianson (1984)|p. 33]] the curriculum had changed little in decades, despite the incompatibility of Aristotelian natural philosophy with Copernican heliocentrism.[[CiteRef::Westfall (1980)|pp. 81-90]][[CiteRef::Smith (2009)]] Like many of the more ambitious students, Newton is known to have 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)]] Descartes had died just over a decade prior, and these 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]]
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, Galileo Galilei and Robert Boyle (1627-1691) had begun to elaborate and practice an experimental approach to knowledge. Much of Newton's natural philosophy was adapted from Descartes' views, but he was skeptical of Descartes' rationalism and rejected his method of hypotheses outright.[[CiteRef::Janiak (2016)]] Instead, his epistemological views drew from Galileo and Boyle and were 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==== Newton on Calculus Mathematics and Natural Philosophy ===
Whereas Descartes did not rely on mathematical reasoning for his deductions of scientific propositions, Newton believed that mathematics was an imperative part of conducting natural philosophy.[[CiteRef::Janiak (2016)]] In Newton’s physics, material objects were not required to be in direct contact with each other in order for motion to occur. Instead, objects react to each other via a force, a new concept which Newton envisioned as a quantifiable property contained in all material objects, the amount of which is directly proportional to the quantity of matter contained in the object. Quantities of force and matter were thus introduced to the mosaic as ontological entities that were measurable. By applying Newton’s three laws of motion, material objects in the universe were compelled to accelerate through action at a distance. Additionally, the laws outlined the mathematical relations between this acceleration and the quantities of force and matter could be explained and predicted mathematically, thereby giving mathematics a new central role in the study of natural philosophy. In The ''Principia'', Newton made extensive use of mathematics in his argument for the unified theory of gravity.[[CiteRef::Smith (2009)]] The mathematical language used in The ''Principia'' was geometry, which was also the basis for many of the major models for celestial mechanics that were studied at the time, including the works of Ptolemy, Copernicus and Kepler.[[CiteRef::Smith (2009)]]
Even though Newton published his key work in the language of geometry, as a mathematician he is primarily role in inventing integral and differential calculus. He is co-credited independently for the calculus alongside his contemporary and rival natural philosopher, Leibniz.[[CiteRef::Cohen and Smith (Eds.) (2002)|pp. 13-14]] 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. 29]] 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.
=== Newton on Method Methodology ===
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 to natural philosophy both in the Aristotelian-scholastic and Cartesian mosaic, was one in which truths about the natural world were proposed as conjectural hypotheses. Newton explicitly rejected the method of hypotheses, and instead demanded that all propositions be deduced from the phenomena and then converted into general principles via induction. In the second edition of The ''Principia'', Newton states:
