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Newton, Isaac (1642–1727)


Isaac Newton formulated the theory of universal gravity, was an inventor of the calculus, and made major discoveries in optics. He has long been regarded as, perhaps, the greatest scientist and as one of the greatest mathematicians ever to have lived. More recently, philosophers have begun to appreciate the extent to which Newton's remarks on scientific method illuminate the seminal contribution he made, especially in his Principia, to the transformation of natural philosophy into the physical sciences as we know them today. We now know, also, that Newton put at least as much effort into alchemy and theology as he did into his celebrated contributions to mathematics and science.


Newton entered Trinity College Cambridge in 1661. In what has come to be called his annus mirabilis, he spent much of 1665 and 1666 at his family home in Woolsthorp while the university was closed because of the plague. This time at home was part of an extraordinarily productive period of intense effort concentrated on mathematics and natural philosophy. The binomial theorem and the fundamentals of the calculus are among the important new results in mathematics he obtained during this period. In natural philosophy he developed mechanics, including an analysis of circular motion. During this period he, also, conducted optical experiments that led to his account of white light and colors. In 1667 Newton became a fellow of Trinity College at Cambridge University.

In 1669 he became Lucasian Professor of Mathematics, presumably through the recommendation of Isaac Barrow (16301677), the first Lucasian Professor. It was Barrow who, in late 1671, delivered the reflecting telescope Newton had designed and built to the Royal Society of London. This led to Newton's being offered a fellowship in the Royal Society and to the publication in the Society's Philosophical Transactions of his account of white light and colors in 1672. This paper occasioned considerable debate. In that debate Newton began to articulate what he called his "experimental philosophy," which sharply distinguishes experimentally established results from conjectured hypotheses. By the late 1670s Newton withdrew from correspondence in natural philosophy.

In late 1679 Robert Hooke (16351703), who had recently become secretary of the Royal Society, wrote to encourage Newton to resume his public participation in natural philosophy. In this letter he invited Newton to use his mathematical methods to determine the trajectory a body would follow under a combination of inertial motion and an inverse-square force directed toward a center. In August 1684 a visit by Edmund Halley (16561742), who later became the Astronomer Royal, convinced Newton of the importance of the relation he had established between elliptical orbits and inverse square centripetal forces. By November Newton had sent Halley a small but revolutionary treatise, De Motu. An extraordinarily intense effort by Newton transformed this small treatise into his masterpiece, the Principia. It was published in 1687. Halley, who appreciated the importance of what Newton had achieved, oversaw the printing and paid for it out of his own pocket.

In 1689 and again in 1701, Newton was elected to represent Cambridge University in Parliament. He was made warden of the mint for England in 1696. By 1698 he had successfully carried out a major recoinage for the English economy. In 1699 he became master of the mint. In 1699 Newton also became an associate member of the French Academy of Sciences. He resigned his professorship at Cambridge in 1701. In 1703 he became president of the Royal Society of London, a post that, along with that of master of the mint, he held until his death. He was knighted in 1705.

In 1704 Newton published the first edition of his Opticks. It included two earlier mathematical papers as supplements, one of which was his first publication on the calculus. Newton's long delay in publishing his work led to his priority dispute with Gottfried Wilhelm Leibniz (1646-1716) over the invention of the calculus. This dispute extended from the mid-1690s until after Leibniz's death and came to focus on differences over natural philosophy as well as the calculus priority claims.

The second edition of Principia was published in 1713, after four years of effort under the able guidance of its editor Roger Cotes (16821716). The third edition was published in 1726. Conspicuous ways in which these two differ from the first edition appear to be responses to objections by Christian Huygens (16291695), Leibniz, and others. Some claims that had been called Hypotheses at the beginning of Book 3 in the first edition became, with changes and additions, Regulae Philosophandi, and others, such as Kepler's area and 3/2 power rules, became Phaenomena. The famous General Scholium clarifying what Newton took to be the proper practice of natural philosophy was added at the end.

The Latin editions of the Optics in 1706 and 1717 included queries that shed further light on his "experimental philosophy," as does his attack on Leibniz in his "Account of the Book Entitled Commercium Epistolicum " published anonymously in 1715. It ends as follows: "And must Experimental Philosophy be exploded as miraculous and absurd, because it asserts nothing more than can be proved by experiments, and we cannot yet prove by Experiments that all the Phaenomena in Nature can be solved by meer Mechanical Causes?" (1715, p. 224).

The Experimental Philosophy in the Light and Colors Debate

Newton's response to Hooke in the debate over his light and colors paper is a good illustration of his experimental philosophy. In that paper Newton claimed that his experiments conclusively established that the phenomenon of the oblong shape of the image of sunlight shined through a round hole and refracted through a prism is caused by sunlight's being made up of rays that are refracted different amounts by the prism. (Newton's reflecting telescope was designed to avoid problems caused by such differential refraction by using mirrors instead of lenses.)

Hooke interpreted Newton as claiming that the experiments established a corpuscular theory of light and argued that his own wave hypothesis could account for the results equally well. Newton responded by pointing out that the hypothesis that light is a body was put forward only as a conjecture suggested by the experiments, and not as part of what he claimed to have been established by them.

But I knew, that the Properties, which I declar'd of Light, were in some measure capable of being explicated not only by that, but by many other Mechanical Hypotheses. And therefore I chose to decline them all, and to speak of Light in general terms, considering it abstractly, as something or other propagated in every way in streight lines from luminous bodies, without determining, what that thing is (1958, pp. 118119).

Newton went on to outline how Hooke's wave hypothesis, as well as several other mechanical hypotheses, could explain the properties of differential refraction of different kinds of light he had concluded from the experiments.

In other contributions to the debate, Newton outlined how, according to his experimental philosophy, diligently establishing properties of things by experiment is to take precedence over framing hypotheses to explain them. He also made clear that the propositions he regarded as conclusively established by experiment were, nevertheless, subject to correction based on detailed criticism of the experimental reasoning establishing them or on further experimental results challenging them.


Newton's mathematical papers include substantial discoveries in algebra, pure and analytic geometry, as well as his extensive work on the calculus and infinite series. His results on converging series allowed mathematicians to treat such infinite series as legitimate alternative forms of the functions they represented. These results also provided the basis for his approach to the calculus. In 1669 Newton first allowed one of his manuscripts on the calculus to circulate.

The basic mathematics of the Principia is not the calculus but a new form of synthetic geometry incorporating limits. Newton's lemmas on first and last ratios, which open Book 1, show that this alternative geometrical approach can recover many of the basic elementary results of the calculus. The need to rely on geometrical figures, however, makes this approach less able to facilitate more complex calculations made accessible by algebraic manipulation in the symbolic calculus.

Studies in Alchemy, Theology, and Chronology

Newton's alchemical work may well have contributed to a corpuscular theory of matter that may have informed his scientific thinking; however, like his conjectured corpuscular account of light, such a theory of matter was not something Newton claimed to have established.

His extensive notes on his alchemical work indicate a number of elaborate chemical experiments carried out from the mid-1670s until 1693. These display Newton's great discipline as an experimenter. The reported results, however, appear to include nothing that would have altered the course of chemistry had they become public at the time.

Newton first became preoccupied with theology in the early 1670s, probably in response to the requirement that he accept ordination to retain his Trinity fellowship. (He was granted a dispensation in 1675.) By 1673 he had rejected the doctrine of the Trinity and concluded that Christianity had become a false religion through a corruption of the scriptures in the fourth and fifth centuries. He returned to these studies and to work on chronology and prophecies in subsequent decades, especially in the last years of his life. During his lifetime he conveyed his radical views to only a few. But, two such manuscripts were published within a few years of his death.

Recent investigations of the alchemical and theological writings suggest that Newton's natural philosophy was to be part of a larger investigation that would look through nature to see God. This may have helped him to free himself from the restraints of the mechanical philosophy. Newton's intense religious faith was no impediment, and may well have aided, his extraordinarily successful applications of his experimental philosophy in pursuit of empirically establishing scientific knowledge. Moreover, Newton's efforts at scientific understanding of nature did not prevent his efforts to inform his faith by the study of scripture.

Space, Time, and the Laws of Motion

Newton's distinction between absolute (or true) and relative (or apparent) motion are based on his laws of motion, which he described as "accepted by mathematicians and confirmed by experiments of many kinds" ([1687] 1999, p. 424). His distinctions between absolute and relative space and time, which have been such salient targets of criticism by philosophers, are mostly designed to accommodate this primary distinction between true and merely relative motions. Newton was aware of the empirical difficulties raised by such distinctions: "It is certainly very difficult to find out the true motions of individual bodies and actually to differentiate them from apparent motions, because the parts of that immovable space in which bodies move make no impression on the senses" (p. 414).

The Principia 's title, Mathematical Principles of Natural Philosophy, refers to the propositions of Books 1 and 2 that Newton demonstrated from his laws of motion. These provide his resources for addressing this difficulty: "But in what follows, a fuller explanation will be given of how to determine true motions from their causes, effects, and apparent differences, and conversely, of how to determine from motions whether true or apparent, their causes and effects. For this was the purpose for which I composed the following treatise" (p. 415). In Book 3 Newton shows how the calculation of centripetal forces and masses of central bodies from orbital motions around them can determine the center of mass of the planetary system. This calculation picks out the sun-centered Keplerian system as approximately true and the corresponding earth-centered Tychonic system as wildly inconsistent with the measured masses.

Such inconsistencies among the measured forces and masses indicate a failure to be dealing with true motions. For Newton, the adequacy of his appeal to absolute space, time, and motion was an empirical issue to be decided by the long term development and application of a science of motion.

Inferences from Phenomena and Rules of Natural Philosophy

The propositions of Books 1 and 2 are powerful resources for establishing conclusions about forces from phenomena of motion. For example, propositions 1 and 2 together establish that Kepler's area rule holds if and only if the force acting on the moving body is centripetal. A corollary adds that the rate at which areas are swept out be radii from the center increases just in case the net force is off-center in the direction of motion, and decreases just in case it is off-center in the opposite direction. These systematic dependencies make the constancy of the areal rate measure the centripetal direction of the force. Similar systematic dependencies are involved in the inferences to the inverse-square variation of orbital centripetal forces from Kepler's 3/2 power rule and from the absence of orbital precession.

Newton was not the first to exploit such theoretical dependencies to draw inferences from phenomena. Huygens had used his laws of pendulums to measure the acceleration of gravity from the lengths and periods of pendulums. But, Newton turned the technique into a general way of using theory mediated measurements to do empirical science.

The rules of reasoning strengthen the inferences that can be drawn from measurements by phenomena.(See Scientific Method) The first two rules, for example, endorse the inference identifying the force holding the moon in orbit with terrestrial gravity on the basis of the moon-test, which shows that the length of a seconds pendulum at the surface of the earth and the centripetal acceleration of the moon's orbit can count as agreeing measurements of a single earth centered inverse-square acceleration field.

The third rule supports the inference that all bodies gravitate toward each planet with weights proportional to their masses. Newton argues that terrestrial pendulum experiments and the moon-test show this for gravitation toward the earth. Similarly, the harmonic laws for orbits about them show this for gravitation toward Saturn, Jupiter, and the sun. In addition, the agreement between the accelerations of Jupiter and its satellites toward the sun, as well as between those of Saturn and its satellites and those of the earth and its moon toward the sun also show this for weight toward the sun. All these count as phenomena giving agreeing measurements of the equality of the ratios of weight to mass for all bodies at any equal distances from the sun or any planet.

The fourth rule authorizes the practice of treating propositions appropriately supported by reasoning from phenomena as either "exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions" (p. 796). It was added in the third edition to justify treating universal gravity as an established scientific fact, notwithstanding complaints that it was unintelligible in the absence of an explanation of how it results from mechanical action by contact. This rule and the related discussion of hypotheses in the General Scholium most distinguish Newton's experimental philosophy from the mechanical philosophy of his critics.

Gravity as a Universal Force of Interaction

The systematic dependencies via which the basic inverse-square forces are measured by Keplerian phenomena are one-body idealizations. Universal gravity entails interactions among bodies, producing perturbations that require corrections to the Keplerian phenomena. Such corrections can count as higher-order phenomena that carry information that can be exploited to develop successively more accurate approximations.

The Principia includes a successful treatment of two-body interactions and some limited results on three-body interactions including Newton's account of the variational inequality in the lunar orbit. Applications of calculus facilitated by the use of Leibniz's notation by such figures as Leonard Euler (17071783), Jean Le Rond d'Alembert (17171783), and Alexis-Claude Clairaut (17131765) led to successful Newtonian treatments of more complex interactions. By the mid-1700s such successes in the treatments of the shape of the earth, the precession of the equinoxes, the lunar precession and motions of comets had led to the virtual abandonment of vortex theories as serious rivals. By the end of that century, the monumental treatise on celestial mechanics by Pierre Simon de Laplace (17491835), with his successful treatment of the long recalcitrant great inequality in Jupiter-Saturn motions as a periodic perturbation, led to general acceptance of a Newtonian metaphysics of bodies interacting under deterministic laws.

Newtonian treatments of perturbations do more than provide the required corrections to Keplerian phenomena. They also show that Newton's original measurements of inverse-square centripetal forces continue to hold to high approximation in the presence of perturbations. Interactions with other bodies account for the precessions of all the planets except Mercury. The zero residuals in these precessions are agreeing measurements of the inverse-square variation of gravity toward the sun.

Even in the case of Mercury the famous forty-three seconds of arc per century residual in its precession yields 2.00000016 as the measure of the exponent, instead of the exact 2 measured for the other planets. That such a small discrepancy came to be a problem at all testifies to the extraordinary high level to which Newton's theory of gravity had realized a standard of empirical success. On this standard of empirical success, a theory succeeds by having its parameters be accurately measured by the phenomena it purports to explain.

In 1915, Einstein discovered that his theory of general relativity explains the missing forty-three seconds. The success of this explanation depends on the capacity of general relativity to also account for the additional precession of about 530 seconds per century explained by Newtonian perturbations of Mercury's orbit. This requires that Newton's theory count as an appropriate approximation for explaining that part of the phenomenon of Mercury's orbital precession.

Einstein's great excitement over this discovery is appropriate because it showed that his theory of general relativity did better than Newton's theory of universal gravitation by Newton's own standard of empirical success. There was and is no need to appeal to additional or different standards to count general relativity as better supported. The subsequent development of testing frameworks for general relativity continues to be guided by the same standard. Newton's methodology of successive approximations supported by the empirical success of theory mediated measurement accommodates, even, the radical conceptual transformation from Newton's metaphysics of bodies under forces of interaction to Einstein's conception of gravity as given by the geodesic structure of curved space-time.

See also Classical Mechanics, Philosophy of; Space.


works by newton

"An Account of the Book Entituled Comerciumm Epistolicum." Philosophical Transactions 29 (342) (1715): 173224.

Observations upon the Prophecies of Daniel, and the Apocalypse of St. John. In Sir Isaac Newton's Daniel and the Apocalypse: With an Introductory Study of Unbelief, of Miracles and Prophecy, by William Whitla. London: J. Murray, 1922. Reprinted in Sir Isaac Newton's Daniel and the Apocalypse with an Introductory Study of Unbelief of Miracles and Prophecy, London, 1733.

Opticks, or, A Treatise of the Reflections, Refractions, Inflections & Colours of Light. Based on the 4th. ed., 1730. New York: Dover, 1952.

Isaac Newton's Papers and Letters on Natural Philosophy and Related Documents, edited by I. B. Cohen and assisted by R. E. Schofield. Cambridge, MA: Harvard University Press, 1958. 2nd, rev. ed., 1978. Contains the publications in the dispute on light and colors as they appeared in the Philosophical Transactions of the Royal Society.

The Correspondence of Isaac Newton, edited by H. W. Turnbull, A. Scott, A. R. Hall, and L. Tilling. 7 vols. Cambridge, U.K.: Cambridge University Press, 19691977.

Unpublished Scientific Papers of Isaac Newton: A Selection from the Portsmouth Collection in the University Library, Cambridge, edited by A. R. Hall and M. B. Hall. Cambridge, U.K.: Cambridge University Press, 1962. Reprint, 1978.

The Background to Newton's Principia:. A Study of Newton's Dynamical Researches in the Years 166484, edited by J. W. Herivel. Oxford, U.K.: Clarendon Press, 1965.

The Mathematical Papers of Isaac Newton, edited by D. T. Whiteside. 8 vols. Cambridge, U.K.: Cambridge University Press, 19671981.

Isaac Newton's Philosophiae Naturalis Principia Mathematica. 3rd ed., 1726, edited by A. Koyré and I. B. Cohen. 2 vols. Cambridge, MA: Harvard University Press, 1972. Contains variant readings.

Certain Philosophical Questions: Newton's Trinity Notebook, edited by J. E. McGuire and M. Tamny. Cambridge, U.K.: Cambridge University Press, 1983. Reprint, 1985.

The Optical Papers of Isaac Newton. Vol. 1, edited by A. E. Shapiro. Cambridge, U.K.: Cambridge University Press, 1984.

Isaac Newton's Mathematical Principles of Natural Philosophy. Translated by I. B. Cohen, and A. Whitman. Los Angeles: University of California Press, 1999.

works about newton


Cohen, I. B. "Isaac Newton." In Dictionary of Scientific Biography, vol. 10, 42103. New York: Scribners, 1974.

Cohen, I. B. The Newtonian Revolution. Cambridge, U.K.: Cambridge University Press, 1980. 2nd rev. ed., 1995.

Cohen, I. B., and G. E. Smith G.E. The Cambridge Companion to Newton. Cambridge, U.K.: Cambridge University Press, 2002.

Gjertsen, D. The Newton Handbook. London: Routledge & Kegan Paul, 1986. Contains a complete listing of Newton's work and an extensive bibliography of secondary sources.

Whiteside, D. T. "The Prehistory of the Principia from 16641686." In Notes and Records of The Royal Society of London, vol. 45, 1161. London: Royal Society of London, 1991.

Wilson, C. "The Newtonian Achievement in Astronomy." In Planetary Astronomy from the Renaissance to the Rise of Astrophysics, edited by R. Taton and C. Wilson. Cambridge, U.K.: Cambridge University Press, 1989.


Gleick, J. Isaac Newton. New York: Pantheon Books, 2003.

Hall, A. R. Isaac Newton: Adventurer in Thought. Oxford, U.K.: Oxford University Press, 1992.

Westfall, R. S. Never at Rest: A Biography of Isaac Newton Cambridge, U.K.: Cambridge University Press, 1980. An abridged version, The Life of Isaac Newton, was published in 1993.

Further References

Bricker, P., and R. I. G. Hughes, eds. Philosophical Perspectives on Newtonian Science. Cambridge, MA: MIT Press, 1990. Among the many excellent collections inspired by the three-hundredth anniversary of the first edition of Principia, this one is especially focused on philosophy.

Earman, J. World Enough and Space-Time Absolute verses Relational Theories of Space and Time. Cambridge, MA: MIT Press, 1989.

Harper, W. L. "Howard Stein on Isaac Newton: Beyond Hypotheses?" In Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics, edited by David Malament, Chicago: Open Court, 2002.

Koyré, A. Newtonian Studies. Chicago: University of Chicago Press, 1968.

Palter, R., ed. The Annus Mirabilis of Sir Isaac Newton, 16661966. Cambridge, MA: MIT Press, 1971. This classic collection contains papers still relevant to most topics.

Smith G. " From the Phenomenon of the Ellipse to an Inverse-Square Force: Why Not?" In Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics, edited by David Malament, Chicago: Open Court, 2002.

Stein, H. "From the Phenomena of Motions to the Forces of Nature: Hypothesis or Deduction?" PSA 90 2 (1991): 209222.

Theerman, Paul, and Adele F. Seeff, eds. Action and Reaction: Proceedings of a Symposium to Commemorate the Tercentenary of Netwton's Principia. Newark: University of Delaware Press, 1993.

William L. Harper (2005)

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