Keill, John

(1671-1721), mathematician and natural philosopher

by John Henry

© Oxford University Press 2004 All rights reserved

Keill, John (1671-1721), mathematician and natural philosopher, was born in Edinburgh on 1 December 1671, the son of Robert Keill, later a writer to the signet, and his wife, Sarah Cockburn (d. 1697), a draper. Her uncle was Patrick Scougall (1607-1682), bishop of Aberdeen, and her brother was John Cockburn (1652-1729), episcopalian clergyman and nonjuror. In 1692, when Keill moved to Oxford, Cockburn wrote a letter recommending him to his fellow nonjuror, Thomas Smith of Magdalen. James Keill (1673-1719), the Newtonian physician, was John's younger brother.

Teaching Newton's principles
Keill entered the University of Edinburgh in 1688 and gained distinction in mathematics and natural philosophy under David Gregory (1661-1708). He was one of Gregory's most accomplished students and, having graduated MA, he followed his preceptor to Balliol College when Gregory became Savilian professor of astronomy at Oxford in 1691. Keill was incorporated MA on 2 February 1694, having been awarded a 'Scotch exhibition' to help him pay his way. Gregory already had a reputation as a committed and pedagogically gifted Newtonian, and his influence upon Keill was manifest. After developing ways of expounding Newtonian principles by experimental demonstrations in his room at Balliol, Keill was appointed as a lecturer in experimental philosophy at Hart Hall. He therefore offered the first course on Newtonian natural philosophy, and the first reputedly based on 'experimental demonstrations', at either of the English universities. Judging from the published version of his lectures (Introductio ad veram physicam, Oxford, 1701), many of his demonstrations were mathematical rather than experimental, being based on 'thought experiments' (imagined experiments) rather than real manipulations. Nevertheless, some of Keill's demonstrations called for real apparatus, and the innovatory nature of his teaching, continued after 1710 by his student John Theophilus Desaguliers (1683-1744), should be recognized.

Keill began his publishing career while at Oxford with his Examination of Dr Burnet's Theory of the Earth (1698), which used Burnet's Sacred Theory of the Earth as an occasion to attack modern 'world-makers' who endeavour to show 'how, by the necessary laws of Mechanisme, without any extraordinary concurrence of the Divine Power, the world and all that therein is might have been produced' (2nd edn, 1734, 12). Blaming in the most contemptuous terms the great French philosopher René Descartes for this trend, Keill also attacks Baruch de Spinoza (1632-1677), Henry More (1614-1687), Thomas Hobbes (1588-1679), Richard Burthogge (1638?-1694?), Nicolas Malebranche (1638-1715), Richard Bentley (1662-1742), and even William Wotton (1666-1727) for his praise of Descartes, before focusing his attention on Burnet (1635-1715). Although Keill begins from the same premise as Burnet, that true philosophy does not contradict scripture, he insists that where Burnet and similar thinkers have gone wrong is by mistaking the true philosophy, which must be based upon observations and calculations. Although Keill praises Newton and his refutation of Descartes, and sees Newton's philosophy as the only one which is based upon observation and calculation, he does not attempt to substitute a Newtonian account of the Noachian flood for Burnet's Cartesian account. He simply insists that 'a much easier and shorter account' can be given by referring to the 'Omnipotent hand of God, who can do whatsoever he pleases' (Examination, 1734, 26-8). The Remarks on Mr Whiston's New Theory of the Earth, which followed on, were more deferential to William Whiston's Newtonian approach but took issue with numerous points of detail in order to undermine Whiston's naturalistic account of biblical events which Keill saw as playing into the hands of atheists. In the following year Keill published an Examination of the Reflections on the Theory of the Earth, in response to an anonymous defender of Burnet, and A Defense of the Remarks Made on Mr. Whiston's New Theory, in response to Whiston himself.

Shortly after this, in 1699, Keill began to fulfil the duties of the Sedleian professor of natural philosophy as deputy to Sir Thomas Millington (1628-1704), who preferred to occupy himself with his duties as president of the Royal College of Physicians in London and as royal physician. Keill now published his lecture course on Newtonian physics. He became a fellow of the Royal Society in April 1701 and became a regular contributor to its Philosophical Transactions. When his Scotch exhibition expired in 1703 he moved to Christ Church, again following Gregory, who had transferred there two or three years before, presumably because he found the high-church ethos of the college under its dean, his friend Henry Aldrich, more congenial than Balliol. Keill failed to win the Sedleian chair after Millington's death and was similarly unlucky in his pursuit of the Savilian professorship after Gregory's death. At this point he sought instead a government post. In 1709 Robert Harley, lord treasurer, helped him to become appointed treasurer of the palatines, that is to say treasurer of the fund subscribed for protestant refugees from the Palatinate. He conducted a party of exiles to New England, returning at the beginning of 1711. Despairing of a new preferment in England, Keill was about to take up an offer as mathematician to the Republic of Venice when Harley finally offered him the post of decipherer to Queen Anne (although, at £100 per annum, at only half the salary of his predecessor, William Blencowe). In 1712 the Savilian chair of astronomy was vacated once again by the death of John Caswell (or Carswell), Gregory's successor. This time Keill was unanimously elected to the post. He was awarded the degree of MD by public act in July 1713.

By now Keill was one of the most influential natural philosophers in Britain, helping to establish and disseminate Newtonian principles. His influence derived not just from his published lecture course but from an important paper published in 1708 in the Philosophical Transactions of the Royal Society on the laws of attraction and other physical properties ('Epistola ... in qua leges attractionis aliaque physices principia traduntur'). Keill had already signalled the importance of the Newtonian principle of attraction between particles in his Examination of Dr Burnet's Theory of the Earth when he took the Cartesians to task for believing that they could explain all the phenomena of nature by the principles of matter and motion 'without the help of attraction and occult qualities' (1734 edn, 12). Now, further inspired by Newton's suggestions in the 'Queries' which he added to the end of his Opticks (1704, and revised Latin edition, 1706), Keill became one of the first to use the notion of attractions between the constituent invisibly small particles of bodies to explain phenomena such as cohesion, fluidity, elasticity, crystallization, dissolution, fermentation (which was then seen as a purely chemical phenomenon, not as a result of biological processes), effervescence, precipitation, and so on. These ideas were immediately taken up by John's brother James, who tried to develop them in physiology and medicine, and by his friend and fellow student of Gregory's, John Freind (1675-1728), who developed them in chemistry. The theories soon became highly influential, particularly among British thinkers, and led to a thriving Newtonian chemistry in the eighteenth and nineteenth centuries.

The use of attractive forces, which looked very much like the occult qualities which Descartes had proudly boasted to have driven out of natural philosophy, attracted a good deal of criticism from continental readers, however. The leading continental philosopher, G. W. Leibniz, writing in the Acta Eruditorum in 1710, rejected these tendencies of 'Keill and his followers', likening talk of attractions to magical talk of sympathy and antipathy, and even linking Keill's name to the notorious early seventeenth-century 'enthusiast', Robert Fludd. These criticisms have been seen as an explanation for the attack on Leibniz which Keill now launched, and which was to initiate and foster bitterness and recrimination between the two leading philosophers of the day, Leibniz and Newton, until their deaths. In another article for Philosophical Transactions ('Epistola ... de legibus virium centripetarum'), which appeared in 1710, Keill took the opportunity to suggest that Leibniz had taken Newton's unpublished mathematical technique of 'fluxions', changed the name and the symbolism, and published it as his own (as what is now known as differential calculus).

Dispute over the invention of calculus
The ensuing priority dispute over the invention of differential calculus, or fluxions, was extremely rancorous and it is hardly possible now to be sure what was said in good faith, and what was said with rhetorical intentions variously motivated. Accordingly, it is one of those episodes which has divided historians. Sir David Brewster, Newton's first biographer, says nothing of Leibniz's attack on Keill and explains Keill's accusation as a justifiable and perfectly reasonable tu quoque in response to a supposed earlier accusation by Leibniz that Newton had plagiarized from him (Brewster, 2.43). Professor A. R. Hall--one of the twentieth century's leading Newton scholars and author of Philosophers at War (1980), the fullest examination of the dispute--by contrast suggests that John Keill was the creator of the rift between the two great philosophers. The accusation of plagiarism allegedly made against Newton by Leibniz appeared in the Acta Eruditorum of January 1705 and was not even noticed as in any way insulting, by Newton or anyone else, until Keill brought it to Newton's attention in 1711, when he (Keill) was called upon to justify his charge against Leibniz. In fact what Leibniz had said in 1705 was that instead of using differentials, Newton had always made elegant use of fluxions, just in the same way that Honoré Fabri had 'substituted the advance of movements for the method of Cavalieri'. It is certainly possible to read this as merely a comment on the close equivalence of the two pairs of techniques, Fabri's and Bonaventure Cavalieri's on the one hand, and Leibniz's and Newton's on the other. Keill, however, pointed out that it was possible to read this as a suggestion that Fabri's technique can be seen as a way of taking one of the infinite number of lines in a geometrical shape which Cavalieri's technique supposed, and making it move across the shape, and so is derivative upon Cavalieri's technique. And that, by the same token, Newton's fluxions can be seen merely as flowing versions of Leibniz's differentials.

Leibniz wrote to Hans Sloane, secretary of the Royal Society, on 4 March 1711 asking that Keill publicly deny the injurious sense which his words in Philosophical Transactions might be taken to have. Keill's response, seen as all but a denial of the charge of plagiarism by Brewster and as a 'counterattack' by Hall, did not placate Leibniz, who now asked that Newton should be brought in to tell the upstart Keill to back down. Instead, Newton drafted a report, usually known by its short title, Commercium epistolicum, supposedly written by a committee appointed by the society but in fact written by Newton himself, which insisted upon Newton's prior invention of the new mathematical technique. This was distributed to suitable recipients early in 1713. It has previously been suggested that Keill edited this report for the committee, even though he was not a member of it, but this is incorrect: Newton had no need of Keill's help. Keill did, however, publish a popularization in French of the Commercium epistolicum in the Journal Literaire de la Haye of May-June 1713. Similarly, in the summer of 1714 he published in the same journal another response to a defence of Leibniz but was unable to add anything new.

During this time Keill also took it upon himself to defend Newton's Principia mathematica against a criticism levelled at it by Johann Bernoulli (Philosophical Transactions, July-September, 1714). In response Bernoulli sought to demonstrate Keill's incompetence in mechanics in an anonymous reply in the Acta Eruditorum (July 1716). Disputes between these two mathematicians continued until Keill's death, and meanwhile Keill continually tried to poison relations between Newton and Bernoulli by reminding Newton of Bernoulli's earlier support of Leibniz. Bernoulli, however, was anxious to forge friendly links with Newton and it is perhaps a sign of Newton's increasing resentment and distrust of Keill that he reconciled himself to Bernoulli in a friendly letter sent in September 1719.

It is hardly surprising that many on the continent regarded Keill as a truculent polemicist and it seems fair to say that he emerges from the calculus priority dispute with even less credit than any of the other protagonists. Evidently he did not allow his championing of Newton to take up all his time. He married in 1717, although his choice of wife was regarded as something of a scandal--Mary (or Moll) Clements (b. c.1696) was held to be of very inferior rank, being the daughter of James Clements, an Oxford bookbinder. Perhaps the attraction for Keill was the fact that she was twenty-five years younger. They had a son who became a linen draper in London (perhaps reverting to the Keill family trade). The year after his marriage Keill published a second set of his lectures, this time on astronomy, Introductio ad veram astronomiam (Oxford, 1718). It is perhaps significant that when this appeared in English translation in 1721 Keill announced in the dedication that it was published 'at the Request, and for the Service of, the Fair Sex' (sig. A3r). He went on to say that 'It was no Flattery to the Ladies, to say, that such of them as delight in Arts and Sciences, as to the Quickness of Perception and Delicacy of Taste, are equal, if not superior to Men' (sig. A3r-v). Perhaps he had learned something from his new wife.

Keill died at his house in Holywell Street in Oxford on Thursday 31 August 1721, as the result of a 'violent fever' which struck him a few days after entertaining the vice-chancellor and other dignitaries of the university with wine and punch. He was buried at nine o'clock in the evening on 2 September, at St Mary's Church. He evidently died intestate even though he had been left a supposedly large fortune by his brother James.


A. R. Hall, Philosophers at war: the quarrel between Newton and Leibniz (1980)
A. Guerrini, 'James Keill, George Cheyne, and Newtonian physiology, 1690-1740', Journal of the History of Biology, 18 (1985), 247-66
A. Guerrini, 'The tory Newtonians: Gregory, Pitcairne, and their circle', Journal of British Studies, 25 (1986), 288-311
R. E. Schofield, Mechanism and materialism: British natural philosophy in an age of reason (1970)
A. Thackray, Atoms and powers: an essay on Newtonian matter-theory and the development of chemistry (1970)
A. Thackray, '"Matter in a nut-shell": Newton's Opticks and eighteenth-century chemistry', Ambix, 15 (1968), 29-53
D. Brewster, Memoirs of the life, writings, and discoveries of Sir Isaac Newton, 2 vols. (1855)
D. Kubrin, 'Providence and the mechanical philosophy: the creation and dissolution of the world in Newtonian thought', PhD diss., Princeton University, 1968
M. Feingold, 'The mathematical sciences and new philosophies', Hist. U. Oxf. 4: 17th-cent. Oxf., 359-448
J. Gascoigne, Cambridge in the age of the Enlightenment (1989)
J. E. Force, William Whiston, honest Newtonian (1985)
A. Kippis and others, eds., Biographia Britannica, or, The lives of the most eminent persons who have flourished in Great Britain and Ireland, 2nd edn, 4 (1789)

CUL, letters, notes |  CUL, Lucasian papers, letters, drafts of lectures, notebooks, inventory of his library

Wealth at death  
a large fortune, chiefly inherited from his brother James: DNB

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