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The Social and Economic Causes of the Revolution in the Mathematical Sciences in Mid-Seventeenth-Century England

Published online by Cambridge University Press:  16 January 2014

Richard P. Ross
Richard P. Ross*
Affiliation:
Central, Connecticut State College
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Extract

Some such expression as “the scientific revolution in England” is often used in referring to the period in seventeenth-century history in which, under English auspices and the leadership of mathematical scientists of whom many were English or worked in England (foremost in whose ranks was Isaac Newton), success was finally achieved in formulating quantitative, empirically sound, and predictive laws of motion. In recent years there have appeared several theories of the social and economic causes of this revolution. These theories have had a constructive effect to the extent that they have prompted serious consideration of previously ignored aspects of the history of science. However, without denying their value in this regard, they are at best inadequate. The purpose of this essay is not to review or to dispute these earlier theories but to propose an alternative to them.

Type
Research Article
Information
Journal of British Studies , Volume 15 , Issue 1 , Autumn 1975 , pp. 46 - 66
Copyright
Copyright © North American Conference of British Studies 1975

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References

1. Important studies, including those with relevant bibliographies, treating the social and economic causes of the scientific revolution are: Hessen, Boris, The Social and Economic Roots of Newton's ‘Principia’ (New York, 1971)Google Scholar [reprinted from Science at the Cross Roads (London, 1931), pp. 151–212]Google Scholar; Clark, George N., Science and Social Welfare in the Age of Newton (1937; reprint, Oxford, 1949), pp. 60–91Google Scholar; Merton, Robert K., Science, Technology and Society in Seventeenth Century England (New York, 1970)Google Scholar [reprinted from Osiris, 4 (1938), 360–632CrossRefGoogle Scholar]; Zilsel, Edgar, “The Origins of William Gilbert's Scientific Method,” Journal of the History of Ideas (hereafter, J.H.I.), 2 (1941), 1–32CrossRefGoogle Scholar; Crombie, Alistair C., Robert Grosseteste and the Origins of Experimental Science (Oxford, 1953), p. 290nGoogle Scholar; (Edward, John) Hill, Christopher, Intellectual Origins of the English Revolution (Oxford, 1965), pp. 14–84Google Scholar; Rattansi, P. M., “The Social Interpretation of Science in the Seventeenth Century,” in Science and Society, 1600-1900, ed. Mathias, Peter (Cambridge, 1972), pp. 1–32Google Scholar.

2. The Works of Francis Bacon, eds. Spedding, J.et al., 15 vols. (Boston, 1860–1865), VI, 215Google Scholar.

3. Ed. J. Upton (London, 1711), p. 14.

4. Science and Religion in Elizabethan England (San Marino, Cal., 1953), p. 157Google Scholar.

5. Elizabethan attitudes towards the sciences are discussed in: Watson, Foster, The Beginnings of the Teaching of Modern Subjects in England (London, 1909)Google Scholar; Johnson, Francis R., Astronomical Thought in Renaissance England: A Study of the English Scientific Writings from 1500 to 1645 (1937; reprint, New York, 1968), pp. 3, 179, 197–98Google Scholar; Merton, , Science, Technology and Society, pp. 55–136, 228–38Google Scholar; Kocher, , Science and Religion, pp. 115, 156–57Google Scholar; Hill, , Intellectual Origins, pp. 69–71Google Scholar.

6. The status of the mathematical arts at Cambridge and Oxford in these times is treated in: Ball, W.W.R., A History of the Study of Mathematics at Cambridge (Cambridge, 1889), pp. 12–14Google Scholar; Johnson, , Astronomical Thought, pp. 10-12, 196–98Google Scholar; Curtis, Mark H., Oxford and Cambridge in Transition: 1558-1642 (Oxford, 1959), pp. 15-17, 50-52, 54–56Google Scholar; Hill, , Intellectual Origins, pp. 301–14Google Scholar; French, Peter J., John Dee: The World of an Elizabethan Magician (London, 1972), pp. 22–27Google Scholar.

7. See note 10 for references to Dee's work.

8. Important works on practical mathematics in Elizabethan England are: Taylor, Eva G. R., Tudor Geography, 1485-1583 (1930; reprint, New York, 1968)Google Scholar; Merton, , Science, Technology and Society, pp. 163–98Google Scholar; Hall, A. R., Ballistics in the Seventeenth Century (Cambridge, 1952), pp. 1–58Google Scholar; Taylor, Eva G. R., Mathematical Practitioners of Tudor and Stuart England (Cambridge, 1954), pp. 7-25, 165-92, 311–51Google Scholar; Waters, David W., The Art of Navigation in England in Elizabethan and Early Stuart Times (London, 1958), pp. 78–250Google Scholar; Webb, Henry J., Elizabethan Military Science: The Books and the Practice (Madison, 1965)Google Scholar.

9. Unless otherwise indicated the place of publication for a sixteenth- or seventeenth-century printed work is London.

10. The Autobiographical Tracts of Dr. John Dee, ed. Crossley, J., (Manchester, 1851), p. 54Google Scholar.

On Recorde, see Johnson, , Astronomical Thought, pp. 125–34Google Scholar, Waters, , The Art of Navigation, pp. 94–95Google Scholar, and, for other references, Kaplan, Edward, “Robert Recorde (c. 1510-1558): Studies on the Life and Work of a Tudor Scientist,” Diss. Abs., 27 (1966)Google Scholar, 1014-A. On Dee, see Taylor, , Tudor Geography, pp. 75–139Google Scholar, Johnson, , Astronomical Thought, pp. 135-40, 150–56Google Scholar, Waters, , The Art of Navigation, pp. 521–26Google Scholar, Trattner, Walter, “God and Expansion in Elizabethan England: John Dee, 1527-1608,” J.H.I., 25 (1964), 17–34Google Scholar, and, for additional references, French, John Dee.

11. The expression “pure mathematics” is being used here in the sense given by Bacon in The Advancement of Learning:

“The Mathematics are either Pure or Mixed. To the Pure Mathematics are those sciences belonging which handle Quantity Determinate, merely severed from any axioms of natural philosophy … Mixed hath for subject some axioms or parts of natural philosophy, and considereth Quantity determined.” The Works of Francis Bacon, VI, 226–27Google Scholar.

12. From the translation in Johnson, , Astronomical Thought, p. 59Google Scholar.

13. From the translation in Stevens, Henry, Thomas Harriot (London, 1900), pp. 78–79Google Scholar.

14. On Digges see Johnson, , Astronomical Thought, pp. 156–71Google Scholar, and, for further references, the article on him in Gillispie, C. C. (ed.), Dictionary of Scientific Biography (hereafter, DSB), (New York, 1970-)Google Scholar. On Harriot see Waters, , The Art of Navigation, pp. 584–91Google Scholar, Pepper, Jon V., “Harriot's Calculation of the Meridional Parts as Logarithmic Tangents,” Archives for History of Exact Science, 4 (1968), 359–413CrossRefGoogle Scholar, and, for additional references, the article on him in Gillispie, DSB. See also note 21 below.

15. “Mathematical Instruments and the Education of Gentlemen,” Annals of Science, 30 (1973), 52Google Scholar.

16. Ibid., 52n. The rise of practical mathematical studies among the English gentry is treated in: Watson, The Beginnings of the Teaching of Modern Subjects; Woodward, William W., Studies in Education During the Age of the Renaissance (1906; reprint New York, 1965), pp. 296–322Google Scholar; Kelso, Ruth, The Doctrine of the English Gentleman in the Sixteenth Century [Illinois Studies in Language and Literature, 14] (Urbana, 1929)Google Scholar; Kearney, Hugh F., Scholars and Gentlemen: Universities and Society in Pre-Industrial Britain, 1500-1700 (London, 1970)Google Scholar; Turner, J. A., “Mathematical Instruments and the Education of Gentlemen,” Annals of Science, 30, 51–88CrossRefGoogle Scholar.

17. On Elizabethan mathematical practitioners see: Johnson, , Astronomical Thought, pp. 171-73, 196-205, 290-91, 301 ffGoogle Scholar; Johnson, Francis R., “Gresham College: Precursor of the Royal Society,” J.H.I., 1 (1940), 413–38Google Scholar; Johnson, Francis R., “Thomas Hood's Inaugural Address as Mathematical Lecturer of the City of London (1588),“ J.H.I., 3 (1943), 94–106Google Scholar; Zilsel, , “The Origins of William Gilbert's Scientific Method,” J.H.I., 2, 1–32Google Scholar; Taylor, , Mathematical Practitioners, pp. 244-64, 311ffGoogle Scholar; Waters, , The Art of Navigation, pp. 495–500Google Scholar; Taylor, Eva G.R., A Regiment for the Sea and Other Writings of Navigation by William Bourne (Cambridge, 1963), pp. i–xxxiiGoogle Scholar; Hill, , Intellectual Origins, pp. 35–52Google Scholar.

Gilbert's debt to Borough and Norman has been taken by some historians (e.g., Zilsel) as evidence for the following twofold thesis: the essential feature of the scientific revolution was the experimental method; this method was in England the work of the practitioners, chiefly as a result of their attention to navigational problems. But, as earlier remarks in this paper indicate, contemporary mathematicians (e.g., Dee, Digges, Harriot) were neither ignorant of nor unwilling to apply the experimental method. Criticism of the “Zilsel thesis” is implicit in Crombie, , Robert Grosseteste, esp. pp. 290–319Google Scholar, in which the history of the experimental method in England is sketched into Newton's time from the time of Grosseteste.

18. Information on the revival of practical mathematics at the two universities is given in: Mullinger, James Bass, The University of Cambridge (Cambridge, 1884), II, 404–13Google Scholar; Ball, , A History of the Study of Mathematics at Cambridge, pp. 153–56Google Scholar; Johnson, , Astronomical Thought, pp. 189–96Google Scholar; Hexter, J. H., “The Education of the Aristocracy in the Renaissance,” Journal of Modern History, 22 (1950), 1–20CrossRefGoogle Scholar; Curtis, , Oxford and Cambridge in Transition, pp. 54-82, 101-14, 227-44, 249–50Google Scholar.

19. This section is based on Taylor, , Mathematical Practitioners, pp. 44–98Google Scholar, and Waters, , The Art of Navigation, pp. 340–494Google Scholar. For very recent studies of Briggs and Gunter see the articles on them in Gillispie, DSB.

20. “The English Virtuoso in the Seventeenth Century (Part I),” J.H.I., 3 (1942), 57–58Google Scholar.

21. Early seventeenth-century English virtuosity is discussed in: Stimson, Dorothy, Scientists and Amateurs: A History of The Royal Society (New York, 1948), pp. 26–45Google Scholar; Houghton, , “The English Virtuoso in the Seventeenth Century (Part I),“ J.H.I., 3, 51–73Google Scholar; Sharkey, John W., “The Scientific Experiments of Sir Walter Raleigh, the Wizard Earl, and Three Magi in the Tower, 1603-1617,” Ambix, 4 (1949), 52–66Google Scholar; Kargon, Robert, “Thomas Harriot, The Northumberland Circle and Early Astronomy in England,” J.H.I., 27 (1966), 128–36Google Scholar. See also note 14 above.

22. From the translation of the Savilian statutes in Ward, G. L. M., Oxford University Statutes, (London, 1845), I, 273Google Scholar.

23. Ibid., p. 273.

24. Ibid., p. 274.

25. Ibid.

26. Lives of Eminent Men (London, 1813), II, Pt. 2, 625–26Google Scholar.

27. This section is based on the works cited in note 19.

The practitioners did not entirely replace mathematicians in navigational mathematics. One problem in particular continued to occupy England's mathematicians after 1650, the determination of longitude at sea. But, through the weakening of the navigational interests' hold on them, the English mathematicians were not constrained to work on this problem, and it became just one of the many that were to occupy their attention (see Part IV.)

28. “The English Virtuoso in the Seventeenth Century (Part I),“ J.H.I., 3, 71–72Google Scholar.

29. Ibid., 62.

30. The Beginnings of the Teaching of Modern Subjects, p. lii.

31. For mid-seventeenth-century English virtuosity see: Clark, , Science and Social Welfare, pp. 9–12Google Scholar; Merton, , Science, Technology and Society, pp. 19-31, 203–06Google Scholar; Houghton, , “The English Virtuoso in the Seventeenth Century (Part I),“ J.H.I., 3, 51–73Google Scholar; Stimson, , Scientists and Amateurs, pp. 27–96Google Scholar; Ornstein, Martha, The Role of Scientific Societies in the Seventeenth Century (reprint of 3rd ed.; London, 1963), pp. 91–112Google Scholar.

Some historians (e.g., Hessen) have argued that the navigational interests dictated the course of development and the subject matter of English mathematics into Newton's time. For criticism of this viewpoint see: Clark, , Science and Social Welfare, pp. 60–91Google Scholar; Merton, , Science, Technology and Society, pp. 206–07Google Scholar; Hall, , Ballistics in the Seventeenth Century, p. 163Google Scholar.

32. The Works of Francis Bacon, VI, 215Google Scholar.

33. Ibid., VIII, 104, Aph. LXXIII.

34. Ibid., VIII, 157, Aph. CXXIV.

35. Ibid., VI, 134.

36. (2nd ed.; Oxford, 1664), pp. 51-52.

A fuller treatment of Bacon's philosophy is given in Purver, Margery, The Royal Society: Concept and Creation (London, 1967), pp. 20–62Google Scholar.

Contrary to accepted opinion, Bacon was not only an admirer of speculative science but also of mathematical science or, as he called it, “mixed mathematics.” In The Advancement of Learning he made the following remarks on its behalf:

“For many parts of nature can neither be invented with sufficient subtilty, nor demonstrated with sufficient perspicuity, nor accommodated unto use with sufficient dexterity, without the aid and intervening of the Mathematics” (The Works of Francis Bacon, VI, 226–27Google Scholar). “And as for the Mixed Mathematics, I may only make this prediction, that there cannot fail to be more kinds of them, as nature grows further disclosed.” (Ibid., VI, 228). See also Purver, , The Royal Society, pp. 57–58Google Scholar.

Merton, , in his Science, Technology and Society (p. 84n)Google Scholar, presented the quotation from Boyle in support of the thesis that the scientific revolution was greatly influenced by Puritanism. But the ideas Boyle was expressing have been held throughout the history of science. Criticisms of the “Puritan thesis” are given in: Feuer, Lewis, The Scientific Intellectual: The Psychological and Social Origin of Modern Science (New York and London, 1963), pp. 1-82, 405–24Google Scholar; Purver, , The Royal Society, pp. 143–58Google Scholar; Shapiro, Barbara, “The Universities and Science in 17th-Century England,” Journal of British Studies, 10(2) (1971), 48–82CrossRefGoogle Scholar; Mulligan, Lotte, “Anglicanism, Latitudinarianism and Science in England,” Annals of Science, 30 (1973), 213–19CrossRefGoogle Scholar.

37. The History of the Royal Society of London (London, 1667), p. 403Google Scholar.

38. Science, Technology and Society, p. 28.

39. Intellectual Origins, p. 59.

40. Ibid., p. 60.

41. Cited in Stimson, , Scientists and Amateurs, p. 58Google Scholar.

42. Cited in Weld, C. R., A History of the Royal Society with Memoirs of the Presidents (London, 1848). p. 31Google Scholar.

43. A recent work on the sciences at the two universities in the seventeenth century is Shapiro, , “The Universities and Science in 17th-Century England,” J.B.S. 10(2) (1971), 48–82Google Scholar.

44. The History of the Royal Society of London, p. 53. Oxford's experimental science club is treated in Purver, , The Royal Society, pp. 101–27Google Scholar.

45. Purver argues that the Royal Society's only true forerunner was Oxford's experimental science club, Gresham College's understanding of the New Philosophy being too narrow and utilitarian to have made any contribution to its establishment. But, as the present essay has maintained, the college's faculty and the Greshamites as well were oriented to speculative concerns by the 1650s. The Royal Society, pp. 182-92. Further evidence that the Gresham professors and the Greshamites did participate with Oxford's experimental science club in founding the Royal Society is given in Sprat, , The History of the Royal Society of London, pp. 57–58Google Scholar, in which it is made clear that the Gresham professors Rooke and Wren along with such Greshamite virtuosi as Viscount Brouncker were active in the Wilkins circle meetings at Gresham College in the years 1658-60.

46. Ornstein, , The Role of Scientific Societies, p. 102nGoogle Scholar.

47. Sprat, , History of the Royal Society, p. 67Google Scholar. Purver, , The Royal Society, p. 237Google Scholar. Also see ibid., pp. 63-100.

Unexpected confirmation of the argument that the early Royal Society was devoted principally to speculative science comes from Merton. Despite his assertion in Science, Technology and Society, that “utilitarianism and instrumentalism … constituted the values about whch the culture of the [Newtonian] period was integrated” (pp. 21-22), a review of the minutes of the Royal Society for four years in the period 1661-1687 led Merton to conclude that “about seventy percent of [its] research had no practical affiliation” (p. 203.)