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Some reflections on Newton's Principia

Published online by Cambridge University Press:  22 December 2008

E. B. DAVIES
E. B. DAVIES
Affiliation:
Department of Mathematics, King's College, Strand, London, WC2R 2LS, UK. Email: E.Brian.Davies@kcl.ac.uk.
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Abstract

This article examines the text of Principia Mathematica to discover the extent to which Newton's claims about his own contribution to it were justified. It is argued that for polemical reasons the General Scholium, written twenty-six years after the first edition, substantially misrepresented the methodology of the main body of the text. The article discusses papers of Wallis, Wren and Huygens that use the third law of motion as set out by Newton in Book 1. It also argues that Newton's use of induction is quite different from and subtler than the ‘logical’ and ‘probabilistic’ notions of induction discussed and then rejected by a number of twentieth-century philosophers.

Type
Research Article
Information
The British Journal for the History of Science , Volume 42 , Issue 2 , June 2009 , pp. 211 - 224
Copyright
Copyright © 2008 British Society for the History of Science

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References

1 I. B. Cohen and A. Whitman, Isaac Newton, The Principia, a New Translation, Berkeley, 1999 (hereafter Cohen and Whitman Principia).

2 Cohen and Whitman Principia, op. cit. (1), 416–17.

3 Cohen and Whitman Principia, op. cit. (1), 382, 424.

4 R. Westfall, Never at Rest: A Biography of Isaac Newton, Cambridge, 1980, 409–20.

5 Halley, E., ‘Review of Newton's Principia’, Philosophical Transactions of the Royal Society (1685–6), 15, 291–7.Google Scholar

6 Cohen and Whitman Principia, op. cit. (1), 405.

7 Cohen and Whitman Principia, op. cit. (1), 418.

8 Cohen and Whitman Principia, op. cit. (1), 419, 420.

9 Cohen and Whitman Principia, op. cit. (1), 109.

10 Cohen and Whitman Principia, op. cit. (1), 424.

11 Cohen and Whitman Principia, op. cit. (1), 117, 118.

12 I. B. Cohen and G. E. Smith, The Cambridge Companion to Newton, Cambridge, 2002, 68.

13 The Mathematical Papers of Isaac Newton (ed. D. T. Whiteside), 8 vols., Cambridge, 1967–81, v, 148, n. 152.

14 Mathematical Papers of Isaac Newton, op. cit. (13), 149, n. 153.

15 Mathematical Papers of Isaac Newton, op. cit. (13), 148, 149, n. 152.

16 Wallis, J. and Wren, C., ‘A summary account of the general laws of motion’, Philosophical Transactions of the Royal Society (1668), 3, 864–8.CrossRefGoogle Scholar

17 He actually uses the word Vis, which we take to mean Vis Insita. This was a well-known term at the time and was used by Newton in Principia, Definition 3. Cohen and Whitman Principia, op. cit. (1), 404.

18 In the context it is tempting to translate Pondus as ‘mass’ rather than ‘weight’. A distinction between the two concepts was made in Cohen and Whitman Principia, op. cit. (1), 404, but it had not been well understood before that.

19 For twentieth-century scientists the quantity V=PC, with P interpreted as mass and C as velocity, is by definition the momentum, but it carries no connotation of being a force, as we understand the latter word.

20 Huygens, C., ‘A summary account of the laws of motion’, Philosophical Transactions of the Royal Society (1669), 4, 925–8.Google Scholar

21 Cohen and Whitman Principia, op. cit. (1), 420.

22 Cohen and Whitman Principia, op. cit. (1), 427.

23 Cohen and Whitman Principia, op. cit. (1), 425–8.

24 Cohen, I. B., ‘Newton's third law and universal gravity’, Journal of the History Ideas (1987), 48, 571–93, 583.CrossRefGoogle Scholar

25 Cohen and Whitman Principia, op. cit. (1), 427, 428.

26 Cohen and Whitman Principia, op. cit. (1), 428.

27 Cohen and Whitman Principia, op. cit. (1), 425.

28 Scott, J. F.: ‘The Reverend John Wallis (1616–1703)’, Notes and Records of the Royal Society (1960), 15, 57–67.CrossRefGoogle Scholar

29 Cohen and Whitman Principia, op. cit. (1), 452.

30 Cohen states that Newton was not in fact familiar with Galileo's work. Cohen and Whitman Principia, op. cit. (1), 113, 146.

31 Cohen and Whitman Principia, op. cit. (1), 793.

32 Cohen and Whitman Principia, op. cit. (1), 529, 532.

33 Cohen and Whitman Principia, op. cit. (1), 539–43.

34 See, for example, Cohen and Whitman Principia, op. cit. (1), 647, 662, 749.

35 Cohen and Whitman Principia, op. cit. (1), 795.

36 Cohen and Whitman Principia, op. cit. (1), 796. The original Latin is ‘In philosophia experimentalis, propositiones ex phaenomenis per inductionem collectae, non obstantibus contraries hypothesibus, pro veris aut accurate aut quamproxime haberidebent, donec alia occurrerint phaenomena, per quae aut accuratiores reddantur aut exceptionibus obnoxiae’.

37 Isaac Newton, Opticks (4th edn, 1730), New York, 1952, 404.

38 K. R. Popper, The Logic of Scientific Discovery, London, 1974, 53.

39 K. Popper, Realism and the Aim of Science, London, 1983, 147.

40 Davies, E. B., ‘The Newtonian myth’, Studies in History and Philosophy of Science (2003), 34, 763–80.CrossRefGoogle Scholar

41 J. M. Keynes, A Treatise on Probability, London, 1921, Chapter 20.

42 Cohen and Whitman Principia, op. cit. (1), 797–801.

43 S. Inwood, The Man Who Knew Too Much: The Strange and Inventive Life of Robert Hooke, Oxford, 2002, 84, 85.

44 Inwood, op. cit. (43), 290.

45 Cohen and Whitman Principia, op. cit. (1), 802.

46 Cohen and Whitman Principia, op. cit. (1), 446 and 801.

47 Cohen and Whitman Principia, op. cit. (1), 800 and 449.

48 Cohen and Whitman Principia, op. cit. (1), 802.

49 Cohen and Whitman Principia, op. cit. (1), 805.

50 Cohen and Whitman Principia, op. cit. (1), 806–8.

51 Cohen and Whitman Principia, op. cit. (1), 939.

52 Inwood, op. cit. (43), 81.

53 Cohen and Whitman Principia, op. cit. (1), 895.

54 Cohen and Whitman Principia, op. cit. (1), 911.

55 Cohen and Whitman Principia, op. cit. (1), 928.

56 P. Duhem, The Aim and Structure of Physical Theory, New York, 1981, 192 (French original 1914); K. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge, London, 1989, 185.

57 Since the Sun is a thousand times the mass of Jupiter, one would expect the ‘constant’ value of a 3/P 2 in Kepler's third law to vary by no more than one part per thousand from one planet to another.

58 Cohen and Whitman Principia, op. cit. (1), 816; original italics.

59 S. Chandrasekhar, Newton's Principia for the Common Reader, Oxford, 1995 (hereafter Chandrasekhar Principia).

60 Cohen and Whitman Principia, op. cit. (1), 295.

61 Chandrasekhar Principia, op. cit. (59), 41.

62 Chandrasekhar Principia, op. cit. (59), 377.

63 Cohen and Whitman Principia, op. cit. (1), 408–15.

64 Westfall, op. cit. (4), 415.

65 Westfall, op. cit. (4), 749, 750.

66 Cohen and Whitman Principia, op. cit. (1), 943.

67 Berkeley, Kant, Laplace and others later decided that physical explanations were entirely unnecessary. Almost no physicist today thinks that we have a physical explanation of the laws of quantum mechanics while many do not even think that we should expect to get one in the future. Nevertheless our mathematical description of how it works is extremely detailed and highly successful.

68 Davies, op. cit. (40).

69 Cohen and Whitman Principia, op. cit. (1), 393.

70 Newton to Cotes, 29 March 1713, cited in Cohen and Whitman Principia, op. cit. (1), 277.

71 Cohen and Whitman Principia, op. cit. (1), 797–801.

72 Cohen and Whitman Principia, op. cit. (1), 276.

73 Einstein, A., ‘Newtons Mechanik und ihr Einfluss auf die Gestaltung der theoretischen Physik’, Naturwissenschaften (1927), 15, 273–6CrossRefGoogle Scholar (English version in idem, The World as I See It, New York, 1934); H. Poincaré, Science and Hypothesis, New York, 1952.

74 S. Drake, Essays on Galileo, 2 vols., Toronto, 2000, ii, 185. In his ‘Corollary on void’, Philoponus states that if one actually drops two substantially different weights, they fall at equal speeds. Place, Void and Eternity. Philoponus: Corollaries on Place and Void, tr. D. Furley, with Simplicus, Against Philoponus on the Eternity of the World, tr. C. Wildberg, London, 1991, 59.