Popper and his commentators on the discovery of Neptune: A close shave for the law of gravitation?

Studies in History and Philosophy of Science Part A

Volumn 27, Issue 2, 1996, Pages 207-232

  Bamford, Greg ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

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EID: 0030159593     PISSN: 00393681     EISSN: 18792510     Source Type: Journal    
DOI: 10.1016/0039-3681(95)00045-3     Document Type: Article

References (143)

1. 1 K. R. Popper, Unended Quest: An Intellectual Autobiography, rev. ed. (London: Fontana, 1976), p. 42, and 'Replies to my Critics', in P. A. Schilpp (ed.), The Philosophy of Karl Popper (La Salle, Ill.: Open Court, 1974), bk. 2, pp. 961-1197, see pp. 1006-1007. Hereafter, I refer to these works as Unended Quest and 'Replies', respectively, and use shortened titles where appropriate for other frequently cited works.
2. 1 K. R. Popper, Unended Quest: An Intellectual Autobiography, rev. ed. (London: Fontana, 1976), p. 42, and 'Replies to my Critics', in P. A. Schilpp (ed.), The Philosophy of Karl Popper (La Salle, Ill.: Open Court, 1974), bk. 2, pp. 961-1197, see pp. 1006-1007. Hereafter, I refer to these works as Unended Quest and 'Replies', respectively, and use shortened titles where appropriate for other frequently cited works.
3. 2 See R. Grant, History of Physical Astronomy (n.p., 1852), reprint edn, The Sources of Science, No. 38 (New York: Johnson Reprint Corporation, 1966), Chaps XII and XIII, and App. III; W. M. Smart, 'John Couch Adams and the Discovery of Neptune', Occasional Notes of the Royal Astronomical Society 2 (August 1947), 1-56, and Celestial Mechanics (London: Longman, Green and Co., 1953), Chap. 16; M. Grosser, The Discovery of Neptune (Cambridge: Harvard University Press, 1962); N. R. Hanson, 'Leverrier: the Zenith and Nadir of Newtonian Mechanics', Isis 53 (September 1962), 359-377; and R. A. Lyttleton, Mysteries of the Solar System (Oxford: Clarendon Press, 1968), Chap. 7, and 'The Rediscovery of Neptune', in A. Beer (ed.), Vistas in Astronomy 3 (1960), 25-46.
4. 2 See R. Grant, History of Physical Astronomy (n.p., 1852), reprint edn, The Sources of Science, No. 38 (New York: Johnson Reprint Corporation, 1966), Chaps XII and XIII, and App. III; W. M. Smart, 'John Couch Adams and the Discovery of Neptune', Occasional Notes of the Royal Astronomical Society 2 (August 1947), 1-56, and Celestial Mechanics (London: Longman, Green and Co., 1953), Chap. 16; M. Grosser, The Discovery of Neptune (Cambridge: Harvard University Press, 1962); N. R. Hanson, 'Leverrier: the Zenith and Nadir of Newtonian Mechanics', Isis 53 (September 1962), 359-377; and R. A. Lyttleton, Mysteries of the Solar System (Oxford: Clarendon Press, 1968), Chap. 7, and 'The Rediscovery of Neptune', in A. Beer (ed.), Vistas in Astronomy 3 (1960), 25-46.
5. 2 See R. Grant, History of Physical Astronomy (n.p., 1852), reprint edn, The Sources of Science, No. 38 (New York: Johnson Reprint Corporation, 1966), Chaps XII and XIII, and App. III; W. M. Smart, 'John Couch Adams and the Discovery of Neptune', Occasional Notes of the Royal Astronomical Society 2 (August 1947), 1-56, and Celestial Mechanics (London: Longman, Green and Co., 1953), Chap. 16; M. Grosser, The Discovery of Neptune (Cambridge: Harvard University Press, 1962); N. R. Hanson, 'Leverrier: the Zenith and Nadir of Newtonian Mechanics', Isis 53 (September 1962), 359-377; and R. A. Lyttleton, Mysteries of the Solar System (Oxford: Clarendon Press, 1968), Chap. 7, and 'The Rediscovery of Neptune', in A. Beer (ed.), Vistas in Astronomy 3 (1960), 25-46.
6. 2 See R. Grant, History of Physical Astronomy (n.p., 1852), reprint edn, The Sources of Science, No. 38 (New York: Johnson Reprint Corporation, 1966), Chaps XII and XIII, and App. III; W. M. Smart, 'John Couch Adams and the Discovery of Neptune', Occasional Notes of the Royal Astronomical Society 2 (August 1947), 1-56, and Celestial Mechanics (London: Longman, Green and Co., 1953), Chap. 16; M. Grosser, The Discovery of Neptune (Cambridge: Harvard University Press, 1962); N. R. Hanson, 'Leverrier: the Zenith and Nadir of Newtonian Mechanics', Isis 53 (September 1962), 359-377; and R. A. Lyttleton, Mysteries of the Solar System (Oxford: Clarendon Press, 1968), Chap. 7, and 'The Rediscovery of Neptune', in A. Beer (ed.), Vistas in Astronomy 3 (1960), 25-46.
7. 2 See R. Grant, History of Physical Astronomy (n.p., 1852), reprint edn, The Sources of Science, No. 38 (New York: Johnson Reprint Corporation, 1966), Chaps XII and XIII, and App. III; W. M. Smart, 'John Couch Adams and the Discovery of Neptune', Occasional Notes of the Royal Astronomical Society 2 (August 1947), 1-56, and Celestial Mechanics (London: Longman, Green and Co., 1953), Chap. 16; M. Grosser, The Discovery of Neptune (Cambridge: Harvard University Press, 1962); N. R. Hanson, 'Leverrier: the Zenith and Nadir of Newtonian Mechanics', Isis 53 (September 1962), 359-377; and R. A. Lyttleton, Mysteries of the Solar System (Oxford: Clarendon Press, 1968), Chap. 7, and 'The Rediscovery of Neptune', in A. Beer (ed.), Vistas in Astronomy 3 (1960), 25-46.
8. 2 See R. Grant, History of Physical Astronomy (n.p., 1852), reprint edn, The Sources of Science, No. 38 (New York: Johnson Reprint Corporation, 1966), Chaps XII and XIII, and App. III; W. M. Smart, 'John Couch Adams and the Discovery of Neptune', Occasional Notes of the Royal Astronomical Society 2 (August 1947), 1-56, and Celestial Mechanics (London: Longman, Green and Co., 1953), Chap. 16; M. Grosser, The Discovery of Neptune (Cambridge: Harvard University Press, 1962); N. R. Hanson, 'Leverrier: the Zenith and Nadir of Newtonian Mechanics', Isis 53 (September 1962), 359-377; and R. A. Lyttleton, Mysteries of the Solar System (Oxford: Clarendon Press, 1968), Chap. 7, and 'The Rediscovery of Neptune', in A. Beer (ed.), Vistas in Astronomy 3 (1960), 25-46.
9. 2 See R. Grant, History of Physical Astronomy (n.p., 1852), reprint edn, The Sources of Science, No. 38 (New York: Johnson Reprint Corporation, 1966), Chaps XII and XIII, and App. III; W. M. Smart, 'John Couch Adams and the Discovery of Neptune', Occasional Notes of the Royal Astronomical Society 2 (August 1947), 1-56, and Celestial Mechanics (London: Longman, Green and Co., 1953), Chap. 16; M. Grosser, The Discovery of Neptune (Cambridge: Harvard University Press, 1962); N. R. Hanson, 'Leverrier: the Zenith and Nadir of Newtonian Mechanics', Isis 53 (September 1962), 359-377; and R. A. Lyttleton, Mysteries of the Solar System (Oxford: Clarendon Press, 1968), Chap. 7, and 'The Rediscovery of Neptune', in A. Beer (ed.), Vistas in Astronomy 3 (1960), 25-46.
10. 3 'Replies', op. cit., p. 1006.
11. 4 Unended Quest, op. cit., p. 43.
12. 5 'Replies', op. cit., p. 986.
13. 6 Ibid., p. 1035.
14. 7 A. O'Hear, Karl Popper (London: Routledge and Kegan Paul, 1980), p. 100.
15. 8 A. Musgrave, 'Falsification and its Critics', in P. Suppes, L. Henkin, A. Joga and G. C. Moisil (eds), Logic, Methodology and Philosophy of Science IV: Proceedings of the Fourth International Congress for Logic, Methodology and Philosophy of Science, Bucharest, 1971 (Amsterdam: North-Holland, 1973), pp. 393-406, see p. 397. Also, A. Musgrave, 'Method or Madness? Can the Methodology of Scientific Research Programmes be Rescued from Epistemological Anarchism?', in R. S. Cohen, P. K. Feyerabend and M. W. Wartofsky (eds), Essays in Memory of Imre Lakatos (Dordrecht: D. Reidel, 1976), pp. 457-491, see p. 459.
16. 8 A. Musgrave, 'Falsification and its Critics', in P. Suppes, L. Henkin, A. Joga and G. C. Moisil (eds), Logic, Methodology and Philosophy of Science IV: Proceedings of the Fourth International Congress for Logic, Methodology and Philosophy of Science, Bucharest, 1971 (Amsterdam: North-Holland, 1973), pp. 393-406, see p. 397. Also, A. Musgrave, 'Method or Madness? Can the Methodology of Scientific Research Programmes be Rescued from Epistemological Anarchism?', in R. S. Cohen, P. K. Feyerabend and M. W. Wartofsky (eds), Essays in Memory of Imre Lakatos (Dordrecht: D. Reidel, 1976), pp. 457-491, see p. 459.
17. 9 G. Radnitzky, 'Progress and Rationality in Research', in M. D. Grmek, R. S. Cohen and G. Cimino (eds), On Scientific Discovery: The Erice Lectures, 1977 (Dordrecht: D. Reidel, 1981), pp. 43-102, see p. 93.
18. 10 For example, I. Lakatos, 'Falsification and the Methodology of Scientific Research Programmes', in I. Lakatos and A. Musgrave (eds), Criticism and the Growth of Knowledge (Cambridge: Cambridge University Press, 1970), pp. 91-195, see p. 137; H. I. Brown, Perception, Theory and Commitment: The New Philosophy of Science (Chicago: University of Chicago Press, 1977), p. 147.
19. 10 For example, I. Lakatos, 'Falsification and the Methodology of Scientific Research Programmes', in I. Lakatos and A. Musgrave (eds), Criticism and the Growth of Knowledge (Cambridge: Cambridge University Press, 1970), pp. 91-195, see p. 137; H. I. Brown, Perception, Theory and Commitment: The New Philosophy of Science (Chicago: University of Chicago Press, 1977), p. 147.
20. 11 K. R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge, 4th edn, rev. (London: Routledge and Kegan Paul, 1972), p. 36, see also note 3, p. 38 and p. 244. For other examples of SPF, see K. R. Popper, The Logic of Scientific Discovery, 8th imp. (London: Hutchinson, 1975), p. 33; K. R. Popper, Objective Knowledge: An Evolutionary Approach (Oxford: Clarendon Press, 1972), note 5, p. 38; Popper, Unended Quest, op. cit., p. 38;
21. 11 K. R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge, 4th edn, rev. (London: Routledge and Kegan Paul, 1972), p. 36, see also note 3, p. 38 and p. 244. For other examples of SPF, see K. R. Popper, The Logic of Scientific Discovery, 8th imp. (London: Hutchinson, 1975), p. 33; K. R. Popper, Objective Knowledge: An Evolutionary Approach (Oxford: Clarendon Press, 1972), note 5, p. 38; Popper, Unended Quest, op. cit., p. 38;
22. 11 K. R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge, 4th edn, rev. (London: Routledge and Kegan Paul, 1972), p. 36, see also note 3, p. 38 and p. 244. For other examples of SPF, see K. R. Popper, The Logic of Scientific Discovery, 8th imp. (London: Hutchinson, 1975), p. 33; K. R. Popper, Objective Knowledge: An Evolutionary Approach (Oxford: Clarendon Press, 1972), note 5, p. 38; Popper, Unended Quest, op. cit., p. 38;
23. 11 K. R. Popper, Conjectures and Refutations: The Growth of Scientific Knowledge, 4th edn, rev. (London: Routledge and Kegan Paul, 1972), p. 36, see also note 3, p. 38 and p. 244. For other examples of SPF, see K. R. Popper, The Logic of Scientific Discovery, 8th imp. (London: Hutchinson, 1975), p. 33; K. R. Popper, Objective Knowledge: An Evolutionary Approach (Oxford: Clarendon Press, 1972), note 5, p. 38; Popper, Unended Quest, op. cit., p. 38;
24. and Popper, 'Replies', op. cit., pp. 979-980, 986-987, and note 78, p. 1187. For Lakatos's well known criticism of this aspect of Popper's methodology, see Lakatos and Musgrave, op. cit., pp. 100-101;
25. also, H. Putnam, 'The "Corroboration" of Theories', in Schilpp (ed.), op. cit., pp. 221-240, see pp. 225-229 and 237.
26. For a criticism of Lakatos and Putnam, see G. Bamford, Popper, Refutation, and 'Avoidance' of Refutation, Ph.D. Thesis, The University of Queensland (1989), pp. 27-38; see also note 24 below.
27. 12 Op. cit., p. 1035.
28. 13 Ibid., p. 998, see also p. 1037.
29. 14 Op. cit., note* 1, p. 101.
30. 15 A veneer of plausibility for SPF derives from Popper's analogy between the law of gravitation and universal generalisations such as 'All swans are white'. In 'Replies', op. cit., p. 987, for example, he says that generalisations of both kinds are falsifiable 'in the simple logical sense of being logically incompatible with some basic statements', that is, with singular existential statements 'describing easily observable states of physical bodies' (Conjectures, op. cit., p. 267). However, a singular existential statement that is inconsistent with this law, for example, 'There is a pair of bodies at k gravitationally attracted to one another as the sum of their masses and inversely as the cube of their separation' does not describe something 'easily observable'. On the other hand, whilst 'All swans are white' can be falsified by a basic statement, the logical structure of the antecedent in the corresponding falsification is typically disguised in ordinary English. Thus, if A is 'X is a swan' and P is 'X is white', it is natural to express the antecedent, (∼P & A), as one basic statement, 'X is a non-white swan', rather than as a conjunction of basic statements.
31. 16 'Replies', op. cit., p. 987.
32. 17 For example, D. W. Miller, Critical Rationalism: A Restatement and Defence (Chicago and La Salle, Ill.: Open Court, 1994), and G Andersson, Criticism and the History of Science: Kuhn's, Lakatos's and Feyerabend's Criticisms of Critical Rationalism (Leiden: E. J. Brill, 1994).
33. 17 For example, D. W. Miller, Critical Rationalism: A Restatement and Defence (Chicago and La Salle, Ill.: Open Court, 1994), and G Andersson, Criticism and the History of Science: Kuhn's, Lakatos's and Feyerabend's Criticisms of Critical Rationalism (Leiden: E. J. Brill, 1994).
34. 18 It might be argued that if a weaker interpretation of 'prima facie refuted' were adopted, there would be no requirement that A be prima facie true in my sense (which sense is, I take it, the ordinary sense of 'prima facie'). For example, suppose we say that T is prima facie refuted merely if P is refuted and there is no reason to think that A is false, which is the case with Uranus's residuals. What follows from having no reason to think that A is false, however, seems to be that we have no reason to think that ∼T is false, that is, on this argument, we have no reason to think that ris true - but is that what Popper et al. intend by 'prima facie refuted'? In any event, on the above definition, A would equally be prima facie refuted because there was likewise no reason to think that T was false.
35. 19 'Replies', op. cit., note 77, p. 1187.
36. 20 Ibid., p. 987.
37. 21 Ibid., p. 986.
38. 22 Ibid., p. 987.
39. 23 J. N. Hattiangadi, 'The Role of Auxiliary Hypotheses', Ratio 16 (1974), 115-120, see p. 117.
40. 1 (or (T & A)). In which case, whither the anomaly of Uranus's orbit?
41. 1 (or (T & A)). In which case, whither the anomaly of Uranus's orbit?
42. 25 See, for example, Logic, op. cit., p. 76; Conjectures, op. cit., p. 244; and 'Replies', op. cit., p. 1035. Also, the 'much older "system of the world"' was already 'affected' - by the discovery of Uranus itself.
43. 25 See, for example, Logic, op. cit., p. 76; Conjectures, op. cit., p. 244; and 'Replies', op. cit., p. 1035. Also, the 'much older "system of the world"' was already 'affected' - by the discovery of Uranus itself.
44. 25 See, for example, Logic, op. cit., p. 76; Conjectures, op. cit., p. 244; and 'Replies', op. cit., p. 1035. Also, the 'much older "system of the world"' was already 'affected' - by the discovery of Uranus itself.
45. 26 If the support for A had been initially stronger than the support for T then one could have reasonably said this of T, but these conditions do not obtain in this case and Popper does not claim that they do.
46. 27 See G. Bamford, 'Popper's Explications of Ad Hocness: Circularity, Empirical Content and Scientific Practice', The British Journal for the Philosophy of Science 44 (June 1993), 335-355.
47. 28 'Falsification', op. cit., p. 397.
48. 29 I have recourse to secondary sources, such as Grant, Smart and Grosser cited above, for much of the historical discussion which follows, though primary sources are used wherever possible. One purpose of this paper, however, is to show that the views of Popper and others are often inconsistent with such well known works, which further suggests their methodological positions or historical claims are the product of Popperian presuppositions.
49. 30 A. F. O'D. Alexander, The Planet Uranus: A History of Observation, Theory, and Discovery (London: Faber and Faber, 1965), p. 102; E. G. Forbes, 'The Pre-Discovery Observations of Uranus', in G. Hunt (ed.), Uranus and the Outer Planets (Cambridge: Cambridge University Press, 1982), pp. 67-80.
50. 30 A. F. O'D. Alexander, The Planet Uranus: A History of Observation, Theory, and Discovery (London: Faber and Faber, 1965), p. 102; E. G. Forbes, 'The Pre-Discovery Observations of Uranus', in G. Hunt (ed.), Uranus and the Outer Planets (Cambridge: Cambridge University Press, 1982), pp. 67-80.
51. 31 Alexander, op. cit., p. 275; Grosser, op. cit., p. 42.
52. 32 Grant, op. cit., pp. 166-167. See also, Grosser, op. cit., pp. 46 and 100; Alexander, op. cit., pp. 94 and 97; and Smart, 'Adams', op. cit., pp. 5 and 7.
53. 33 Grant, op. cit., pp. 176-177.
54. 34 Smart, 'Adams', op. cit., p. 7.
55. 35 Ibid, p. 7; Grant, op. cit., pp. 177-178.
56. 36 D. B. Herrmann says Bessel suggested this hypothesis in a letter to Olbers in 1823, see his The History of Astronomy from Herschel to Hertzsprung (Cambridge: Cambridge University Press, 1984), p. 36;
57. Forbes (op. cit., p. 72) says Bessel suggested it in a letter to Gauss in 1824; see also Grosser, op. cit., pp. 49-57.
58. 37 Smart, 'Adams', op. cit., pp. 15-17; Grant, op. cit., pp. 168-172 and 177-178.
59. 38 J. C. Adams, 'An Explanation of the Observed Irregularities in the Motion of Uranus, on the Hypothesis of Disturbances Caused by a More Distant Planet; with a Determination of the Mass, Orbit, and Position of the Disturbing Body', in W. G. Adams (ed.), The Scientific Papers of John Couch Adams, 2 vols (Cambridge: Cambridge University Press, 1896), vol. 1, p. 7.
60. 39 Alexander, op. cit., p. 90; Forbes, op. cit., p. 75.
61. 40 Planetary nebulae, however, are similar in appearance. In his 'Biographical Introduction' to J. L. E. Dreyer (ed.), The Scientific Papers of Sir William Herschel, 2 vols (London: The Royal Society and The Royal Astronomical Society, 1912), vol. 1, p. xxix, Dreyer remarks that if Herschel had previously seen a suitable planetary nebula he might well have mistaken Uranus for such a star.
62. 41 Forbes, op. cit., p. 69, says that when Tobias Mayer measured the position of Uranus one evening in 1756, for example, he did the same for a hundred or so stars, in less than three and a half hours.
63. 42 Grosser, op. cit., pp. 40-41.
64. 43 C. T. Kowal and S. Drake, 'Galileo's Observation of Neptune', Nature 287 (25 September, 1980), 311-313.
65. 44 Neptune was at opposition on 28 April 1960, and its period is 60,190 days, so it was previously at opposition in (roughly) late April 1795.
66. 45 Grant, op. cit., pp. 204-205; Flammarion, op. cit., p. 324. See also S. Newcomb, Popular Astronomy (London: Macmillan, 1878), p. 363.
67. 45 Grant, op. cit., pp. 204-205; Flammarion, op. cit., p. 324. See also S. Newcomb, Popular Astronomy (London: Macmillan, 1878), p. 363.
68. 46 I am extremely grateful to Dr David Dewhirst for discussing this and other practical (and historical) aspects of the discovery of Neptune, and for the generous assistance of the Institute of Astronomy at Cambridge.
69. 47 J. A. Bennett, 'The Discovery of Uranus', Sky and Telescope 61 (March 1981), 188-191, see p. 191.
70. 48 Op. cit., p. 191.
71. 49 See, for example, R. L. Bishop (ed.), Observer's Handbook 1988 (Toronto: Toronto University Press, 1988), pp. 128-130.
72. 50 See A. P. Norton and J. G. Inglis, A Star Atlas and Reference Handbook for Students and Amateurs, R. M. G. Inglis (ed.), 15th edn (Edinburgh: Gall and Inglis, 1966), pp. 42 and 45; and T. W. Webb, Celestial Objects for Common Telescopes (London: Longmans, Green, 1873), pp. 171-172. Charles Messier, 'the ferret of comets', was astonished by Herschel's discovery of the unremarkable Uranus, because he thought someone could only have found such a planet by its apparent motion - see Alexander, op. cit., pp. 29-30.
73. 50 See A. P. Norton and J. G. Inglis, A Star Atlas and Reference Handbook for Students and Amateurs, R. M. G. Inglis (ed.), 15th edn (Edinburgh: Gall and Inglis, 1966), pp. 42 and 45; and T. W. Webb, Celestial Objects for Common Telescopes (London: Longmans, Green, 1873), pp. 171-172. Charles Messier, 'the ferret of comets', was astonished by Herschel's discovery of the unremarkable Uranus, because he thought someone could only have found such a planet by its apparent motion - see Alexander, op. cit., pp. 29-30.
74. 51 Grosser, op. cit., pp. 27-37; Grant, op. cit., pp. 237-241.
75. 52 Grosser, op. cit., p. 39.
76. 53 P. Moore, Guide to the Planets (London: Eyre and Spottiswood, 1955), p. 117.
77. 54 Grant, op. cit., p. 242.
78. 55 Ibid., pp. 238-239.
79. 56 Dreyer, op. cit., Vol. 2, p. 197.
80. 57 Grant, op. cit., p. 191. To assist the search for asteroids, C. Harding, who discovered Juno, prepared Atlas Novus Coelestis, 27 feuilles, Gotingae, 1822. A. Clerke, History of Astronomy during the Nineteenth Century, 4th edn, rev. (London: Adam and Charles Black, 1902), p. 77, suggests Harding's atlas was 'the first systematic attempt to represent to the eye the telescopic aspect of the heavens'. The atlas maps stars down to the 10th magnitude from the North Pole to -30° south. The atlas contains 40,000 stars and so cannot be complete, and must have relied heavily on existing star catalogues. According to Grosser, op. cit., p. 117, Galle regarded Harding's chart of the area where he was to search for Neptune as not worth using.
81. 58 Herrmann, op. cit., p. 30; Grant, op. cit., pp. 241-242.
82. 59 See the entry, Akadamie der Wissenschaften in Berlin, Theil des Himmels zwischen 15° südlicher bis 15° nördlicher Abweichung. 24 feuilles, Berlin, 1858. in J. C. Houzeau, Vade-Mecum de L'Astronome (Brussels, 1882), p. 848.
83. 60 G. van Biesbroeck, 'Star Catalogues and Charts', in G. P. Kuiper (ed.), Stars and Stellar Systems, p. 479, vol. 3 of 9, in K. A. Strand (ed.), Basic Astronomical Data (Chicago: Chicago University Press, 1978); A. Pannekoek, A History of Astronomy (London: George Allen and Unwin, 1961), p. 479.
84. 60 G. van Biesbroeck, 'Star Catalogues and Charts', in G. P. Kuiper (ed.), Stars and Stellar Systems, p. 479, vol. 3 of 9, in K. A. Strand (ed.), Basic Astronomical Data (Chicago: Chicago University Press, 1978); A. Pannekoek, A History of Astronomy (London: George Allen and Unwin, 1961), p. 479.
85. 61 Houzeau, loc. cit.
86. 62 Grant, op. cit., pp. 191-192 and 242.
87. 63 Norton and Inglis, op. cit., p. 32. Neptune's orbit is inclined at less than 2° to the ecliptic.
88. 64 Smart, 'Adams', op. cit., p. 20.
89. 65 Houzeau, loc. cit. These charts were for hour 2, 10, 12, 13, 14, 21, 22 and 23 - see Fig. 2.
90. 66 By the same token, if it were in the area it would likely remain there a long time.
91. 67 Smart, 'Adams', op. cit., p. 49; this fact is not cause to doubt their methods, however, see pp. 50-51.
92. 68 See R. L. Bishop (ed.), Observer's Handbook 1985 (Toronto: Toronto University Press, 1988), p. 107.
93. 69 Grant, op. cit., pp. 239-240.
94. 70 Ibid., pp. 238-241.
95. 71 Fr. von Zach, Monatliche Correspondez zur Beförderung der Erd-und Himmels-Kunde, vol. 5 (Gotha, 1802), p. 499, gives the discovery position for Pallas as right ascension, 184° 56′ 49″, declination, +11° 33′; the chart is interleaved between pp. 504 and 505. Consider also the orbital data for, say, Ceres and Vesta. The ascending nodes of these asteroids are approx. 81° and 103°, respectively. So they reach their highest points above the ecliptic in or near, respectively, Olbers's search area in Virgo. Since their orbits have moderately steep inclinations to the ecliptic, 10.6° and 7.1°, respectively, it is clear that when they are visible in Virgo it is away from the ecliptic.
96. 72 Grant, op. cit., p. 242. How many asteroids did Olbers and Hencke miss? For the years 1981-88, for example, which is roughly half the duration of each of their searches, more than a dozen of the brightest asteroids for those years that were undiscovered at the time of their searches appeared in or near one or other of Olbers's two search areas.
97. See J. R. Percy (ed.), Observer's Handbook 1981 (Toronto: Toronto University Press, 1981), and for the years 1982-88 under the editorship of R. L. Bishop.
98. 73 Grant, op. cit., pp. 242-243.
99. 74 J. S. Encke to H. C. Schumacher, 26 September 1846, reprinted in H. Shapely and H. E. Howarth (eds), A Source Book in Astronomy (New York: McGraw Hill, 1929), pp. 252-254, see p. 254; Grosser, op. cit., pp. 116-119.
100. 74 J. S. Encke to H. C. Schumacher, 26 September 1846, reprinted in H. Shapely and H. E. Howarth (eds), A Source Book in Astronomy (New York: McGraw Hill, 1929), pp. 252-254, see p. 254; Grosser, op. cit., pp. 116-119.
101. 75 J. C. Adams to Professor J. Thompson, 26 November 1846, cited in J. W. L. Glaisher, 'Biographical Notice', in W. G. Adams (ed.), op. cit., 76ol. 1, pp. xv-xlviii, see p. xxxii.
102. 76 Yet this way of talking about the case is resolutely persistent. See, for example, M. Forster and E. Sober, 'How to Tell When Simpler, More Unified, or Less Ad Hoc Theories Will Provide More Accurate Predictions', The British Journal for the Philosophy of Science 45 (March 1994), 1-35, see p. 17.
103. 77 For example, Grant, Smart and Lyttleton. See also, Newcomb, op. cit., pp. 358-364; A. Pannekoek, 'The Discovery of Neptune', Centaurus 3 (1953), 126-137; and C. J. Brookes, 'On the Prediction of Neptune', Celestial Mechanics 3 (1970), 67-80. The Astronomer Royal, G. B. Airy, did express doubts in the 1830s about the possibility of discovering such an exterior planet by mathematical means - see pp. 388-389 and 391 of his 'Account of some Circumstances historically connected with the Discovery of the Planet exterior to Uranus', Memoirs of the Royal Astronomical Society XVI (1847), pp. 385-414. Airy supported the exterior planet hypothesis once Leverrier communicated his results to him and he saw how closely they agreed with Adams's calculations (p. 398). He also acknowledged that by the 1840s astronomers were impressed with 'the absolute necessity of seeking some external cause of disturbance' (p. 393). Airy did have one concern about Leverrier's and Adams's proposed solution, however - he questioned whether an exterior planet would also remove the discrepancies in Uranus's radius vector, a problem he was later to describe as an 'experimentum crucis' (p. 397). Airy wrote to Leverrier with this question on 26 June 1846, but then publicly announced the 'extreme probability' of finding the new planet before Leverrier's reply could reach him on 1 July (pp. 399-400). So how serious was his concern?
104. 77 For example, Grant, Smart and Lyttleton. See also, Newcomb, op. cit., pp. 358-364; A. Pannekoek, 'The Discovery of Neptune', Centaurus 3 (1953), 126-137; and C. J. Brookes, 'On the Prediction of Neptune', Celestial Mechanics 3 (1970), 67-80. The Astronomer Royal, G. B. Airy, did express doubts in the 1830s about the possibility of discovering such an exterior planet by mathematical means - see pp. 388-389 and 391 of his 'Account of some Circumstances historically connected with the Discovery of the Planet exterior to Uranus', Memoirs of the Royal Astronomical Society XVI (1847), pp. 385-414. Airy supported the exterior planet hypothesis once Leverrier communicated his results to him and he saw how closely they agreed with Adams's calculations (p. 398). He also acknowledged that by the 1840s astronomers were impressed with 'the absolute necessity of seeking some external cause of disturbance' (p. 393). Airy did have one concern about Leverrier's and Adams's proposed solution, however - he questioned whether an exterior planet would also remove the discrepancies in Uranus's radius vector, a problem he was later to describe as an 'experimentum crucis' (p. 397). Airy wrote to Leverrier with this question on 26 June 1846, but then publicly announced the 'extreme probability' of finding the new planet before Leverrier's reply could reach him on 1 July (pp. 399-400). So how serious was his concern?
105. 77 For example, Grant, Smart and Lyttleton. See also, Newcomb, op. cit., pp. 358-364; A. Pannekoek, 'The Discovery of Neptune', Centaurus 3 (1953), 126-137; and C. J. Brookes, 'On the Prediction of Neptune', Celestial Mechanics 3 (1970), 67-80. The Astronomer Royal, G. B. Airy, did express doubts in the 1830s about the possibility of discovering such an exterior planet by mathematical means - see pp. 388-389 and 391 of his 'Account of some Circumstances historically connected with the Discovery of the Planet exterior to Uranus', Memoirs of the Royal Astronomical Society XVI (1847), pp. 385-414. Airy supported the exterior planet hypothesis once Leverrier communicated his results to him and he saw how closely they agreed with Adams's calculations (p. 398). He also acknowledged that by the 1840s astronomers were impressed with 'the absolute necessity of seeking some external cause of disturbance' (p. 393). Airy did have one concern about Leverrier's and Adams's proposed solution, however - he questioned whether an exterior planet would also remove the discrepancies in Uranus's radius vector, a problem he was later to describe as an 'experimentum crucis' (p. 397). Airy wrote to Leverrier with this question on 26 June 1846, but then publicly announced the 'extreme probability' of finding the new planet before Leverrier's reply could reach him on 1 July (pp. 399-400). So how serious was his concern?
106. 77 For example, Grant, Smart and Lyttleton. See also, Newcomb, op. cit., pp. 358-364; A. Pannekoek, 'The Discovery of Neptune', Centaurus 3 (1953), 126-137; and C. J. Brookes, 'On the Prediction of Neptune', Celestial Mechanics 3 (1970), 67-80. The Astronomer Royal, G. B. Airy, did express doubts in the 1830s about the possibility of discovering such an exterior planet by mathematical means - see pp. 388-389 and 391 of his 'Account of some Circumstances historically connected with the Discovery of the Planet exterior to Uranus', Memoirs of the Royal Astronomical Society XVI (1847), pp. 385-414. Airy supported the exterior planet hypothesis once Leverrier communicated his results to him and he saw how closely they agreed with Adams's calculations (p. 398). He also acknowledged that by the 1840s astronomers were impressed with 'the absolute necessity of seeking some external cause of disturbance' (p. 393). Airy did have one concern about Leverrier's and Adams's proposed solution, however - he questioned whether an exterior planet would also remove the discrepancies in Uranus's radius vector, a problem he was later to describe as an 'experimentum crucis' (p. 397). Airy wrote to Leverrier with this question on 26 June 1846, but then publicly announced the 'extreme probability' of finding the new planet before Leverrier's reply could reach him on 1 July (pp. 399-400). So how serious was his concern?
107. 78 Lyttleton, Mysteries, op. cit., p. 228.
108. 79 J. Dorling, 'Bayesian Personalism, the Methodology of Scientific Research Programmes, and Duhem's Problem', Studies in History and Philosophy of Science 10 (1979), 177-187, see p. 178. See also, C. Howson and P. Urbach, Scientific Reasoning: The Bayesian Approach (La Salle, Ill.: Open Court, 1989), pp. 92-102.
109. 79 J. Dorling, 'Bayesian Personalism, the Methodology of Scientific Research Programmes, and Duhem's Problem', Studies in History and Philosophy of Science 10 (1979), 177-187, see p. 178. See also, C. Howson and P. Urbach, Scientific Reasoning: The Bayesian Approach (La Salle, Ill.: Open Court, 1989), pp. 92-102.
110. 80 Op. cit., pp. 179-180.
111. 81 Ibid., pp. 183-184.
112. 82 It is not clear, however, that Dorling's analysis offers a solution to the Duhem/Quine problem. His analysis shows how an anomaly can undermine the probability of A, which provides a reason to investigate replacing A rather than T, but it does not show that A is false or to be rejected.
113. 83 T. S. Kuhn, The Structure of Scientific Revolutions, 2nd edn (Chicago: University of Chicago Press, 1970), pp. 115-116.
114. 84 R. H. Austin, 'Uranus Observed', British Journal for the History of Science 3 (June 1967), 275-284.
115. 85 See also Andersson, op. cit., Chap. 6.2.1.
116. 86 Op. cit., p. 116.
117. 87 Ibid., p. 115.
118. 88 Not having reduced his observations, Lemonnier may not have known he was even observing the same body on each occasion.
119. 89 Op. cit., p. 133.
120. 90 Similarly, see A. Musgrave, 'Evidential Support, Falsification, Heuristics and Anarchism', in G. Radnitzky and G. Andersson (eds), Progress and Rationality in Science (Dordrecht: D. Reidel, 1978), pp. 181-201, see p. 188; John Worrall, 'Research Programmes, Empirical Support, and the Duhem Problem: Replies to Criticism', in Radnitzky and Andersson, op. cit., pp. 321-338, see p. 334; and A. Grünbaum, 'Ad Hoc Auxiliary Hypotheses and Falsificationism', The British Journal for the Philosophy of Science 27 (1976), 329-362, see p. 360.
121. 90 Similarly, see A. Musgrave, 'Evidential Support, Falsification, Heuristics and Anarchism', in G. Radnitzky and G. Andersson (eds), Progress and Rationality in Science (Dordrecht: D. Reidel, 1978), pp. 181-201, see p. 188; John Worrall, 'Research Programmes, Empirical Support, and the Duhem Problem: Replies to Criticism', in Radnitzky and Andersson, op. cit., pp. 321-338, see p. 334; and A. Grünbaum, 'Ad Hoc Auxiliary Hypotheses and Falsificationism', The British Journal for the Philosophy of Science 27 (1976), 329-362, see p. 360.
122. 90 Similarly, see A. Musgrave, 'Evidential Support, Falsification, Heuristics and Anarchism', in G. Radnitzky and G. Andersson (eds), Progress and Rationality in Science (Dordrecht: D. Reidel, 1978), pp. 181-201, see p. 188; John Worrall, 'Research Programmes, Empirical Support, and the Duhem Problem: Replies to Criticism', in Radnitzky and Andersson, op. cit., pp. 321-338, see p. 334; and A. Grünbaum, 'Ad Hoc Auxiliary Hypotheses and Falsificationism', The British Journal for the Philosophy of Science 27 (1976), 329-362, see p. 360.
123. 91 Op. cit., p. 111.
124. 92 Ibid., p. 109.
125. 93 T. S. Kuhn, 'The Function of Dogma in Scientific Research', in A. C. Crombie (ed.), Scientific Change: Historical Studies in the Intellectual, Social and Technical Conditions for Scientific Discovery and Technical Invention, from Antiquity to the Present (London: Heinemann, 1963), pp. 347-369, see pp. 365-366.
126. 94 W. H. Newton-Smith, The Rationality of Science (Boston: Routledge and Kegan Paul, 1981), p. 81.
127. 95 Op. cit., p. 234.
128. 96 P. K. Feyerabend, 'Consolations for the Specialist', in Lakatos and Musgrave (eds), op. cit., pp. 197-230, see p. 205.
129. 97 Unended Quest, op. cit., p. 42.
130. 98 J. W. N. Watkins, Against 'Normal Science', in Lakatos and Musgrave (eds), op. cit., pp. 25-37, see p. 28.
131. 99 Op. cit., pp. 101 and 107.
132. 100 Unended Quest, op. cit., p. 42.
133. 101 'Method or Madness?', op. cit., p. 466.
134. 102 It might be objected that it is precisely because Newton's theory was a good theory that attributing successive predictive failures to the various As was a strategy that worked time and again. This is true, but as an objection it simply fails to explain why T, in particular, should appear false on every such occasion. Why is the good T rather than, for example, the succession of convenient or plausible As specifically threatened by these predictive failures?
135. 103 Op. cit., p. 149.
136. 104 Grant, op. cit., pp. 189-190;
137. Norton and Inglis, op. cit., pp. viii and 32.
138. 105 Grant, op. cit., pp. 190 and 192; Grosser, op. cit., pp. 116-119; Lyttleton, 'Rediscovery', op. cit., p. 44; Encke in Shapely and Howarth (eds), op. cit., pp. 253-254. Clerke, op. cit., p. 80, says Leverrier claimed that the planet would be an 8th magnitude body; Smart, 'Adams', op. cit., pp. 28-29, says Adams claimed that the planet would be no duller than the 9th magnitude.
139. 106 Smart, 'Adams', op. cit., p. 7.
140. 107 Glaisher, loc. cit.
141. 108 Unended Quest, op. cit., p. 42.
142. 109 A related example is the later unsuccessful attempt to solve the problem of Mercury's perihelion by recourse to the hypothetical planet, Vulcan - see Hanson, 'Leverrier', op. cit.
143. 110 In 'Reflections on my Critics', in Lakatos and Musgrave (eds), op. cit., pp. 231-278, Kuhn says that as scientists 'can ordinarily take current theory for granted, exploiting rather than criticising it' they are 'freed to explore nature to an esoteric depth and detail otherwise unimaginable', which process 'will inform them when and where they can most usefully become Popperian critics' (p. 247). As I have indicated above, however, Leverrier or Adams could equally have been 'Popperian critics', so his distinction between exploiting and criticising a theory collapses here. The critic in this case would need to take current theory for granted to tease out what follows from it when a different assumption is made about the inventory of perturbing influences on Uranus, albeit in the expectation of finding that what follows is false and so turning up the heat on the theory. Contra Kuhn, one can think with a theory without being committed to it.