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Fields and the Intelligibility of Contact Action

Published online by Cambridge University Press:  21 April 2015

David Sherry
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Abstract

This article concerns arguments for the impossibility of contact action and, subsequently, the use of force fields to render intelligible apparent cases of contact action. I argue that instead of unraveling the mystery of contact action, fields only deepen the mystery. Further, I show that there is a confusion underlying arguments for the impossibility of contact and present an analysis of contact, based upon Körner's treatment of empirical continuity, which restores intelligibility to apparent cases of contact action.

Type
Research Article
Information
Philosophy , Volume 90 , Issue 3 , July 2015 , pp. 457 - 477
Copyright
Copyright © The Royal Institute of Philosophy 2015 

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References

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14 Ibid.

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20 Op. cit. note 3, 2.

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22 But see §3 below.

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24 Op. cit. note 3, 3–6. The practice has its critics: See Geach, Peter Logic Matters (Berkeley: University of California Press, 1972), 313ffGoogle Scholar., Harré, Rom and Madden, Edward Causal Powers (Totowa, NJ: Rowman and Littlefield, 1975), 109–112 Google Scholar et passim., and op. cit. note 17, 220ff.

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27 Ibid.

28 Op. cit. note 9, 27.

29 Op. cit. note 3, 34–5.

30 Ibid., 26.

31 Ibid., 34.

32 Ibid., 163n2.

33 Ibid., 166–7.

34 Ibid., 29–30.

35 Indeed, Dretske has detailed a number of difficulties with the notion of a moving event; see Dretske, Fred, ‘Can Events Move’, Mind 76 (1967)Google Scholar, especially 489. Hacker has questioned whether existence can even be intelligibly predicated of events; see Hacker, Peter, ‘Events, Ontology and Grammar’, Philosophy 57 (1982), 479 CrossRefGoogle Scholar.

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37 Lange argues that it is a problem insofar as it violates conservation of energy and momentum. See op. cit. note 3, 112ff.

38 Ibid., 32.

39 Ibid., 1. Cf. Telushkin, Joseph, Jewish Humor (New York: Morrow, 1992), 60Google Scholar.

40 Ibid.

41 See, for example, Grunbaum, Adolf, Modern Science and Zeno's Paradoxes (London: George Allen and Unwin 1968), 121ffGoogle Scholar. Grunbaum argues that since there are uncountably many points on a line, and since measure theory assigns no meaning to summing an uncountable infinity of lengths, Zeno's conclusion does not follow. But this is only an ad hoc solution to the problem, because uncountable summations can be defined - as the supremum of all possible finite sums (cf. Sherry, David, ‘Zeno's Metrical Paradox Revisited’ Philosophy of Science 55 (1988), 65 CrossRefGoogle Scholar.)

42 See Sorabji, Richard, Time, Creation, and the Continuum (Ithaca: Cornell University Press, 1983)Google Scholar, chapter 26.

43 Körner, Stephan, ‘Empirical Continuity’, The Monist 47 (1962), 1–19 CrossRefGoogle Scholar.

44 Ibid., 8.

45 If a given class Pi admits further division into Pi1 and Pi2, then a transition from Pi to Pi+1 that omits a discernible class would be discontinuous. Cf. op. cit. note 43, 10.

46 Ibid., 14.

47 Ibid., 12.

48 Op. cit. note 25, Phys. 226b23 and 243a34.

49 Smith, Sheldon, ‘Continuous Bodies, Impenetrability, and Contact Interactions: The View from the Applied Mathematics of Continuum Mechanics’, British Journal for the Philosophy of Science 58 (2007), 503–538 CrossRefGoogle Scholar. Smith calls the skeptical argument ‘the root argument’.

50 Ibid., 535.

51 Ibid., 508–9.

52 Ibid., 534.

53 Ibid., 504–5.

54 Ibid., 527.

55 Ibid.

56 Ibid. Contact in this sense is possible between open bodies, i.e., bodies that do not contain their boundaries, such as a sphere all of whose points are less than a distance r from its center. The reduced boundaries of these bodies can intersect, even though the bodies do not contain them. Cf. ibid., 526 for the rather involved definition of ‘reduced boundary’.

57 Ibid., 525.

58 Ibid., 526–7.

59 Smith treats the concept of impenetrability similarly; cf. ibid., 511–518. The axiom of impenetrability can be relaxed to allow overlap between material points as long as the region of overlap has Lebesgue measure zero. Here, too, it is the available mathematics that drives the conceptualization of the bodies involved.

60 Ibid., 533.

61 Ibid., 508.

62 Ibid., 508–9.

63 Ibid.

64 Ibid., 503.

65 Ibid., 509.

66 See Wapner, Leonard, The Pea and the Sun (Wellesley, MA: A.K. Peters, Ltd., 2005)Google Scholar for a semi-popular exposition of this theorem. Strictly speaking, the theorem decomposes a ball that includes its boundary. The decomposition proceeds in two stages: First the boundary is decomposed, and then the interior, on the basis of the former. Smith's billiard balls do not include their boundary, but that would not prevent us from using their closure to carry out the Banach-Tarski decomposition.

67 I owe thanks to Peter Kosso for useful stylistic advice.