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Published online by Cambridge University Press: 08 January 2010
In these prefatory remarks, which are designed to locate my topic within the complex and wide-stretching field of Popper's thought and writings, I shall not say anything that those familiar with his work will not already know. Moreover, what I do say will take as understood many of the problems and theories, not to mention the terminology, that I shall later be doing my best to make understandable. My apologies are therefore due equally to those who know something about Popper's discussions of indeterminism and of the propensity interpretation of probability, and to those who know nothing.
1 Magee, Bryan, Modern British Philosophy (London: Seeker and Warburg, 1971), p. 66.Google Scholar
2 Compare the assessment of The Postscript on p. 455 of Anthony O'Hear's critical notice, Mind94 (1985) pp. 453–471.Google Scholar
3 The point is elaborated in Chapter 2.2g, pp. 39–41, of Miller, David, Critical Rationalism. A Restatement and Defence (Chicago and La Salle: Open Court, 1994).Google Scholar
4 Russell, Bertrand, ‘On the Notion of Cause’, Mysticism and Logic (London: Allen & Unwin, 1918), p. 202; (Melbourne, London, & Baltimore: Pelican edition, 1953), p. 190Google Scholar
5 Ibid., p. 203; Pelican edition, pp. 191f.
6 Earman, John, A Primer on Determinism, The University of Western Ontario Series in Philosophy of Science, volume 32 (Dordrecht: D. Reidel Publishing Company, 1986), pp. 13f.Google Scholar
7 Compare Russell's remark that ‘in advanced sciences such as gravitational astronomy, the word “cause” never occurs’ (Russell, ‘On the Notion of Cause’, p. 189; Pelican edition, p. 171).Google Scholar
8 Watkins, John, Science and Scepticism (London: Hutchinson 1984), p. 205.Google Scholar
9 Earman, , A Primer on Determinism, Chapter III.CrossRefGoogle Scholar
10 Russell ‘On the Notion of Cause’, pp. 203–205, Pelican edition, pp. 192–194, and Earman, A Primer on Determinism, Chapter 11.5.Google Scholar
11 Compare Earman, ibid., p. 13, who limits himself to distinguishing between deterministic and indeterministic worlds. As far as I can see, the only formulation of determinism given is that the actual world is a deterministic world. Much of Earman's book is devoted to the task of investigating whether the principal theories of classical and modern physics are prima facie deterministic.
12 Cartwright, Nancy, How the Laws of Physics Lie (Oxford: Clarendon Press, 1983),CrossRefGoogle Scholar and Forster, Macolm and Sober, Elliott, ‘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 (1994), pp. 1–35,CrossRefGoogle Scholar are examples of contemporary writers who, not always for identical reasons, reject the view that real science is exact science.
13 Laplace, P. S., Essaiphilosophique sur les probabilites (1819).Google Scholar
14 The distinction is not registered by Honderich, who concludes that ‘successful predictions within neuroscience are evidence for determinism, even overwhelming evidence’. The version of determinism espoused by Honderich does not maintain that measurements of ever-increasing precision are possible—indeed, it seems to deny it—and accordingly it falls short of—or contradicts—scientific determinism. See Honderich, Ted, A Theory of Determinism (Oxford: Clarendon Press, 1988), Chapter 6.6, especially p. 356.Google Scholar
15 Duhem, Pierre, The Aim and Structure of Physical Theory (Princeton University Press 1954), Part II, Chapter III.3.Google Scholar
16 For details consult almost any book on chaos, for example, Stewart, Ian, Does God Play Dice?, (Oxford: Blackwell, 1989), pp. 155–164.Google Scholar A graph of the first 400 values of the logistic function for λ = 4, f(0) = 0.75000000012 may be found in Miller, Critical Rationalism, p. 155.
17 Earman, A Primer on Determinism, p. 9. It is on quite different grounds that Earman himself takes metaphysical determinism to fail in classical physics.Google Scholar
18 For example, Hunt, G. M. K., ‘Determinism, Predictability and Chaos’, Analysis 47 (1987), pp. 129–133.CrossRefGoogle Scholar
19 Earman, A Primer on Determinism, p. 10.Google Scholar
20 Meyerson, Emile, Identity and Reality (London: Allen & Unwin, 1930), Chapter V.Google Scholar
21 It is the central topic of Part III of Gillies, D. A., An Objective Theory of Probability (London: Methuen, 1973).Google Scholar See also Miller, Critical Rationalism, Chapter 9.3.
22 Hence the criticism of the propensity interpretation given in section 3.3 of Howson, Colin, ‘Theories of Probability’, The British Journal for the Philosophy of Science, 46 (1995), pp. 1–32,CrossRefGoogle Scholar is not a criticism of the propensity interpretation.
23 On this point see Miller, Critical Rationalism, pp. 104f.Google Scholar for further discussion and defence of the propensity interpretation, see ibid., Chapter 9.6.
24 See section 2.4 of Watkins, J. W. N., ‘The Unity of Popper's Thought’, in Schilpp, P. A. (ed.), The Philosophy of Karl Popper, The Library of Living Philosophers, volume XIV (La Salle: Open Court, 1974), pp. 371–412.Google Scholar
25 See p. 13 of Watkins, John, ‘Second Thoughts on Landés Blade’, Journal of Indian Council of Philosophical Research II (1985), pp. 13–19.Google Scholar
26 Ibid.
27 See pp. 369f. of Mackie, J. L., ‘Failures in Criticism: Popper and his Commentators’ [Review article of Schilpp, The Philosophy of Karl Popper, The British Journal for the Philosophy of Science, 29 (1978), pp. 363–375.]CrossRefGoogle Scholar
28 He seems even to hold that the indeterminist too has to accept that ‘the set-up is beset by various little asymmetries and disturbing influences, but these do not have any systematic bias towards either left or right’ (‘Second Thoughts on Lande's Blade’, p. 16). This is surely a mistake. Indeterminism assumes at most the constancy of the propensity of balls to fall one way or another, and is unbothered by whether or not there are asymmetries present.Google Scholar
29 Ibid.
30 Ibid., p. 18.
31 David Hume, A Treatise of Human Nature (1739), edition of L. A. Selby-Bigge (1888), p. 171, quoted in ‘OCC’ (OK, p. 227).Google Scholar
32 This has been a standard criticism of the propensity interpretation of probability. See, for example, Mellor, D. H., The Matter of Chance (Cambridge University Press, 1971), p. 158,Google Scholar and O'Hear, Anthony, Karl Popper (London: Routledge, 1980), pp. 136f.Google Scholar The reader is referred to the text to note 23 above.
33 See the Editor's Foreword to QTSP, p.xiii.Google Scholar
34 If p(a, c) = 0 then p(ab, c) = 0 by Bl and (18) of LSD, appendix *v. By M2, p(a, bc)p(b, c) = 0. Thus b can raise above 0 the probability of a, given c, only if b's own probability, given c, is 0.Google Scholar
