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Wittgenstein pp 112-136 | Cite as

Compulsions, Conventions and Codifications

  • David Bloor
Chapter
Part of the Theoretical Traditions in the Social Sciences book series

Abstract

We often construct arguments in which we move deductively from premises to conclusions. Suppose we assert one proposition, call it ‘p’, and then another to the effect that ‘if P, then q’ From these we can deduce the proposition represented by ‘q’ The principle ‘p, if p then q, therefore q’ is called modus ponens. What is the character of these deductive steps? Wittgenstein offers a purely naturalistic account: they are customs, set within a biological framework.1

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Notes and References

  1. 1.
    ‘I mean: this is simply what we do. This is use and custom among us, or a fact of our natural history’ (RFM, I, 63).Google Scholar
  2. 2.
    Cf. also RFM, II, 30 and V, 28.Google Scholar
  3. 3.
    A. Prior, ‘The Runabout Inference Ticket’, Analysis, vol.21, 1960, pp.38–9.CrossRefGoogle Scholar
  4. 4.
    Cf. also RFM, V, 1–8.Google Scholar
  5. 5.
    N. Belnap, ‘Tonk, Plonk and Plink’, Analysis, vol.22, 1962, pp.130–34.CrossRefGoogle Scholar
  6. For a valuable further discussion of the ramifications of Prior’s paper and the problem of justifying deduction, see: S. Haack, ‘The Justification of Deduction’, Mind vol.85, 1976, pp.112–19CrossRefGoogle Scholar
  7. S. Haack, ‘Dummett’s Justification of Deduction’, Mind, vol.XCI, 1982, 216–39.CrossRefGoogle Scholar
  8. 6.
    Belnap, ‘Tonk, Plonk and Plink’, p.131.Google Scholar
  9. 7.
    When it is argued that animals can reason, the evidence takes the form of showing that they can combine information in the way summed up by the rule of transitivity. The classic experiments are by Maier. See, for example, N. Maier, ‘Reasoning in Rats and Human Beings’, Psychological Review, vol.44, 1937, pp.365–78. The development of these claims can be followed in any decent textbook on learning-theory.CrossRefGoogle Scholar
  10. 8.
    N. Goodman, Fact, Fiction and Forecast, Indianapolis, Bobbs-Merrill, 1965, p.67. Similar claims have been made in the theory of rationality. For criticisms similar to those advanced below, see B. Barnes, ‘Vicissitudes of Belief’, Social Studies of Science, vol.9, 1979, pp.247–63.CrossRefGoogle Scholar
  11. 9.
    R. Rudner, in P. Edwards (ed.), The Encyclopedia of Philosophy, London, Collier-Macmillan, 1967, vol.3, p.371.Google Scholar
  12. 10.
    It is interesting to observe how, in emergencies, philosophers make sudden discoveries. For example, it is discovered that circular arguments are not, after all, things to be avoided. We have seen Goodman invoke the idea of virtuous rather than vicious circles. Similarly Dummett says that circular arguments are fine provided that our aim is to explain rather than persuade — he then proceeds to conflate explanation with justification: M. Dummett, ‘The Justification of Deduction’, Proceedings of the British Academy, vol.LIX, 1973, pp.201–32, p.207.Google Scholar
  13. It is also discovered that not all arguments are either deductive or inductive. Deduction can be justified by a new third mode of proof: see J. Bickenbach, ‘Justifying Deduction’, Dialogue, vol.18, 1979, pp.500–16. This is, in fact, an interesting line of argument but, on inspection, Bickenbach’s new method of proof turns out to be a disguised form of the inductive reasoning, from particulars to particulars, used in science. In other words, he is trying to justify deduction by induction, and this is bound to be too weak.CrossRefGoogle Scholar
  14. 11.
    ‘It is not a question of opinion. They are determined by a consensus of action: a consensus of doing the same thing, reacting in the same way. There is consensus but not a consensus of opinion’ (LFM, pp.183-4). Cf. OC, 110, 253.Google Scholar
  15. 12.
    M. Dummett, ‘Wittgenstein’s Philosophy of Mathematics’, Philosophical Review, vol.LXVIII, 1959, pp.324–48CrossRefGoogle Scholar
  16. (reprinted in G. Pitcher (ed.), Wittgenstein, London, Macmillan, 1968, pp.420–47, pp.425–6).Google Scholar
  17. 13.
    Ibid, p.434.Google Scholar
  18. 14.
    Ibid, p.438.Google Scholar
  19. 15.
    B. Russell, The Principles of Mathematics, Cambridge, Cambridge University Press, 1903, p.15.Google Scholar
  20. 16.
    C. Lewis, ‘Implication and the Algebra of Logic’, Mind, vol.21, 1912, pp.522–31.CrossRefGoogle Scholar
  21. 17.
    Ibid, p.530.Google Scholar
  22. 18.
    Ibid, p.531.Google Scholar
  23. 19.
  24. 20.
    A. Anderson and N. Belnap, Entailment. The Logic of Relevance and Necessity, vol.1, Princeton, Princeton University Press, 1975Google Scholar
  25. A. Anderson, ‘An Intensional Interpretation of Truth-Values’, Mind, vol.81, 1972, pp.348–71CrossRefGoogle Scholar
  26. A. Anderson and N. Belnap, ‘Enthymemes’, Journal of Philosophy, vol.LVIII, no.23, 1961, pp.713–23.CrossRefGoogle Scholar
  27. 21.
    Anderson, ‘An Intensional Interpretation’, p.368.Google Scholar
  28. 22.
    This is the position of E. Nelson, ‘Intensional Relations’, Mind, vol.39, 1930, pp.29–453.Google Scholar
  29. 23.
    Anderson and Belnap, Entailment, p.296.Google Scholar
  30. 24.
    D. Makinson, Topics in Modern Logic, London, Methuen, 1973.Google Scholar
  31. 25.
    T. Smiley, ‘Entailment and Deducibility’, Proceedings of the Aristotelian Society, new series vol.LIX, 1958–9, pp.233–54, p.250.Google Scholar
  32. 26.
    Anderson and Belnap, Entailment, p.165.Google Scholar
  33. 27.
    B. Bosanquet, Logic or the Morphology of Knowledge, Oxford, Clarendon Press, 1911, vol.1, p.323. (The first edition was in 1888.)CrossRefGoogle Scholar
  34. 28.
    F. Bradley, The Principles of Logic, Oxford, Oxford University Press, 1922, vol.1, p.130. (The first edition was in 1883.)Google Scholar
  35. 29.
    Ibid, p.139.Google Scholar
  36. 30.
  37. 31.
    Smiley, ‘Entailment and Deducibility’, p.233.Google Scholar
  38. 32.
    T. Carlyle, ‘Signs of the Times’, in his Critical and Miscellaneous Essays, London, Chapman and Hall, n.d. (four volumes in two), vol.1, p.104 (this essay was first published in 1829)Google Scholar
  39. J. Passmore, A Hundred Years of Philosophy, London, Duckworth, 1957, ch.7,’ some Critics of Formal Logic’.Google Scholar
  40. 33.
    This is the stance taken, for example, by H. Reichenbach, in Nomological Statements and Admissible Operations, Amsterdam, North Holland, 1954, pp.14–15.Google Scholar
  41. 34.
    The critic is J. Bennett, quoted in Anderson, ‘An Intensional Interpretation’, p.364.Google Scholar
  42. 35.
    See Makinson, Topics in Modern Logic, pp.27-41.Google Scholar
  43. 36.
    A measure of the complexity of this relationship may be gathered from the rigorous development provided by A. Church, Introduction to Mathematical Logic, vol.I, Princeton, New Jersey, Princeton University Press, 1956.Google Scholar
  44. 37.
    ‘There correspond to our laws of logic very general facts of daily experience. They are the ones that make it possible for us to keep on demonstrating those laws in a very simple way (with ink on paper, for example)’ (RFM, I, 118).Google Scholar

Copyright information

© David Bloor 1983

Authors and Affiliations

  • David Bloor
    • 1
  1. 1.University of EdinburghUK

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