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
‘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).
Cf. also RFM, II, 30 and V, 28.
A. Prior, ‘The Runabout Inference Ticket’, Analysis, vol.21, 1960, pp.38–9.
Cf. also RFM, V, 1–8.
N. Belnap, ‘Tonk, Plonk and Plink’, Analysis, vol.22, 1962, pp.130–34.
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.112–19
S. Haack, ‘Dummett’s Justification of Deduction’, Mind, vol.XCI, 1982, 216–39.
Belnap, ‘Tonk, Plonk and Plink’, p.131.
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.
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.
R. Rudner, in P. Edwards (ed.), The Encyclopedia of Philosophy, London, Collier-Macmillan, 1967, vol.3, p.371.
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.
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.
‘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.
M. Dummett, ‘Wittgenstein’s Philosophy of Mathematics’, Philosophical Review, vol.LXVIII, 1959, pp.324–48
(reprinted in G. Pitcher (ed.), Wittgenstein, London, Macmillan, 1968, pp.420–47, pp.425–6).
Ibid, p.434.
Ibid, p.438.
B. Russell, The Principles of Mathematics, Cambridge, Cambridge University Press, 1903, p.15.
C. Lewis, ‘Implication and the Algebra of Logic’, Mind, vol.21, 1912, pp.522–31.
Ibid, p.530.
Ibid, p.531.
Ibid.
A. Anderson and N. Belnap, Entailment. The Logic of Relevance and Necessity, vol.1, Princeton, Princeton University Press, 1975
A. Anderson, ‘An Intensional Interpretation of Truth-Values’, Mind, vol.81, 1972, pp.348–71
A. Anderson and N. Belnap, ‘Enthymemes’, Journal of Philosophy, vol.LVIII, no.23, 1961, pp.713–23.
Anderson, ‘An Intensional Interpretation’, p.368.
This is the position of E. Nelson, ‘Intensional Relations’, Mind, vol.39, 1930, pp.29–453.
Anderson and Belnap, Entailment, p.296.
D. Makinson, Topics in Modern Logic, London, Methuen, 1973.
T. Smiley, ‘Entailment and Deducibility’, Proceedings of the Aristotelian Society, new series vol.LIX, 1958–9, pp.233–54, p.250.
Anderson and Belnap, Entailment, p.165.
B. Bosanquet, Logic or the Morphology of Knowledge, Oxford, Clarendon Press, 1911, vol.1, p.323. (The first edition was in 1888.)
F. Bradley, The Principles of Logic, Oxford, Oxford University Press, 1922, vol.1, p.130. (The first edition was in 1883.)
Ibid, p.139.
Ibid.
Smiley, ‘Entailment and Deducibility’, p.233.
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)
J. Passmore, A Hundred Years of Philosophy, London, Duckworth, 1957, ch.7,’ some Critics of Formal Logic’.
This is the stance taken, for example, by H. Reichenbach, in Nomological Statements and Admissible Operations, Amsterdam, North Holland, 1954, pp.14–15.
The critic is J. Bennett, quoted in Anderson, ‘An Intensional Interpretation’, p.364.
See Makinson, Topics in Modern Logic, pp.27-41.
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.
‘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).
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© 1983 David Bloor
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Bloor, D. (1983). Compulsions, Conventions and Codifications. In: Wittgenstein. Theoretical Traditions in the Social Sciences. Palgrave, London. https://doi.org/10.1007/978-1-349-17273-3_6
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