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Do We Need Predication?

Published online by Cambridge University Press:  05 May 2010

Nicholas Griffin
Nicholas Griffin
Affiliation:
McMaster University
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Extract

In recent papers Fred Sommers and Michael Lockwood have independently argued that the distinction between the ‘is’ of predication and the ‘is’ of identity (henceforth: the IP-distinction) is not well-founded. This claim is somewhat obscure since, on the theories they advocate, it is not only still possible to distinguish between the ‘is’ of predication and the ‘is’ of identity, but important to do so on pain of turning good arguments bad. Sommers' way of putting it, namely that we don't need identity, is no better. Of course we don't need identity since, in second-order quantification logic, identity is definable in terms of predication. Perhaps the best way of putting their point is by means of Sommers' claim (op. cit. p. 500) that identity statements can be formalized by monadic relations. We can therefore mark the IP-distinction by the essentially polyadic nature of identity.

Type
Articles
Information
Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 16 , Issue 4 , December 1977 , pp. 653 - 663
Copyright
Copyright © Canadian Philosophical Association 1977

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References

1 Sommers, , ‘Do We Need Identity?’, Journal of Philosophy, 66 (1969), pp. 499–504CrossRefGoogle Scholar. Lockwood, , ‘On Predicating Proper Names’, Philosophical Review, 84 (1975), pp. 471–98CrossRefGoogle Scholar. A similar view is also taken by Stephen Voss in an unpublished paper ‘The Meaning of “is”.’

2 Even in a first-order logic we could dispense with identity for a language sufficiently impoverished to satisfy Wittgenstein's requirement that every item could be referred to by no more than one singular term. Cf. Tractatus Logico-Philosophicus, transl. Pears, D.F. and McGuinness, B.F., (London: Routledge and Kegan Paul, 1963)Google Scholar, 5.53–5.534. Such a language would, however, be very impoverished indeed.

3 Sophist, 256A10–256B4. See Ackrill, J. L., ‘Plato and the Copula’, Journal of Hellenic Studies, 77 (1975), 1–6CrossRefGoogle Scholar for this interpretation.

4 Lockwood, op. cit., p. 479n.

5 Formal Logic (London, 1847), pp. 49–50Google Scholar. The fact that de Morgan doesn't argue for the distinction suggests that it may have been common even earlier.

6 ‘On Concept and Object’ in Geach, P. and Black, M. (eds.) Translations from the Philosophical Writings of Gottlob Frege (Oxford: Blackwell, 1952), p. 44Google Scholar. Lemmon, E. J., Beginning Logic (London: Nelson, 1965), p. 160Google Scholar uses the same argument.

7 Lockwood, op. cit., p. 476. It ought to be shown, however, that the predicate does in fact come first in (1).

8 Strawson, , Subject and Predicate in Logic and Grammar, (London: Methuen, 1974), pp. 106–08Google Scholar.

9 ‘Is Consciousness a Brain Process?’ in Borst, C.V. (ed.), The Mind-Brain Identity Theory (London; Macmillan, 1970), p. 44CrossRefGoogle Scholar.

10 I use ‘T1’, ‘T2’ etc. as variables taking terms, singular or general, substantival or adjectival, for their values. Henceforth I shall amend quotations to conform with this notation.

11 This is Thomason's, R.H. argument. Symbolic Logic — An Introduction (New York: Macmillan, 1970), pp. 144–45Google Scholar.

12 Frege, op. cit., p. 44. This is essentially the revised version of Place's criterion mentioned above.

13 Mill, J. S., A System of Logic (London: Routledge, 1892)Google Scholar, Book I, Chapter ii, § 5, p. 23; quoted Lockwood, p. 477.

14 Ibid., pp. 27–28.

15 William of Ockham, Summa Logicae, III, 1, 8; 38va.

16 Presentation here follows that of Hughes, and Londey, , The Elements of Formal Logic (London: Methuen, 1965), pp. 306ffGoogle Scholar.

17 Sommers, op. cit., p. 502.

18 De Interpretation, 20a23–20a31, translated by Edghill, E. M., in Ross, W. D. (ed.) The Works of Aristotle (Oxford: Oxford University Press, 1955), vol. IGoogle Scholar.

19 This policy has at least one benefit, namely it decides the issue for mass terms. If ‘N*’ is a mass term then (21) clearly fails, whereas there is some difficulty in deciding whether mass terms apply to only one item. See, e.g., Quine's, Word and Object (Cambridge. Mass.: M.I.T. Press, 1960), pp. 91ffGoogle Scholar.

20 See R. Routley and N. Griffin, ‘Towards a Logic of Relative Identity’ (forthcoming) for formal details; and see Griffin, , Relative Identity (Oxford: Oxford University Press, 1977Google Scholar) for a general defence of relative identity.

21 Reference and Generality (Ithaca, N.Y.: Cornell University Press, 2nd ed. 1968), p. 191Google Scholar.

22 Alternatively, add a special relative identity relation ‘= s’ (read: ‘is the same species as’). For each general term ‘ø’ we need some paradigmatic ø-item, say a ø. Then we define:

ø(x) = Df.x = saø.

Cf. Cresswell, M.J., ‘What is Aristotle's Theory of Universals?’ Australian Journal of Philosophy, 53 (1975), pp. 238–47CrossRefGoogle Scholar, but especially p. 242. In my own theory the relation ‘= s’ would be present but not marked out for special attention.

23 The fact that we have many relative identity relations doesn't, of course, mean that ‘is the same… as’ is ambiguous.

24 I'm grateful to former colleagues at Victoria University of Wellington, in particular to John Bigelow, Max Cresswell and George Hughes, and to the referees for Dialogue for many helpful comments.