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Ayers on Relative Identity

Published online by Cambridge University Press:  01 January 2020

Nicholas Griffin
Nicholas Griffin*
Affiliation:
McMaster University
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Extract

In a recent paper M.R. Ayers attacks two widely held doctrines:

  • (I) Non-arbitary individuation requires principles of individuation and these are supplies only by sortal general terms.

  • (R) It is possible for an item a to be the same as b but not the same as b.

I shall follow Ayers in calling a theory which includes both (I) and (R) ‘conceptualist’ or ‘sortalist’ (although I shall also use the more familiar label ‘relative identity theory’), but I shall not allow him to appropriate the honorific term ‘realist’ for his own theory, which I shall term ‘absolutist’. My sole purpose here is to defend (I) and (R) in turn against Ayers’ attacks on them. Thus I shall ignore intermediate positions which accept (R) but reject (I) or vice-versa.

Ayers’ paper is long and in many respects obscure; there are many points in it which require discussion but which can't receive it here for lack of space. In particular, I shall ignore his lengthy comments on the constitutive ‘is’, and also the wider metaphysical remarks in his conclusion and the postscript on Dummett.

Type
Research Article
Information
Canadian Journal of Philosophy , Volume 6 , Issue 3 , September 1976 , pp. 579 - 594
Copyright
Copyright © The Authors 1976

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References

1 ‘Individuals without Sortals’, Canadian Journal of Philosophy, IV (1974-5), pp. 113–148. (All references are to this paper unless otherwise indicated.)

2 (I) should not be confused with the more stringent claim, (D), that such sortals must be packed with the identity relation. The forthcoming second edition of Wiggins, David’ Identity and Spatia- Temporal Continuity (Oxford: Blackwell; 1st ed. 1967Google Scholar) makes the distinction clear, as does my Relative Identity (Oxford: Oxford University Press, 1976), Chapter 7. (See also J.R. Perry, Identity (Cornell University, doctoral dissertation, 1968) for further comment.) Many, including myself, have attributed (D) to Wiggins whereas in fact he holds only the weaker (I).

3 In fact Ayers uses ‘natural structure’ (p.114), ‘natural thing’ (p.116), ‘concrete individual’ (p.119), ‘objectively discrete unity or structure’ (p. 128) and ‘individual substance’, (p. 135). I shall take all these to be synonymous with 'natural unity’ for, if they are not synonymous in Ayers’ usage, their differences are subtle enough to be ignored here.

4 Since ‘the same matter cannot be subject to more than one principle of unity at the same time’ (p. 133).

5 See Enc, Berent ‘Numerical Identity and Objecthood’, Mind, LXXXIV (1975), pp. 10–26Google Scholar for a good account of the special difficulties posed by these cases for the Absolutist ― though Enc doesn't give as systematic a resolution of them as is possible for the relativist.

6 On the next page he suggests that the principle of unity for a family is ‘historical or social’ ― which deals with an obvious counter-example to the blood- relationship principle.

7 It is significant that Ayers concedes to sortalism in the case of events for exactly this reason: ‘Events do not have natural boundaries, spatial or temporal: the movement of the tides is part of a wider process, but there is no single, determinate answer to the question of which wider process.’ (p. 144)

8 For a better attempt at an example, though one which still, I believe, fails see Nelson, jack ‘On the Alleged Incompleteness of Certain Identity Claims’, Canadian Journal of Philosophy, III (1973-4), p.112.Google Scholar

9 Spinoza, Letter L, to Jellis, Jarig in Works,ed. Elwes, R.H.M. (New York: Dover, 1955), vol II, p. 369Google Scholar; Frege, Foundations of Arithmetic,transl. Austin, J.L. (Oxford: Blackwell, 1950), p.62.Google Scholar

10 Frege, op.cit., p.34. Incidentally, the example occurs in the course of an argument to show that the fact that sortal concepts are required for enumeration does not imply that number ‘is something subjective’ (cf. Frege, pp. 33–38). Frege's argument, if valid, undermines Ayers’ attempt to associate the sortalist position with an undesirable subjectivism (Ayers, passim, but especially p. 117 & n.). It is surprising, therefore, that Ayers devotes only that footnote to a (very inadequate) consideration of Frege's argument. Moreover, if Ayers is right in associating sortalism with subjectivism his own theory runs into the same objection since it still requires categorial terms in place of sortals (pp. 113–114, 143-144). In fact, his attempt to prove guilt by association is a resounding failure.

11 See David Wiggins, op.cit (1st edn.) pp. 35–6,42. I have also benefited from an unpublished paper by Peter Herbst, ‘Names and identities and Beginnings and Ends’.

12 Op.cit., pp. 59–60.

13 See, for example, Mayr, Ernst ‘llliger and the Biological Species Concept’, Journal of the History of Biology, 1 (1968), p. 172nCrossRefGoogle Scholar and, more generally, his Systematics and the Origin of Species, (New York: Columbia University Press, 1942).

14 Some relativists accept this result easily. For example, Pitcher, George ‘About the Same’, in Ambrose, A. and Lazerowitz, M (eds.), Ludwig Wittgenstein: Philosophy and Language(London: Allen and Unwin, 1971), pp. 120–139Google Scholar (an explicit statement occurs on p. 123).

15 For one version of the theory see Geach, P.T. ‘Good and Evil’, Analysis, XVII (1956), pp.33-42Google Scholar, and for another Aristotle's Topics A 107a 4-12.

16 Ayers is not alone in conflating the two claims, Wiggins does so, op.cit. pp. 30–34.

17 That (A) is inconsistent is provable in all current formalizations of relative identity theories. Cf Stevenson, Leslie ‘A Formal Theory of Sortal Quantification’, Notre Dame Journal of Formal Logic, XVI (1975), pp. 185–207Google Scholar; Richard Routley and Nicholas Griffin, ‘Towards a Logic of Relative Identity’ (forthcoming).

18 See e.g., Rescher, N. and Urquhart, A. Temporal Logic,(New York: Springer Verlag, 1971), p. 242CrossRefGoogle Scholar; alternative means to the same end are available, e.g. limiting the second-order quantifier in (LL) to dated predicates. I shall refer to such principles as ‘tensed Leibniz’ Law'.

19 See Herbst, op.cit., pp. 30–40, where he argues that he is identical with Alexander the Great.

20 Rejection of temporally limited identity leads to many complications. One has to deny, for example, that Ford is identical with the President of the United States. Some account has then to be given of the relation between the two: for example, Dummett's, claim that Ford realizes the President of the United States (Frege: Philosophy of Language (London: Duckworth, 1973) p. 571)Google Scholar. The key notion of ‘realization’, however, is left completely unexplicated.

21 On the limited substitutivity of relative identity see Richard Routley and Nicholas Griffin, ‘Towards a logic of Relative Identity’, and Griffin, op.cit., 8.2.

22 Ayers does not provide an argument for this principle but merely cites Locke. ln fact, Locke claims only that two items of the same kind cannot occupy the same place at the same time (cf. Essay, Bk. II, Ch. 27, 1). Even this principle fails as leibniz noted (Nouveaux Essais, Bk.ll, Ch. 27, 1).1ncidentally, were the principle Ayers subscribes to true, temporary identities would have to be admitted ― for we would scarcely claim that Ford and the President of the United States were never in the same place at the same time.

23 Significantly, Wiggins op.cit., p.23, considers, and rejects, this version of the indiscernibility of identicals as one which might be used to save (R). I'm grateful to Max Cresswell for pointing out to me the possible viability of this policy (given a preparedness to revise predicate logic) but neither of us think it worthwhile.

24 Of course, the relativist is not claiming that an individual ceases to exist whenever a loop of wool is straightened ― merely that a loop of wool does, for where once there was a loop there is one no longer.

25 See Treatise, Bk. I, Pt. IV, Chapter 6 and Penelhum, Terence ‘Hume on Personal Identity’ in Chappell, V.C. (ed.), Hume: A Collection of Critical Essays,(London: Macmillan, 1966), pp. 213–239Google Scholar for an excellent discussion. Ayers’ use of natural unities to rope together a succession of items is clearest in his discussion of temporal parts (pp. 122–123).

26 There are a few cases of (R) which fail this first condition and which are not resolvable by consideration of times. Cf. my Relative Identity, 10.1. Ayers mistakenly assumes that the relativist only requires sortals for diachronic, and not synchronic, identity statements (p. 119).

27 Ayers does make one concession to (R) in that he allows cases in which one conjunct is covered by a sortal and the other by a mass term; e.g. ‘the bottle is the same glass (material) as the jampot but they are not the same container.’ (cf. pp. 125–6).