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The Doctrine of the Trinity and the Logic of Relative Identity1

Published online by Cambridge University Press:  24 October 2008

James Cain
James Cain
Affiliation:
Department of Philosophy, Princeton University, U.S.A.
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Extract

The doctrine of the Trinity says that there is just one God and three distinct divine persons, each of whom is God. This would seem to imply that there are three divine persons, each a different person the other persons but the same God as the other persons. If we accept what I believe is the most popular account of identity current among logicians then we must hold that this apparent consequence is contradictory. We see this as follows (it will suffice to consider just the relation of Father and Son): logicians generally treat relativized identity expressions of the form ‘is the same A as’ (here ‘A’ stands in for a term which relativizes the identity) as being analysable in terms of absolute (or unrelativized) identity according to the following equivalence schema, (E):

(E) a is the same A as b if and only if a is identical to b and a is an A and b is an A.

The view under consideration affirms the following three sentences:

(1) The Father and the Son are persons.

(2) The Father is not the same person as the Son.

(3) The Father is the same God as the Son.

Type
Research Article
Information
Religious Studies , Volume 25 , Issue 2 , June 1989 , pp. 141 - 152
Copyright
Copyright © Cambridge University Press 1989

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References

page 141 note 2 Morris, Thomas appears to take a position along these lines in The Logic of God Incarnate (Ithaca and London: Cornell University Press, 1986).Google Scholar See the first and last chapters, esp. pp. 28–9 and 214.

page 142 note 1 There are two aspects to Geach's theory of relative identity. One is negative: the rejection as incoherent of the unrelativized notion of identity. The second is a positive account of how relative identity concepts function. These are, to some extent, independent. For example, even if Geach were wrong in denying the coherence of absolute identity, he might be right in holding that there are relative identities that cannot be given the standard analysis in terms of absolute identity. None of our considerations will turn on an acceptance of the negative thesis.

page 142 note 2 ‘Aquinas’ in Anscombe, G. E. M. and Geach, P. T., Three Philosophers (Ithaca and London: Cornell University Press, 1961), p. 118.Google Scholar

page 143 note 1 Reference and Generality: An Examination of Some Medieval and Modern Theories, third edition (Ithaca and London: Cornell University Press, 1980), pp. 173–6.

page 143 note 2 Ibid. p. 206.

page 144 note 1 I am not sure whether Geach is explicitly committed to this last sentence. In any case, it is a natural way in which to develop the theory of relative identity.

page 144 note 2 Ibid. pp. 68–71.

page 144 note 3 We might instead want to say here that ‘Jesus’ is associated with the criterion of identity for being the same person. More will be said later on this alternative.

page 144 note 4 Sameness and Substance (Cambridge, Mass.: Harvard University Press, 1980), pp. 29 and 37–42.

page 145 note 1 This schema is the law of substitutivity of identity, (x) (y) (x = y & Fx ⊃ Fy), with the identity predicate relativized. Thus we might call it the substitutivity of relative identity.

page 145 note 2 Wiggins uses ‘the Son’ rather than ‘Jesus’ in his example. But to do so brings in a further complication, for one may wish to say that only if it is taken as short for, say, ‘As a man the Son was crucified’ can ‘The Son was crucified’ be regarded as true. (Cf. one may both say ‘The Son was not created’ and ‘The Son as a man was created’.) When we say ‘Jesus was crucified’ there is no need to qualify the predicate ‘ … was crucified’ with the phrase ‘as a man’.

page 146 note 1 Reference and Generality, p. 71.

page 147 note 1 As pointed out earlier, Wiggins's example uses ‘the Son’ rather than ‘Jesus’. Note that ‘the Son’, like ‘the Father’, corresponds to the criterion of identity for being the same divine person, not for being the same God, and so we would still not have an instance of (P1) even if we replaced ‘Jesus’ by ‘the Son’.

page 147 note 2 This, in our notation, is a version of a principle that Wiggins suggests (Sameness and Substance, p. 40), only to discard later. He complains that though the ‘as’-construction has several different uses there is none with the universal applicability needed to make (P2) a general substitution principle. We will define our ‘as’-construction in a way that solves this problem.

page 148 note 1 For example, one might think we could write a consistent story, along the lines of Lewis's, C. S., NarniaGoogle Scholar series, in which the Son is both incarnate as a talking lion in Narnia and as a human on earth. We might say in the story, ‘The son as an animal lived in Narnia’.

page 148 note 2 We see this as follows: nothing can be the same A as different A's, for if x is the same A as y and the same A as then, by the transitivity and symmetry of identity, y is the same A as z. So if there is an A which is the same A as x and (that A), then there is just one A which is the same A as x and f (that A). The converse of this last statement also clearly holds, so we have the equivalence mentioned in the text.

page 149 note 1 Or perhaps we should say that we associate the name with a criterion of identity along the lines of: being the same mass of stuff, for we probably would not want our identification of Squishy to depend on our having correctly identified the kind of stuff out of which it is made. But I do not want to bog down our example in considerations of such details.

page 149 note 2 Actually, on our theory more than one reading could be given to this sentence, depending on the relative scopes of the negation, the ‘as’-construction (which will admit of scope ambiguity similar to Russellian definite descriptions), and tense; e.g. (I) ‘There is a statue which is the same statue as Squishy and it did not exist yesterday’ (true), and (2) ‘It was not the case yesterday that: there is a statue which is the same statue as Squishy and it exists’ (perhaps false, depending on Squishy's history). (I) gives the intended reading for this example.

page 149 note 3 One must be careful in making this comparison. I do not want to rest the adequacy of the account of language used to describe the Trinity on the adequacy of this treatment of the statue/clay piece example. We certainly have intuitions (e.g. that the statue is a clay piece) that lend themselves to this treatment in terms of the theory of relative identity. It might be the case, however, that other intuitions could be found supporting an analysis in terms of absolute identity. Here it could turn out that our use of language dictates one semantic account (the relativist's or the absolutists's) to the exclusion of the other, or it might be the case that neither is the correct account and our use of language leaves open which account is applicable. In any case, it seems that there could be a language very similar to English in which people do talk in the way suggested in the statue/clay piece example. We may then compare our use of language to speak about the Trinity to this usage of language.

page 150 note 1 Summa Theologica, Pt. III, Q 16, Art. 8 (New York: Benziger Brothers Inc., 1947).

page 151 note 1 Ibid. Pt. III, Q 16, Art. 9.