The Doctrine of the Trinity and the Logic of Relative Identity
Cain (James)
Source: Religious Studies, Vol. 25, No. 2 (Jun., 1989), pp. 141-152
Paper - Abstract

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Author’s Introduction

  1. 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.from the other persons but the same God as the other persons.
  2. 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.
  3. 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):
      “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.”
  4. 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.
  5. If we are given an instance of equivalence schema (E) by substituting 'person' for 'A' and 'the Father' and 'the Son' for 'a' and 'b', then, by truth-functional logic, (1) and (2) imply 'The Father is not identical to the Son'.
  6. On the other hand, if in (E) 'A' is replaced by 'God', and 'a' and 'b' by 'the Father' and 'the Son', then from (3) we get 'The Father is identical to the Son'.
  7. Thus we see that if (E) is accepted we end in the contradiction: 'The Father is not identical to the Son and the Father is identical to the Son.'
  8. There are at least two ways one might respond to this appearance of inconsistency.
  9. One might hold that while we can say there is one God, this should not be taken to imply that the divine persons are all the same God: oneness is to be taken as expressing some form of unity (perhaps to be found in such features of the divine persons as necessary harmony of will) but not as expressing identity. We will not concern ourselves here with this line of response.
  10. Rather, we will consider the view that
    • (a) holds that the three divine persons are all the same God and
    • (b) rejects the account of relative identity1 which tells us that every identity expression of the form 'a is the same A as b' is equivalent to 'a is identical to b and a is an A and b is an A'.
  11. In recent years several philosophers, most notably Peter Geach, have developed theories of relative identity2 which reject schema (E) as giving an analysis of relative identity3.
  12. In this paper we explore one way in which an account of relative identity4 developed along the lines of Geach's theory might be applied to the way we speak of the Trinity. At the end of the paper an alternative approach, still in terms of relative identity5, will also be suggested.

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