DOI: 10.4324/9780415249126-K105-1
Version: v1,  Published online: 1998
Retrieved May 11, 2021, from

1. The logical problem of the Trinity

The words ‘the Trinity’ are the English equivalent of the Latin word Trinitas, which was coined by the early Christian writer Tertullian. The word, which, etymologically, means something like ‘the tripleness’, is used to refer collectively to the Father, the Son and the Holy Spirit. (Tertullian also originated the use of the word ‘person’ (persona) as a common noun that applies to the Father, the Son and the Holy Spirit. Outside theology, the Latin word means a mask of the sort worn by characters in a classical drama, and, by extension, a dramatis persona, a character in a drama. What Tertullian’s application of this word to the Father, the Son and the Holy Spirit was intended to suggest is disputed.) Theologians writing in Latin have generally said that, although God is a single substantia, there are in God three personae. Theologians writing in Greek have generally said that, although God is a single ousia, there are in God three hypostases. These two pairs of terms have caused some confusion, owing to the fact that substantia and hypostasis have the same literal or etymological meaning: ‘that which stands under’.

The purpose of this entry is neither theological nor historical. Its purpose is rather to discuss the philosophical difficulties presented by the ‘developed’ doctrine (as it is to be found in the Athanasian Creed, of around ad 500). These difficulties are mainly logical. They are well stated in an anonymous seventeenth-century work that has been ascribed to the Socinian John Biddle:

You may add yet more absurdly, that there are three persons who are severally and each of them true God, and yet there is but one God: this is an Error in counting or numbering; which, when stood in, is of all others the most brute and inexcusable, and not to discern it is not to be a Man.

(quoted in Hodgson 1940)

The author of this passage is, essentially, charging that the doctrine of the Trinity implies a violation of the principle of the transitivity of identity, for it implies that the Father is identical with God, God is identical with the Son, and the Father is not identical with the Son. (For a full development of this charge, see Cartwright 1987.) The central problem that faces the doctrine of the Trinity is this: how can the doctrine be stated in a way that is orthodox, clear and does not violate the principle of the transitivity of identity?

The doctrine of the Trinity is one of the Christian mysteries, which means that it cannot be seen to be true, or even to be possible, by the use of unaided human reason. This does not mean, however, that human beings, employing only their unaided reason, cannot usefully discuss the question whether the doctrine is formally self-contradictory. (If it could be demonstrated that the doctrine of the Trinity was formally self-contradictory, that would, of course, show that it was impossible; but the converse entailment does not hold.) The task undertaken in this entry does not, therefore, rest on a failure to appreciate the fact that the doctrine is held by those who accept it to be a mystery.

This entry will consider two recent attempts to avoid the conflict with Leibniz’s Law that the doctrine of the Trinity seems to face (see Identity of indiscernibles §1). One proceeds by affirming that the Father, the Son and the Holy Spirit are numerically distinct from one another, and attempting to show that this thesis is consistent with historical orthodoxy. The other proceeds by denying the ultimate reality of numerical identity – and thus by denying that Leibniz’s Law has anything to apply to. The first risks falling into tritheism, the heresy that there are three Gods. The second risks incoherence if not outright unintelligibility.

Citing this article:
van Inwagen, Peter and Dan Howard-Snyder. The logical problem of the Trinity. Trinity, 1998, doi:10.4324/9780415249126-K105-1. Routledge Encyclopedia of Philosophy, Taylor and Francis,
Copyright © 1998-2021 Routledge.

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