If we accept the Aristotelian solution to the problem of material constitution, then, as we have seen, the familiar particulars ofexperience must be conceived of as hylomorphic compounds—that is, as matter-form structures related to other things sharing their matter by the relation of accidental sameness. The relevance of this Aristotelian solution to the problem of the Trinity is perhaps already clear. For like the familiar particulars of experience, the Persons of the Trinity can also be conceived of in terms of hylomorphic compounds. Thus, we can think of the divine essence as playing the role of matter; and we can regard the properties being a Father, being a Son, and being a Spirit as distinct forms instantiated by the divine essence, each giving rise to a distinct Person. As in the case of matter, moreover, we can regard the divine essence not as an individual thing in its own right but rather as that which, together with the requisite "form'', constitutes a Person. Each Person will then be a compound structure whose matter is the divine essence and whose form is one of the three distinctive Trinitarian properties. On this way of thinking, the Persons of the Trinity are directly analogous to particulars that stand in the familiar relation of material constitution.
Of course, there are also some obvious disanalogies. For example, in contrast to ordinary material objects, the role of matter in the case of the Trinity is played by immaterial stuff, and so the structures or compounds constituted from the divine essence (namely, the divine persons) will be 'hylomorphic' only in an extended sense. Also, in the case of material objects, the form of a particular hylomorphic compound will typically only be contingently instantiated by the matter. Not so, however, in the case of the Trinity. For Christian orthodoxy requires us to say that properties like being a Father and being a Son are essentially such as to be instantiated by the divine essence. As we have seen, moreover, the relation of accidental sameness on which our solution is modeled is, in Aristotle
27 For example, Cartwright (1987: 193) claims to detect an appeal to relative identity in a letter of Anselm, as well as the Eleventh Council of Toledo, on just these grounds. The same sort of reasoning may also help to explain Anscombe & Geach's (1961: 118) attribution of the Relative-Identity solution to Aquinas.
anyway, paradigmatically a relation between a substance (e.g., a man) and a hylomorphic structure built out of the substance and an accidental property. The Persons, however, are not like this. Thus, it is at best misleading to say that the relation between them is one of accidental sameness. Better instead to go with the more general label we have used throughout this paper: the Persons stand in the relation of numerical sameness without identity.
As far as we can tell, none of these disanalogies are of deep import. It seems not at all inappropriate to think of the divine Persons on analogy with hylomorphic compounds; and once we do think of them this way, the problem of the Trinity disappears. Return to the analogy with material objects: According to the Aristotelian solution to the problem of material constitution, a statue and its constitutive lump are two distinct hylomorphic compounds; yet they are numerically one material object. Likewise, then, the Persons of the Trinity are three distinct Persons but numerically one God. The key to understanding this is just to see that the right way to count Gods resembles the right way to count material objects. Thus:
(G1) x is a God iff x is a hylomorphic compound whose "matter" is some divine essence; x is the same God as y iff x and y are each hylomorphic compounds whose "matter" is some divine essence and x's "matter'' is the same "matter" as ys; and there is exactly one God iff there is an x such that x is a God and every God is the same God as x.
And, in light of G1, the following principle also seems reasonable:
(G2) x is God iff x is a God and there is exactly one God.
If these principles are correct, and if (as Christians assume) there are three (and only three) Persons that share the same divine essence, then we arrive directly at the central Trinitarian claims T1—T3 without contradiction. For in that case, there will be three distinct Persons; each Person will be God (and will be the same God as each of the other Persons); and there will be exactly one God. Admittedly, if G1 is taken all by itself and without explanation, it might appear just as mysterious as the conjunction of T1—T3 initially appeared. But that is to be expected. What is important is that once the parallel with M2 is appreciated, and the doctrine of numerical sameness without identity is understood and embraced, much of the mystery goes away.
We are now in a position to see how our Aristotelian account of the Trinity meets the desiderata we set out earlier for an adequate solution to the problem of the Trinity (namely, D1—D5). As should already be clear, our solution resolves the apparent inconsistency of T1—T3 in the same basic way that Relative-Identity and Social-Trinitarian solutions do: namely, by rejecting the idea that the words 'is God' in Trinitarian statements like "Each of the Persons is God'' mean 'is absolutely identical with God'. According to our solution, these words should be interpreted to mean 'is numerically the same as the one and only God'. But once this interpretation of T2 is adopted—together with a proper understanding of the relata of the relation of numerical sameness without identity—the apparent inconsistency of T1—T3 is resolved, and in a way that satisfies D1 and D2. For inasmuch as the Persons of the Trinity are distinct hylomorphic compounds, they are distinct from one another (hence T1 is true); and inasmuch as they are each numerically the same as the one and only God, each of them is God and there is only one God (hence T2 and T3 are true). Moreover, since our solution implies that each of the Persons is a divine individual who is one in number with each of the other two Persons, it is consistent with the claim that there are three Persons but exactly one divine individual (thus satisfying D1),28 and it also seems to preserve the intention of traditional formulations of the doctrine of the Trinity (thereby satisfying D2).
It should also be clear how our solution meets the other desiderata. Unlike (pure) Relative-Identity solutions, ours is compatible with the claim that classical identity exists and is as fundamental as any other sameness relation (and hence satisfies D4). Moreover, it supplies an explanation for why 'x = y does not follow from 'x is the same God as y. Unlike Social-Trinitarian strategies, on the other hand, ours is clearly compatible with the view that God is an individual rather than a society, and that the Persons are not parts of God (and hence satisfies D3). Furthermore, our story about the unity ofthe Persons exploits what we take to be a plausible story about the unity of distinct hylomorphic compounds, whereas no similarly plausible analogy seems to be available to the Social Trinitarian, Finally, though we deny that it makes sense to say, unequivocally, that each of the Persons is absolutely identical with God, our view—unlike either of the other two strategies—allows us to say that the Father is identical with God, the Son is identical with God, the Holy Spirit is identical with God, and yet the Father, Son and Holy Spirit are distinct from one another. And it can do all of this without introducing any anti-realist commitments in metaphysics (thus satisfying D5). Consider a parallel drawn from one of our earlier examples: Athena is identical to the material object in R; Lump is identical to the material object in R; but Athena is distinct from Lump. Since 'the material object in R' is ambiguous, there is no threat of contradiction; and the doctrine of numerical sameness without identity blocks an inference to the claim that Lump and Athena are co-located material objects. Likewise in the case of the Trinity.
For all these reasons, therefore, our Aristotelian solution to the problem ofthe Trinity seems to us to be the most philosophically promising and theologically satisfying solution currently on ofler.
28 Assuming, anyway, that counting divine individuals is more like counting Gods than counting Persons. But this assumption seems clearly legitimate in context of D1.
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