Brower and Rea, Understanding the Trinity (PDF)
Rea and Brower, Material Constitution and the Trinity (PDF)
Craig, Does the Problem of Material Constitution Illuminate the Trinity?
I've already pointed out that my view of the problem of the Trinity is that the rumors of it are greatly exaggerated; but it's still worthwhile to consider what this approach might yield. I don't have a full-blown position on this, but here are some preliminary thoughts.
Suppose we have a lump of clay that is formed into a statue. What is the relation between the lump of clay and the statue it makes up? As Baker notes in her article, Unity Without Identity: A New Look at Material Constitution (PDF) it's fairly common to assume the following dichotomy:
For any x and y that are related as the lump of clay is to the statue that it makes up, either x is identical to y, or x and y are separate entities, independent of each other.
To say that x and y are related by a constitution-relation is to say that this dichotomy should be rejected: we are not forced to choose between identity and separate entity, because it is possible for things to be non-identical but non-separate. In other words, if x constitutes y, x is not identical to y, but y 'borrows' something of its nature from x, so they are not separate. As Baker puts the point:
We need constitution to be similar to identity in order to account for the fact that if x constitutes y, then x and y are spatially coincident and share many properties; but we also need constitution to differ from identity in order to account for the fact that if x constitutes y, then x and y are of different kinds and can survive different sorts of changes.
So we have constitution as identity-like, but not a form of identity.
When people appeal to this in Trinitarian discussions as an analogy, they can be doing several things. Their primary concern, for instance, could be to reject some equivalent of the dichotomy above, namely,
Either the Father and the Son are both identical to God, or at least one of the two (Father and Son) is a separate entity from God.
or:
Either the Father and the Son are simply identical to each other, or they are separate entities.
This use of the material constitution analogy points out that things are not so simple: there is at least one other sort of relation (constitution) which requires neither identity nor separation, so it could well be that the relation between the Father and God (for instance) is analogous to this. It is this that Rea and Brower are talking about when they are talking about numerical sameness without identity. In essence, this use of the analogy just means: we should not be too quick to rule out the Trinity on considerations of identity, because we need to consider complications like those we find in material constitution problems.
Well and good. But one could go further, as Rea and Brower do, and hold that the Trinity is not merely analogous to material constitution in the rejection of the identity/separation dichotomy, but that the Trinity is itself analogous to an actual case of material constitution. As they say in "Material Constitution and the Trinity":
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.
This is a much stronger use of the analogy; while Rea and Brower note that there are disanalogies, this involves thinking of the Trinity on the model of a particular case of material constitution. It is also, I think, a much more dubious, or at least more problematic, use of the analogy, as Craig points out in his response. (I am less convinced by Craig's wholesale rejection of numerical sameness without identity, since his objection about diachronic identity can fairly easily be handled by material constitution views, like Baker's, for instance. But it's possible -- I'd need to look more closely -- that the problem here is not Craig but the particular version of material constitution formulated by Brower and Rea.)
Incidentally, Craig and Moreland have proposed a different approach that, perhaps equally odd, should at least be better known than it is (I think it is untenable, but it's worthy of mention), namely, that the analogy should be to one soul with three sets of rational faculties. I think something similar may be said about it: the analogy might just be used in such a way that it points out a complication that should induce us to be wary about jumping to the conclusion that the doctrine of the Trinity is inconsistent. Or we could use it in a stronger way as a (perhaps fuzzy) parallel; in which case it is quite as dubious as, and perhaps even more problematic than, the stronger use of the material constitution analogy, since it appears to cut directly against the tendency of all the ecumenical councils from at least Ephesus on (in particular, I think it ends up wreaking havoc with consubstantiality and the unity of the Trinity as traditionally understood). In other words, the strong Craig-Moreland analogy does no more to illuminate the orthodox doctrine of the Trinity than the strong Brower-Rea analogy, although it perhaps shows how one might formulate a doctrine of the Trinity.
