A new Thomistic view of the Trinity

I think the historical Aquinas’ solution to how God is one in three persons is a relative identity view that posits two kinds of identity:

1. Individual identity: the lack of a real distinction, where real distinction might come from a difference of matter (as in material substances), a difference of form (as in angels) or an opposition of real relations (as in the Trinity).

2. Sameness of essence: having the numerically same substantial form.

While this is a relative identity account, it has an advantage over more standard relative identity accounts in that it nicely explains our intuitions about absolute identity. For on Aquinas’ solution, as far as we know, except where God is involved, the two identities are co-extensive. For Aquinas (like perhaps Aristotle) believes in individual forms of creatures, so all creatures that are distinct by individual identity have numerically distinct substantial forms, and conversely there are no mere creatures with two substantial forms. Thus when we are not dealing with God, we can afford to be ambiguous between the two kinds of identity, and hence talk as if there was absolute identity. (As far as I know, Thomas never makes this point.)

The point of this post, however, is to offer an alternative version of Aquinas’ two-identities account. The alternative is thoroughly Thomistic, but it’s not what Thomas has. Here it is. We have two kinds of identity. The first is individual identity, as in the historical Aquinas’ solution. The second is:

3. Sameness of esse: having the numerically same esse or act of being.

Just as in the historical Aquinas’ solution, the alternate account has the feature that apart from theological cases, the two kinds of identity are co-extensive. Distinct individual creatures have distinct acts of being, and no creature has two acts of being.

A disadvantage of this view is that “sameness of esse” doesn’t fit quite as well as “sameness of essence” with the Nicene Creed’s “homoousion”. But some things are worth noting. The previous English translation of the Nicene Creed in the Catholic Church actually had “sameness of being”. The word ousia is the abstract form of einai, to be. And in God essence and act of being are the same by divine simplicity. So I think the disadvantage can perhaps be overcome.

An advantage, however, is that sameness of esse seems even more identity-like and unifying than sameness of form. If x and y have the very same act of being, it is hard to deny that there is a real unity between x and y. Here is one way to see the point. On Platonist metaphysics, unlike on Thomastic metaphysics, you and I have sameness of form: we each have the numerically same Form of Humanity. Granted, Platonist metaphysics may be false. But the fact that you and I count as having sameness of form on Platonist metaphysics should make a little less happy about using that as an account of the unity in the Trinity. On the other hand, once we supplement Platonist metaphysics with an act of being, it is clear that you and I will get different acts of being, since each of us can exist without the other doing so.

Moreover, this account may help cast a light on the thorny question of why Aquinas at one point posits a human esse in the incarnate Christ distinct from the divine esse (though elsewhere he denies it). For suppose that there is only one esse in Christ and we accept the sameness-of-being account. Then we would be able say that the Jesus Christ as human is God, since the one and only esse in Jesus Christ, whether as human or as God, is the divine esse, and this we shouldn’t say (and indeed Aquinas denies it). Thus if we accept the sameness of esse account, we get an argument for the two esse view of the Incarnation. Of course, we can turn this around. We might say that the two esse view is false, and hence the sameness of esse account is false.

Trinity, quaternity and naming God

One now-classic solution to some of the challenges of the doctrine of the Trinity is relative identity. On relative identity accounts of the Trinity, we do not heretically say, e.g., that the Father is absolutely identical with the Son, but instead we posit a same-essence (or same-God) relative identity relation, and say that the Father is same-essence as the Son. Now, most of the time proponents of relative identity views deny that there is any such thing as absolute identity at all. All identities are relative to a sortal. However, in their famous “Material Constitution and the Trinity”, Brower and Rea offer an account of the Trinity using relative identity within a system where there is such a thing as absolute identity, governed by the standard rules of first-order logic.

Any account of the Trinity that allows for absolute identity governed by classical logic faces an interesting problem. Suppose:

1. There is such a thing as absolute identity, denoted by “=” and governed by its standard first-order logic rules.

2. There is a name for God as such, “G”, and names for the Father, Son and Holy Spirit, respectively, “F”, “S” and “H”.

3. F ≠ S

4. S ≠ H

5. F ≠ H

6. For all x, if x = F or x = S or x = H while y = F or y = S or y = H, and if x = G, then y = G.

7. If x = x, y = y, z = z, w = w, x ≠ y, x ≠ z, y ≠ z, x ≠ w, y ≠ w and z ≠ w, then x, y, z and w are four, counting by absolute identity.

8. Then F, S, H and G are four, counting by absolute identity.

9. Heresy! In no sense is there a divine quaternity!

Premise (6) captures the idea that the persons of the Trinity have equality with respect to divinity, and hence if x and y are persons of the Trinity, then if either of x and y “is God” in some sense of “is” and “God”, then the other “is God” in the same sense.

Proof of 8 from 1–7:

1. If F = G or S = G or H = G, then F = G and S = G and H = G. By 6

2. If F = G and S = G, then F = S. By 1

3. So F ≠ G or S ≠ G. By 3 and ii

4. So F ≠ G and S ≠ G and H ≠ G. By i and iii

5. F = F, S = S, H = H. By 1

6. G = G. By 1

7. So, F, S, H and G are four, counting by absolute identity. By 3–5, iv–vi and 8

There is a way out of this, in van Inwagen’s work on the Trinity. Van Inwagen denies that there are names for the Father, Son, Spirit and God: there are just predicates, like “is divine” and “is a Father”.

This is overkill for getting out of the above. It is difficult for a Christian to completely deny the existence of divine names. After all, you become a Christian by having someone pour water over you while saying: “I baptize you in the name of the Father, and of the Son and of the Holy Spirit.”

I think the quaternity argument leaves Christians who want to uphold classical absolute identity with two options:

1. There is no name for God.

2. There are no names for the Father, Son or Holy Spirit.

Here, “name” means “proper name”, since that’s the kind of name that classical logic talks about.

Accepting both (a) and (b) is not, I think, an option. Of the two, I think (b) is the more problematic. Names are too central to human relationships with persons. Thus, I think, the Christian who wants to uphold classical absolute identity should accept (a). And there is some support in Christian tradition for denying that God has a name.

(This is not what Brower and Rea do. In footnote 7, they talk of “the name ‘God’”, albeit in the context of discussion of a heretical view, but as I read the footnote they have no reservation about “God” being a name.)

While (a) is the less problematic of the two options, I still think (a) is problematic. Grammatically, “God” and “the Trinity” and the tetragrammaton all function as proper names. While there is some precedent in the Christian tradition for denying that God has a name, that still seems a bit of a stretch.

I think that if one is going to adopt a relative-identity account of the Trinity, then one should either deny that there is such a thing as absolute identity or at least one should deny that it is governed by the rules of classical logic.

I tentatively propose the following modification to the classical theory of absolute identity as a way of getting out of the quaternity argument. Restrict the identity-introduction rule that says that for any name N we get to write down N = N to the case of what one might call hypostatic or individual names (or, perhaps, to non-essence names). Thus, we get to write “Father=Father” but not “God=God”. Now everything in the quaternity argument goes through, except we don’t get (vi) and and hence we can’t infer (vii) or (8).

Relative identity and relative shape

Take a classic case of relative-identity. At time 1, we have a lump of clay, Lumpy1, that is formed into a statue of a horse, a statue I will call "Bucephalus". At time 2, the lump continues to exist as Lumpy2, but is reformed into into a statue of a big man, a statue I will call "Goliath". Then Lumpy1 is the same lump as Lumpy2, Lumpy1 is the statue as Bucephalus, Lumpy2 is the same statue as Goliath, but it does not follow that Lumpy1 is the same statue as Lumpy2, since we only have transitivity of relative identity when we keep the kind fixed.

Now suppose a four-dimensionalism that says that ordinary objects are four-dimensional (no further commitments on temporal parts, etc.). Then it seems we have a very odd thing. Lumpy1 the lump has a different shape and size from Bucephalus the statue. For Lumpy1 the lump is extended temporally up to and including at least time 2, while Bucephalus the statue does not extend temporally up to time 2. So shape and size are kind-relative. As a lump, Lumpy1 has one four-dimensional shape and size. As a statue, it's Bucephalus and it has a different four-dimensional shape and size. The causal powers are different, too. Lumpy1 can still be seen at time 2, while Bucephalus can no longer be seen then (except in photographs). So the causal powers of a thing are kind-relative, too. Moreover, this kind of thing happens routinely--it's not a miracle as when Christ is omnipresent qua God but only in Jerusalem qua human. It seems implausible that we would have routine kind-relative variation of size and shape.

This makes relative identity not so plausible given four-dimensionalism. But four-dimensionalism (in the weak sense I'm using) is clearly true. :-)

Relative identity and relative parthood

Advocates of relative identity say that identity is always relative to a kind. This seems to have an interesting and underappreciated consequence: If there is such a thing as parthood, it's relative to a kind too. For:

1. Necessarily: x=y if and only if x is a part of y and y is a part of x.

This is very plausible and is a consequence of the antisymmetry of parthood axiom. So if we had an absolute parthood relation, we would automatically get an absolute identity relation out of it.

Is it crazy to think parthood is relative to a kind? Maybe not. Consider classic apparent counterexamples to the transitivity of parthood like: My right foot is a part of me and I am part of the Admissions Committee, but my right foot is not a part of the Admissions Committee. Well, we could say: my right foot is a part of me qua organism, while I am a part of the Admissions Committee qua organization. It's unsurprising that can't chain "___ is a part of ___ qua F" and "___ is a part of ___ qua G" together. On the other hand, perhaps we can say that my right foot is a part of me qua physical object and I am a part of the Admissions Committee qua physical object, so my right foot is a part of the Admissions Committee qua physical object. That sounds just right! So the kind-relativity of parthood seems to be a helpful thesis, at least in this regard.

Still, having to say that parthood is kind-relative is additional baggage for the relative identity theorist to take on board. Can she escape from the weight of that load? Maybe. She could say that diachronic identity is relative but synchronic identity is absolute. If she says that, then she could say that (1) holds but only for synchronic identity and synchronic (three-dimensionalist) parthood. (I think, though, that one shouldn't make diachronic identity be any different from synchronic identity. They are both, just, identity.)