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How useful is the ‘constitution model’ of the Trinity?

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By Bartlomiej Staniszewski, Oxford University

Disclaimer (14/12/2021):

When I wrote this, I was quite dissatisfied with the conclusion, given its humility, but now it seems to me that it would indeed be too ambitious to hope for anything less humble. It seems to me that a Trinitarian theologian can only give you a story about what the Trinity could be, and never about what it univocally is. The Constitution Model sets out to give us a story which responds to the Logical Problem of the Trinity, and it does just that.

What the essay does not do is consider alternative models of the Trinity (Leftow, for example, has his own). I happen to think they are inferior, for reasons not mentioned in the essay, but the reader may think otherwise, and I invite them to give them due consideration.

What perhaps deserved mentioning in the essay that I did not mention is that the Model seems well-equipped to deal with the processions between the Persons of the Trinity. Consider that a statue-pillar composite may only exist because a sculptor sets out to make a statue, which ends up also being used as a pillar. Then, the pillar clearly proceeds from the statue. The Son could proceed from the Father in a relation that is analogous, except intrinsic to the Father (unlike the pillar in this example, which only stands in the relation of procession from the statue because of a fact about some external being, i.e. the sculptor).

How useful is the ‘constitution model’ of the Trinity?

The constitution model of the Trinity is useful in avoiding the Logical Problem of the Trinity but is of only limited use in illuminating the Trinity otherwise. This is because, aside from establishing the metaphysical possibility of the existence of the Trinity, it does not provide us with a good understanding of the nature of the Trinity’s existence. To show this, I will explicate how Brower and Rea’s constitution model of the Trinity responds to the Logical Problem of the Trinity and examine Ryan Wasserman’s, William Lane Craig’s, Brian Leftow’s, William Hasker’s, Alexander Pruss’, and Christopher Hughes’ objections to the model.

The Logical Problem of the Trinity is the problem of cohering seemingly incompatible propositions which constitute the historical doctrine of the Trinity. Richard Cartwright (1990, pp. 188-189) lists those propositions as the following:

(1) The Father is God.

(2) The Son is God.

(3) The Holy Spirit is God.

(4) The Father is not the Son.

(5) The Father is not the Holy Spirit.

(6) The Son is not the Holy Spirit.

(7) There is exactly one God.

If the ’is’ in (1-6) is read as an ’is’ of numerical identity (as (7) may be read to suggest), then the following argument can be deemed valid and sound:

P1) The Father is God. (1)

P2) The Father is not the Son. (4)

C) God is not the Son.

C contradicts with (2), rendering the set of (1-6) internally incoherent. Furthermore, a similar argument could be produced to contradict any one of (1-3) in the conclusion (using one of (1-3) in P1 and one of (4-6) in P2), or to contradict any one of (4-6) (using two of (1-3) in both P1 and P2).

The constitution model of the Trinity attempts to avoid the incoherency by reading ’is’ in (1-3) as an ’is’ of numerical sameness without identity (from now on, ’NSWI’). Consider a pillar, composed of some marble, that simultaneously serves as a statue. Brower and Rea (2005, p. 69) write that the persons of the Trinity stand in a relation analogous to that of the statue and the pillar to each other. They are distinct entities, for they have different identity conditions. For example, acid rain may destroy the statue without destroying the pillar. This is because the statue and the pillar share exactly the same matter (some marble occupying a certain region of space) but have different forms, in virtue of which they have different identity conditions – the form of a statue and the form of a pillar. As such, they are distinct hylomorphic compounds (compounds of matter and form), yet, because they are compound of exactly the same matter, they are the same lump of marble (ibid., p. 60; Rea, 2011, pp. 418-419).

Analogously, the persons of the Trinity are the same God. They share exactly the same divine substance (analogous to the matter in a hylomorphic compound), yet they are different persons (personhood being analogous to form), for they have different identity conditions (i.e., the divine processions: ‘begetting’, ‘being begotten’, or ‘spirating’).

But it is not clear that the statue and pillar are indeed distinct. Wasserman (2018) highlights that the statue and pillar share all their physical parts, and therefore to suggest that there is some property of the statue that the pillar lacks entails either the rejection of the plausible thesis that the properties of things must be grounded in one of their parts, or the rejection of physicalism (Molto, 2018, p. 413). However, choosing the second option should not be a problem for somebody interested in defending the doctrine of the Trinity, for the doctrine itself entails that physicalism is false.

Furthermore, the problem highlighted by Wasserman is one that applies only contingently. Even if it is the case that no two things that share all their physical parts may have disparate properties, this is only contingently true. For those who reject the existence of non-physical properties or parts generally consider that not to be a matter of metaphysical necessity. But for NSWI to serve as an analogy for the Trinity, NSWI need not be instantiated in this world. It would suffice for NSWI to be only possibly instantiated, as then the Trinity could still be analogous to material constitution as it happens in some possible world. NSWI need only be metaphysically possible to be used in a proposed solution to the Logical Problem of the Trinity. As such, the constitution model of the Trinity is only at threat from objections to NSWI that show it to be not just a non-existent relation, but a metaphysically impossible relation.

Hasker makes such an objection; NSWI is incompatible with “the standard definition of number-concepts in terms of identity,” such as that “there is exactly one F” means “there is some x which is F, and if there is any y which is F, y is numerically identical to x” (Hasker, 2010, p. 326). Under NSWI, we can say that there is exactly one lump of marble, and that there is a statue which is the same as the lump, and also that there is a pillar which is the same as the lump, but that nonetheless the statue is not numerically identical to the pillar. As such, NSWI goes against what seems “extremely plausible and intuitive to a great many philosophers over a considerable period of time” (ibid.). Hughes has similarly challenged NSWI on the basis that “no one uncorrupted by philosophy would doubt that [there cannot be more material entities than there are lumps of matter]” (Hughes, 2009, p. 303). Since the laws of identity are generally held to be metaphysically necessary, if NSWI violates them, it cannot explicate the relation between the divine substance and the persons of the Trinity.

But, as Wasserman (2018) shows, at least one solution (of which NSWI is one) to the problem of material constitution (the problem of the relationship between a material entity and the matter it is composed of) must be true, and every single one of them has consequences which pre-theoretically seem counter-intuitive. Moreover, a philosophical idea going against what seemed plausible and intuitive for many philosophers does not necessarily count against it. Edmund Gettier’s paper Is Justified True Belief Knowledge? went against a definition of knowledge that seemed plausible and intuitive to philosophers for millennia, yet no serious objector to Gettier would employ that as an argument against the case Gettier makes in his paper. Similarly to Smith and Jones being a counter-example to knowledge as justified true belief (Gettier, 1963, p. 122), the case of the pillar and the marble seems to be a counter-example to the standard definition of number-concepts in terms of identity.

The most serious conceptual problem with NSWI is explicated by Pruss, who writes that it is not just numerical sameness that can exist between two relata without numerical identity, but it is also numerical identity that can hold between two relata without numerical sameness. Suppose I gradually replace an old pillar with new marble. The current pillar is numerically identical to the old pillar, but they do not share their matter. However, X and Y can only stand in the relation of NSWI if they share exactly the same matter. So, the current pillar is not the same as the old pillar despite being identical to it (Pruss, 2009, p. 319). This seems an implausible way of modeling numerical sameness. “[W]hat kind of a numerical sameness is it if x doesn’t bear it to x?” (ibid., p. 320).

But Pruss also writes that “apart from a form, matter would have no particularity, and hence the identity of the matter is derivative from that of the form” (ibid., p. 317). As such, a hylomorphic compound always has exactly the same matter – the identity of matter through time comes from it being the matter of a particular hylomorphic compound, and so it cannot be replaced any more than, in classical dualism, I can have my soul replaced. Just as in classical dualism I am me in virtue of my soul, for Aristotle, matter is that particular matter in virtue of the form it is compounded with. In that, numerical identity does entail numerical sameness. And although (arguably) Aristotle thinks that the same matter can only ever be compounded with one form at the same time (the form that gives the matter its identity), it seems coherent to suppose that matter could get its identity from being compounded with a particular set of forms (ibid., p. 318). If that were so, analogously, the divine substance could be the divine substance in virtue of being shared exactly by the three persons of the Trinity, which seems plausible.

Even if the relation of NSWI is metaphysically possible, it remains unclear whether such a relation can serve as an appropriate analogy for the Trinity. For unlike the statue and the pillar, the persons do not share exactly the same matter. Christ’s body does not constitute the Father and the Holy Spirit, despite constituting the Son (Molto, 2018, p. 413). One solution to this problem is embracing Stump’s account of the Incarnation, according to which Christ’s two natures are to be understood as two parts (Stump, 2002, p. 207). Under that account, we can say that it is Christ’s divine nature only that stands in the relation of NSWI to the divine substance. Molto highlights, however, that this solution raises the spectre of Arianism, as it means that the composite Son bears a different relation to godhood than the Father and the Holy Spirit – a relation only held in virtue of one of his multiple parts (Molto, 2018, p. 415).

An additional disanalogy occurs from the fact that matter and form in a hylomorphic compound may seem only to be compounded contingently (Brower and Rea, 2005, p. 69) – the matter and the form can divorce (for example, the same matter can be reshaped so that it has a different form, such as a lump of marble being reshaped from a Corinthian pillar into a copy of David). Yet the persons of the Trinity cannot be divorced from the divine substance. However, it is coherent to suppose that the relation that holds between matter and form in a hylomorphic compound could hold necessarily, and not only contingently. And indeed, if matter gets its identity from the form it is compounded with, as Pruss (2009, p. 318) writes, the same matter and form cannot divorce, for if some matter is divorced from the form it was compounded with, it is no longer that particular matter.

Matter only being individuated by virtue of being compounded with some form also helps to block Leftow’s objection that material constitution modifies the Trinity into a quaternity – a divine composite of four, and not three, divine beings (Leftow, 2018, p. 368). For if the divine substance has no particularity apart from the three persons of the Trinity, then it is not a fourth divine being.

Leftow also contends that the constitution model results in tri-theism. For God must mean either ‘a being with divine nature’ or ‘the being with divine nature.’ But if there are three such beings, as is the case in the constitution model, there is no ‘the’ being with divine nature. Yet to say that God can refer to any of some beings with divine nature is the same as to say that Brian can refer to any of some Brians, Leftow writes, and the Brians are not one unity. Therefore, in material constitution, just as there are many Brians, there are many gods (ibid., p. 372).

The disanalogy between God and Brian is that each ‘God’ being shares exactly the same analogue of matter, while each Brian does not (ibid.). Leftow responds that sharing matter does not block the point. Suppose that the Greek pantheon began to merge their matter, eventually becoming one blob, whereby each member of the pantheon shares exactly the same matter. “Would that make Greek paganism monotheist? My own intuitions say no,” writes Leftow (ibid., p. 373). But the comparison to the Greek pantheon is unfair. Each member of the Greek pantheon retains a separate consciousness, while the Trinity is one psychological subject.

A further disanalogy is pointed out by Craig. He writes that in “the orthodox view God is not composed out of any sort of stuff” (Craig, 2009, p. 285), quoting Basil of Caesarea: “in the case of God the Father and God the Son there is no question of substance anterior or even underlying both; the mere thought and utterance of such a thing is the last extravagance of impiety” (ibid., p. 286). Yet references to divine substance, or ousia, are not only orthodox, but common in Christian theology. Craig himself explains that ousia is meant to refer to “the same generic nature” and not “some common stuff or substratum” (ibid.). But such an understanding is compatible with the constitution model. To solve the Logical Problem of the Trinity, a relation analogous to NSWI is needed between ousia and the persons of the Trinity. However, this does not mean that ousia needs to be like matter, or that personhood needs to be like form. A relation R that holds between X and Y can also hold between µ and α, whereby X and Y are completely unlike µ and α. Consider the relation ‘is causally affected by’. Mary is causally affected by the Angel Gabriel. The Baltic Sea is causally affected by the Moon. Yet Mary and the Angel Gabriel are completely unlike the Baltic Sea and the Moon.

Still, this might be because we have a general enough understanding of what it means for X to be causally affected by Y to apply it to any X with causal powers and any mutable Y. On the other hand, we do not have an understanding of NSWI general enough to apply it to immaterial entities or a ‘generic nature’. Rea himself characterises NSWI as “if a and b are [in the relation of NSWI] at a certain time, then a and b share all of their parts in common at that time” (Rea, 1998, p. 322). But it is unclear what it means for immaterial entities to have parts in common. Furthermore, this definition of NSWI would suggest that the Triune God has parts, which would put material constitution at odds with the doctrine of divine simplicity.

The latter concern can be easily dismissed. For the persons of the Trinity can still be in a relation analogous to NSWI if they only have one part, that is, an indivisible unity. And Hughes provides a more general characterisation of NSWI, writing that it is a relation that “neither is nor implies strict identity…it is irreflexive, asymmetric, and non-Euclidean…it does not hold between disjoint things” (Hughes, 2009, p. 313). Pruss also finds the application of NSWI to immaterial beings unproblematic, writing that NSWI is “a more general concept than mere identity of matter since it can also be applied to angels, which have no matter” (Pruss, 2009, p. 324).

But Hughes’ characterisation is apophatic, giving us no positive notion of NSWI, and Pruss only asserts that NSWI can be applied to angels without explaining how this can be done. Indeed, Leftow writes, the positive content of NSWI comes from aspects which are intrinsically material: “shape, occupying space, having spatial relations, being divisible, having spatially discrete parts.” We do not understand what it means for something immaterial to be the same as but not identical to some immaterial substance. (Leftow, 2018, p. 363)

One way in which we could gain a positive notion of NSWI as applied to the Trinity is by considering God’s omnipresence. For God has immediate knowledge about what is going on at any place and has immediate control over anything in any location (Swinburne, 2004, p. 95). And if God is omnipresent, then all the persons of the Trinity do share all their parts in common at any one time – they all share every part that there is. However, this seems to be a too strong understanding of omnipresence. Even if God is omnipresent, the matter in the world is not the same as God. Otherwise, counter-intuitive statements such as “I am sitting on [a part of] God” would be true, not to mention the issues it would cause for doctrines such as transubstantiation, divine simplicity, or the bodily resurrection of Christ.

It seems, therefore, that just what it means for the persons of the Trinity to be the same God remains unclear in that the constitution model of the Trinity is not useful in illuminating the nature of the Trinity. However, it would be too ambitious to expect otherwise. Firstly, it is already unclear just how matter, which has no particularity of its own, can be compounded with an immaterial form. And secondly, the lack of clarity leaves room for the mystery that is intrinsic to the Trinity. The stated aim of Brower and Rea’s constitution model is to show that it is possible for the Trinity to be modeled in a way that is coherent (Brower and Rea, 2005, p. 59), an aim it succeeds at.


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Craig, W. L. (2009) ‘Does the Problem of Material Constitution Illuminate the Doctrine of the Trinity?’ in McCall, T. H. and Rea, M. C. (eds.) Philosophical and theological essays on the Trinity. Oxford: Oxford University Press.

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Rea, M. C. (1998) ‘Sameness Without Identity: An Aristotelian Solution to the Problem of Material Constitution’, Ratio, 9(3), pp. 316-328.

Rea, M. C. (2011) ‘The Trinity’, in Flint, T. P. and Rea, M. C. (eds) The Oxford Handbook of Philosophical Theology. Oxford: Oxford University Press.

Stump, E. (2002) ‘Aquinas’ Metaphysics of the Incarnation’, in Davis, S. T., Kendall, D., and O’Collins, G. (eds) The Incarnation: An Interdisciplinary Symposium on the Incarnation of the Son of God. Oxford: Oxford University Press.

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