No new problem for the Trinity: A reply to Mooney

Abstract

The Father is God, the Son is God, the Holy Spirit is God, but there is only one God – this is the traditional problem of the Trinity. Recently, a new problem for the doctrine of the Trinity has been developed. God is triune, the Son is God, but the Son is not triune – that’s the new Triunity Problem. In this article, I show that adopting any solution to a traditional problem makes it possible to solve the new problem without incurring additional costs. I distinguish possible types of solutions to the traditional problem and point out the costs involved. I then show how each of these solutions can be used and developed to solve the new problem.

Problems with the Trinity: old and new

Most Christians believe that the Father is God, the Son is God, the Holy Spirit is God, but the Father is not the Son, the Son is not the Spirit, and the Spirit is not the Father. At the same time, they maintain that there is one God. The paradoxical nature of these sentences plagued the theologians of the first centuries of Christianity, and it plagues analytic philosophers today. The so-called Logical Problem of the Trinity (hereafter LPT) consists in showing how these sentences can be coherent (Cartwright 1987). In other words, to solve this problem one must propose a non-contradictory and orthodox¹ interpretation of these sentences.

Most of the contemporary analytical discussion on the Trinity concerns the LPT. Recently, however, Mooney (2018) posed another problem for the doctrine of the Trinity, which he gave the name of the Triunity Problem. God is triune. The Son is God. But the Son is not triune. The same problem also arises, of course, for the Father and the Spirit. Each of the Persons is God and neither of the Persons is triune. This seems contradictory. The Triunity Problem (hereafter TP) is to propose a non-contradictory and orthodox interpretation of these sentences or to justify which one to reject.²

Having set out the problem, Mooney considered three possible solutions. About each of them he concluded that it was costly and it would be better to look for an alternative. He concluded that no matter which one is chosen, it cannot be done for free. My aim here is to show that this claim is false in a sense. Solving the TP does not generate any new costs. The costs are real – but they have already been paid. This is because they appear already at the stage of solving the LPT, before one even begins to deal with triunity. They are neither new nor additional. The bad news is that due to the limited possibilities of solving the LPT these costs seem unavoidable. The good news is that if one has already accepted any solution to the LPT, the solution for the TP will come for free.

My argument goes as follows. First, it seems reasonable to claim that if someone is looking for a TP solution, they also want an LPT solution. This seems reasonable, because the motivation in both cases is concern about whether the doctrine of the Trinity is coherent. So, it can be assumed that the person looking for a TP solution is not definitively rejecting every possible LPT solution. If they are looking for a solution at all, they must hope that there is one. This does not necessarily mean, of course, that they fully accept any of the currently existing accounts of the Trinity. They may believe that such a solution has yet to be discovered, or that any of the currently proposed positions should be further developed or modified. However, I assume that such a person believes that there is some acceptable LPT solution.

The second premise is that there is a limited number of possible types of solutions to the LPT (actually, what I present below is based on Branson’s (2019) argument, which leads to the conclusion that there are no new solutions to the LPT). These types are distinguished by the logical form of the solution. For two solutions belonging to the same logical type, the ontologies of the Trinity underlying their acceptance may be quite different. But from a logical point of view, the proposed taxonomy is exhaustive. Therefore, if one accepts any LPT solution, it will belong to some of these possible solution types.

Now each of these types of solutions brings some costs to accept. These costs are a result of the logical forms of each of the solutions. There is no way to get rid of them other than to choose a different formalization. But if one does so, one just gets different costs to pay, because none of the solutions is without them. The final step is to show that each of the distinguished types of the LPT solutions allows solving the TP without incurring additional costs. I show this for each LPT solution in turn. This is enough to reach a conclusion: the TP cannot pose difficulties to a philosopher dealing with the Trinity that they have not encountered before. All the costs that need to be incurred have already been incurred in solving the LPT.

The article is structured in the following way. First, I outline the TP posed by Mooney and the costs of the possible solutions he identified. In the next section, I present the LPT in detail and construct an exhaustive taxonomy of its possible solutions. I point out the unavoidable costs of these solutions. It turns out that there are four types of solutions that are neither contradictory nor obviously unorthodox. In the four remaining sections, I show in turn for each of these solution types how their adoption allows the TP to be solved.

The new problem

The traditional LPT arises from the tension between the claim that God is one, while the Persons are many. According to Mooney, ‘the Problem of Triunity proceeds from the fact that, in one sense or another, God is many, and yet each divine person on his own is just one’ (Mooney 2018, 1). It seems that Christians are committed to the claim that

(I)   God is triune.

Mooney considers (I) a succinct way of expressing the statement derived from the Athanasian Creed that Christians worship ‘one God in Trinity and Trinity in Unity’. He does not strictly define what he means by ‘triune’. However, he states that ‘triunity minimally involves being in some sense three-personed’. He gives numerous examples of philosophers dealing with the Trinity who embrace this kind of thesis (Mooney 2018, 2).

Another thesis is:

(II)   The Son is not triune.

Mooney finds this statement uncontroversial. It seems that the Son is not ‘three-personed’. The Son is one person.

The traditional doctrine of the Trinity undoubtedly also includes the statement:

(III)   The Son is God.

Mooney concludes that ‘(I)–(III) form an inconsistent triad; any two of them entail the negation of the third’ (2018, 2; thesis numeration changed). The problem was formulated for the Son, but of course it arises just the same for the Father and the Spirit.

But is the (I)–(III) triad really inconsistent? To determine this, I propose to formalize claims (I)–(III). However, in order to do so, it is necessary to clarify, at least slightly, the terms appearing in them to establish the logical form of these sentences. Let’s start with the ‘is’ of (III). Should we treat it as expressing classical identity? Then we should read (III) as ‘The Son is identical to God’. The problem could be formalized as follows:

(TP1-I)   Triune(god) (TP1-II)   ∼Triune(son) (TP1-III)   son = god

The contradiction is very clear. The same entity cannot have and not have a given property. This would break the principle of the indiscernibility of identicals, which governs classical identity. However, such a formalization is not good. If we accept it, we immediately close the way to the solution of the LPT. Note that the same thing that can be said about the Son can also be said about the Father: ‘The Father is identical to God’. However, classical identity is symmetric and transitive. Hence, we get that The Father is classically identical to the Son. This is clearly unorthodox, strictly speaking, modalistic – even a minimal difference between the Persons is negated.³

Mooney claims that ‘Some writers – typically social Trinitarians – argue that we should read statements like (III) as predications rather than identity claims’ (2018, 3). However, it turns out that formalizing (III) as (TP1-III) is not only rejected by some authors – it must be rejected by all authors who want to avoid modalism. It is therefore necessary to look for a different formalization of the problem.

Let’s try to treat ‘is God’ as a predication. Then (I) will read as ‘All that is God is triune’ or ‘If something is God, it is triune’. In formal notation:

(TP2-I)   ∀(x) God(x) → Triune(x)

One can also read this phrase in a more ontologically committing way as ‘triunity is a property included in the divine nature’ (see Mooney 2018, 4) or ‘triunity is essential to divinity’ (see Willenborg 2022, 458 and footnote 9).

The next point (II) remains unchanged:

(TP2-II)   ∼Triune(son)

(III) is formalized using the predicate:

(TP2-III)   God(son)

This interpretation of (I)–(III) is clearly contradictory and seems to illustrate the problem well.

To solve the problem at least one of the three statements should be rejected or modified so that they do not generate a contradiction.

We can reject (TP2-I), and thus recognize that being God does not entail being triune in Mooney’s sense. The problem with this move is that according to Mooney, triunity, as one of the perfections, is contained in the nature of God, so a fortiori it is a quality of God (Mooney 2018, 9–10). However, in order to reject (TP2-I), one must deny that triunity as understood by Mooney is a quality possessed by God.

Rejection of (TP2-II) is, according to Mooney, the least promising path (Mooney 2018, 7–9). Indeed, it does not seem possible without a significant redefinition of triunity. It is difficult to imagine how the Son could be ‘in some sense three-personed’.

Rejection of (TP2-III) also carries a high cost. It turns out that the Son is not God in the strict sense, or at least that he is a God of some other kind than the Triune God.

I now turn to a discussion of the structure of the LPT and its possible solutions. In what follows I show how the choice of LPT solution affects the solution of the TP. It turns out that two of the LPT solution types discussed below entail rejection of (TP2-I), and the other two entail rejection of (TP2-III).

Back to the old problem

In this section, I present the classical formulation of the LPT and then argue (similarly to Branson 2019),⁴ that there are only four possible types of solutions to this problem that are both coherent and possibly orthodox (not obviously heretical). This will later allow me to show that each possible solution of the LPT brings a solution to the TP at no additional cost. However, if one finds the argument of this section unconvincing, the following sections of the article may convince one of the weaker thesis: every existing LPT solution brings a solution to the TP at no additional cost.

The Christian doctrine of the Trinity includes the following seven statements:

1. (1) The Father is God.

2. (2) The Son is God.

3. (3) The Holy Spirit is God.

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

5. (5) The Father is not the Holy Spirit.

6. (6) The Son is not the Holy Spirit.

7. (7) There is one God.

The LPT is that sentences (1)–(7) seem contradictory. Why? Because of the possible interpretations of these sentences, the two most intuitive are contradictory. The first intuition is usually to treat ‘God’ as the name of an individual, and ‘is’ as classical identity. We then get the following formalization of sentences 1–7:

(LPT1-1)   father = god (LPT1-2)   son = god (LPT1-3)   spirit = god (LPT1-4)   father ≠ son (LPT1-5)   father ≠ spirit (LPT1-6)   son ≠ spirit (LPT1-7)   ∃!(x) x = god

This formalization, of course, is contradictory, since, for example, (LPT1-1) and (LPT1-2) entail father = son, and therefore the negation of (LPT1-4).

The second obvious possibility is to treat ‘is God’ as a predicate. We would then get the following set of sentences (cf. Branson 2019, 1056–1057):

(LPT2-1)   God(father) (LPT2-2)   God(son) (LPT2-3)   God(spirit) (LPT2-4)   father ≠ son (LPT2-5)   father ≠ spirit (LPT2-6)   son ≠ spirit (LPT2-7)   ∃!(x) God(x)

(LPT2-7) can be expanded in the typical way the expression ‘there exists exactly one’ is understood in logic. Thus, we get ‘There exists x, which is God, and for every y, if y is God, then y is identical to x’. In formal notation:

(LPT2*-7)   ∃(x)∀(y) (God(x) & (God(y) → y = x))

It is easy to see that this interpretation is also contradictory. Just substitute father for x and son for y in (LPT2*-7) to get father = son, contradicting (LPT2-4).

How to solve the problem of the Trinity posed in this way? It is impossible to do so by rejecting any of the points (1)–(7), since they all belong to or follow from the doctrine. This would be equivalent to simply rejecting the doctrine. Rather, some other non-contradictory formalization of these sentences should be proposed and shown to be better⁵ to the two presented above.

Such formalization can be achieved by answering a series of questions. Each successive decision either excludes certain ways of formalization or establishes them. This creates an exhaustive taxonomy of possible LPT solutions. Other solutions do not exist because all formalization options have been considered.

Below, following (Branson 2019, 1075–1076) I make two assumptions: first, I assume that standard versions of predicate logic with identity are suitable for formalizing claims (1)–(7).⁶ Second, I assume that ‘the Father’, ‘the Son’, and ‘the Holy Spirit’ are univocal singular terms.

I will now consider seven questions in turn and show what possible answers they allow. These questions concern the difference between the Persons, univocal or equivocal interpretation of the term ‘God’, the reading of ‘is’ in the phrase ‘is God’, and deciding how to understand the claim that there is one God. It will turn out that there are only four sets of answers that are neither contradictory nor obviously incompatible with Christian orthodoxy.

1. 1. Are you going to interpret ‘is not’ in (4) (‘The Father is not the Son’) as implying that the Father and the Son are at least not identical, and same in (5)–(6)?

Accounts of the Trinity vary on the difference between the divine Persons. In some, the Persons differ only in their relations of origin, while in others they have separate knowledge, will, self-consciousness, action (this position is typical of Social Trinitarians, but not only of them). However, all agree that for any two divine Persons there is some predicate true of the one and false of the other (e.g. the Father is unbegotten and the Son is not). And since they differ in what can be predicated of them, they cannot be classically identical.⁷ This is a conceptual necessity, arising from the very notion of classical identity, which is subject to the principle of indiscernibility of identicals. Accordingly, (4)–(6) should be formalized as:

(ABDC-4)   father ≠ son (ABCD-5)   father ≠ spirit (ABCD-6)   son ≠ spirit

The alternative to this interpretation of the doctrine is modalism: the denial of even a minimal difference between the Persons. I do not explore this option below, since we are only interested in potentially orthodox solutions, of which modalism is not one.

1. 2. Are you going to treat ‘is God’ as univocal in (1)–(3) (‘The Father/Son/Spirit is God’)?

In other words: are you going to accept that the Son is God in the same sense in which the Father is God (and so is the Spirit)? Or, for example, when referring to the Son, does ‘is God’ mean something different than when referring to the Father?

Embracing the equivocation on ‘is God’ in (1)–(3) provides some way to get rid of the contradiction. For example, one can consider that only the Father is God in the proper sense of the word, and the Son and the Spirit are divine in some other way. In that case, saying that there is one God does not generate problems – there is one God in the proper sense. Or, for example, one can consider that there are three different equally good senses of being God, one each for Father, Son, and Spirit. Then, no matter which sense one chooses there will be only one God of a given type.

Such interpretations of sentences (1)–(7) avoid contradiction, but are clearly unorthodox. The first is found, for example, in Eunomius (formally condemned by the Council of Constantinople in 381), who believed that God could not originate or proceed from anyone, so claimed that neither the Son nor the Spirit is a God in the proper sense (Mira 2009, 318–319). The second was proposed by some Arians (see Branson 2019, 1068–1071 on Arianism). The adoption by the Council of Nicaea of the statement that the Son is consubstantial with the Father, and the subsequent defence of this thesis by fourth-century orthodox theologians, was aimed precisely at rejecting any attempt to introduce a difference as to deity between the Father and the Son and the Spirit.

Since we are only interested in potentially orthodox solutions, below I assume that ‘is God’ in (1)–(3) is unambiguous (whatever exactly ‘is God’ means).

1. 3. Are you going to interpret ‘is’ in (1)–(3) (‘The Father/Son/Spirit is God’) as implying that the Father/Son/Spirit is identical to something called ‘God’?

If you do so, a contradiction immediately arises. If the Father is identical to God, and the Son is identical to God, it follows that the Father is identical to the Son (from symmetry and transitivity of the classical identity relation). And above (at question 2) we assumed that no two Persons of the Trinity are identical. (In fact we have just arrived at the first intuitive but contradictory interpretation presented earlier in this section.) Since we do not want a contradiction, below I assume that the ‘is’ in (1)–(3) should not be interpreted as (classical) identity.

From this point on, the scheme will begin to get complicated. So far the questions have only sought to block certain options because of their logical inconsistency or evident contradiction with orthodoxy. Now questions will come up that philosophers dealing with the Trinity actually answer differently.

1. 4. Are you going to interpret ‘is’ in (1) (‘The Father is God’) as ‘the Father is in some special relation to God’ where this special relation is other than classical identity (and analogously in (2)–(3))?

In the debate, there is a view that it is best to consider the Trinity as a whole as God, and to consider the Persons divine in some secondary sense, because of the relationship they have to God. For example, Craig (2009, 96) writes: ‘we could think of the persons of the Trinity as divine because they are parts of the Trinity, that is, parts of God’. So each person is in a ‘is a part of’ relation to God. A solution similar in logic is proposed by Hughes (2009, 309): God is not the Trinity, but ‘divine matter’ and it constitutes each divine Person. So, for example, the Father is to God in a ‘is materiated by’ relationship. Solutions of this kind avoid contradictions. There is only one God in the proper sense (the whole Trinity or ‘divine matter’), and the Persons are to this God in some relation (being parts or being constituted). (1)–(3) should be formalized as:

(A-1)   R(father, god) (A-2)   R(son, god) (A-3)   R(spirit, god)

where R is some special relation between a divine Person and God, for example, some sort of part/whole relation or constitution relation. As long as this relation doesn’t entail identity of its relata, this formalization avoids contradiction.

Such a solution is, of course, controversial. On its grounds, none of the Persons is God in the strict sense. But precisely because of this it is possible to claim that there is one God.

If we reject such a solution we are left only to treat ‘is God’ as a predicate. The formalization looks as follows:

(BCD-1)   God(father) (BCD-2)   God(son) (BCD-3)   God(spirit)

We have now established the formalization of (1)–(6). It remains to decide how to interpret (7) (‘There is one God’).

1. 5. Are you taking (7) (‘There is one God’) as the assertion that there exists exactly one thing which is God?

This question may sound tautological, but it is not so at all. Some philosophers dealing with the Trinity propose different readings of this statement. They want to interpret the unity of God not as a statement that there is exactly one thing which is God, but as a thesis of a strong unification of the divine Persons. For example, Swinburne (1994, 180) writes of the rejection of polytheism: ‘I suggest that they [the Councils] were denying that there were three, independent divine beings, any of which could exist without the other; or which could act independently of each other.’⁸ Yandell (2009, 251–252), in turn, defines the unity of God by stating four conditions to be fulfilled by Persons (among them, for example, is the necessary coexistence). Such claims can be called, following Leftow, ‘qualitative monotheism’ (Yandell 2009, 77) – the claim that ‘there is one God’ is not really about how much of something there is. Rather, it tells us what the divine Persons are like (and they are exceptionally strongly united).

If one decides on such a ‘qualitative’ interpretation, (7) can be put as follows: for any two objects, if each of them is God, they remain in some special relation (of unity). The formalization looks as follows:

(B-7)   ∀(x)∀(y) (God(x) & God(y) → R(x,y))

where R is some special relation of unity. Note that this statement says in what relations two divine Persons must be to each other. It does not say anything about the number of anything (actually it does not even say anything about existence).⁹ Again, as long as this relation does not entail identity of its relata, this formalization avoids contradiction.

This interpretation avoids contradiction but some philosophers have doubts if it counts as monotheism at all (Leftow 2009, 74–76). ‘There is one God’ was paraphrased up to the point where it took the form of ‘There are no divine beings independent of each other’. Is this really equivalent? Is this strong enough to count as monotheism? Is this really what the Councils meant?

If your answer is ‘no’, you will probably want to interpret (7) as ‘There exists exactly one God’. In symbols, it would be:

(ACD-7)   ∃!(x) God(x)

But there are two last moves we can make. The first is the introduction of equivocation, and the second is a change in the way we count.

1. 6. Are you going to equivocate on ‘is God’ between (1)–(3) (‘Father/Son /Spirit is God’) and (7) (‘There is one God’)?

Another possible way to avoid contradiction is to introduce two senses of being God. In the first sense, God is the Father, the Son, and the Spirit. The second sense is used when it is said that there is one God. This one God can be, for example, Trinity as a whole or the divine nature. This was the position proposed by Plantinga (1988, 52–53). The formalization is as follows:

(B-1)   God₁(father) (B-2)   God₁(son) (B-3)   God₁(spirit) (B-7)   ∃!(x) God₂(x)

This formalization avoids contradictions, but achieves it by introducing two senses of being God. This move is controversial. It turns out that although in one sense there is one God, in another sense there are three. However, if we do not want equivocation, all that remains is to change the way we count. Therefore, the final question is:

1. 7. Are you going to count by classical identity in (7) (‘There is one God’)?

As I mentioned above there is a standard way logicians expand the formula

∃!(x) God(x)

namely:

∃(x)∀(y) (God(x) & (God(y) → y = x))

Here we count by classical identity, that is, we say that x and y are the same God if they are identical. But we can count Gods by relation other than standard identity. How? Imagine a phone that reads your fingerprint when you try to unlock it. What does it mean that exactly one person tried to unlock the phone today? It means that there is someone who tried to unlock the phone, and everyone who tried to unlock the phone had the same fingerprint. In this case, we can count the people unlocking the phone according to the relationship of having the same fingerprints. In the same way, we can count Gods according to a relation other than classical identity. The scheme will look as follows:

(D-7)   ∃(x)∀(y) (God(x) & (God(y) → R(y,x)))

where R is some relation we count by. This scheme differs from the previous one only in that it is more general: R can be a relation other than classical identity. What relation exactly? Proponents of some positions that focus solely on the logic of the solution call this relationship simply ‘is the same God as’ (or ‘is the same Being as’) (Baber 2015; Van Inwagen 2009). Others try to propose a metaphysics of the Trinity that justifies why it is legitimate to change the way of counting. For example, according to Brower and Rea (2005) the Persons stand in the relation of numerical sameness without identity, which in turn is grounded in having the same divine essence playing the role of matter. Branson, on the other hand, formalizes Gregory of Nyssa’s position by counting according to the relation of having a common action (Branson 2014, 247–249).¹⁰

Now, let’s go back to question 7. Are you going to count by classical identity? If yes, you will get a contradiction. We have God(father) (1) and God(son) (2). So from (7) we can derive father = son. Which is obviously contradictory to father ≠ son (4). (This time we arrived at the second intuitive but contradictory interpretation presented earlier in this section.)

So to avoid contradiction one has to count by some other relation which is not classical identity (and which doesn’t entail classical identity). This is what proponents of the relative identity trinitarianism do (the counting scheme is given explicitly for example in Van Inwagen (2009) 263 and Brower and Rea (2005) 69). There is no contradiction involved. But there is a price to be paid: the standard way of counting has to be changed.

This was the last option. There are no more decisions to make. The whole process is illustrated in the decision tree (figure 1). Obtained solutions are presented in table 1.

Figure 1: Trinitarian options.

Table 1: Noncontradictory and possibly orthodox solutions to the LPT

As can be seen, there are only four types of solutions that avoid contradictions and have a chance to be orthodox. Each of these types is controversial, but there are no others. Denying the Persons of the Trinity the fullness of deity, swapping God’s singularity for unity, adopting two senses of being God, or changing the way we count – each of these moves avoids contradiction, but is some kind of cost that burdens the solution. However, to get any LPT solution, one of them has to be chosen.

In the next four sections, I will show how the adoption of a given LPT solution enables a TP solution at no additional cost.

Solution A: persons not strictly divine

As I wrote above, this solution is to claim that none of the Persons is God in a strict sense. God is one, and the three Persons remain in some special relationship to Him.

How will considering the Persons only as being in some relation to God resolve the problem of triunity? A proponent of this position can agree that triunity in Mooney’s sense is a property contained in the divine nature (or, more weakly, that if something is God it is triune). Accordingly, the formalization of the first sentence ‘God is triune’ remains unchanged:

(TP-AI)   ∀(x) God(x) → Triune(x)

In this view, none of the Persons is triune, so the formalization of the second sentence remains unchanged:

(TP-AII)   ∼Triune(son)

However, in solving the LPT a proponent of the solution A has already agreed to formalize ‘The Son is God’ as:

(TP-AIII)   R(son, god)

Thus, we have achieved a non-contradictory interpretation of the sentences that make up the TP by drawing consequences from the logical movement made when solving the LPT.

Mooney finds this type of solution problematic. Commenting on the position of Craig and Moreland he writes:

In general, the traditional doctrine of the Trinity is understood as affirming that the Son (as well as the other divine persons) has the full divine nature. The creeds are clear that the Son shares the very same nature as the Father, and while there is dispute about whether that shared nature is concrete or abstract, as the creeds are typically understood, that shared nature is no less than the divine nature – the full nature of God. Consequently, most Christian philosophical theologians will not accept this solution to the Problem of Triunity (Mooney 2018, 3).

Mooney is, of course, absolutely correct that denying the Persons full divine nature is problematic. However, the real consequence of his words is that most Christian philosophical theologians who will not accept this solution must choose some of the LPT and TP solutions of another type – along with its costs.

Solution B: unity instead of oneness

This solution holds that the Divine Persons are very closely united, and this is what we mean when we say that there is one God. The Father is God, the Son is God, and the Spirit is God, but not the Trinity as a whole. Thus, being God does not entail being triune in Mooney’s sense of ‘being in some sense three-personed’. Rather, being God is linked to being a member of a trinity.

How can a proponent of such a solution respond to the TP? If they want to ascribe triunity to God, they will have to redefine it. They would probably want it to mean something like ‘being a member of a trinity’. Of course, this trinity must be united strongly enough so that it does not turn out that too many entities are triune. This is the kind of solution Willenborg (2022) chose when constructing his answer to the problem posed by Mooney. He proposed a definition of triunity: ‘“X is triune” = def X’s nature is possessed by three persons, each of whom exists only if the other two exist as well’ (Willenborg 2022, 457). The solution lies in rejecting the second element of Mooney’s trilemma, that is, the claim that the Son is not triune. In this way, we avoid a contradiction. On the other hand, if we ask the question of whether God is triune in Mooney’s sense, the solution would be to reject the first member of the trilemma – the claim that God is triune in Mooney’s sense. Of course, also the Son is not triune in Mooney’s sense, so the contradiction does not arise.

The formalization is as follows:

(TP-BI)   ∼(∀(x)God(x)→Triune_M(x))& ∀(x) God(x) → Triune_W(x) (TP-BII)   ∼Triune_M(son)& Triune_W(son) (TP-BIII)   God(son)

where Triune_M means ‘is triune in Mooney’s sense’ (or something similar; roughly ‘is in some sense three-personed’), while Triune_W means ‘is triune in Willenborg’s sense’ (or something similar; roughly ‘is a member of a trinity’). The first parts of the above conjunctions deny triunity in Mooney’s sense, and the second parts attribute triunity in Willenborg’s sense.

Is such a redefinition legitimate? It’s hard to settle the answer to this question, since the meaning of the term ‘triune’ does not seem to be strictly defined, and we may have very different intuitions about it. However, if one is not convinced by the statement that each of the Persons of the Trinity is triune, one may consider another solution – one may not consider the phrase ‘God is triune’ as a commitment to ascribing a property to God at all. To answer in this way, one must assume that when we say ‘God is triune’ we want to put the complex doctrine of the Trinity succinctly. This is the thesis of Radde-Gallwitz – the Greek patristics’ scholar: ‘I find modern phrases like “the triune God” or “the tripersonal God” problematic shortcuts. Perhaps such tags are useful provisionally, but they threaten to reduce the inherently complex concept described by the Cappadocians to something incoherent’ (Radde-Gallwitz 2020, 67).

Surprisingly, even excerpts from Mooney’s text support Radde-Gallwitz’s treatment of triunity. In presenting the TP, Mooney reasoned why a Christian should accept the claim ‘God is triune’. He began by noting that it is similar to the fragment of the Athanasian Creed which says that Christians worship ‘one God in Trinity and Trinity in Unity’ (Mooney 2018, 1). It seems that this similarity should be about signifying more or less the same thing, conveying more or less the same content. This suggests that the statement ‘God is triune’ is something of a shorthand way of expressing the truth contained in the creed. And it is possible to agree with the creed without committing oneself to the existence of some feature of triunity possessed by God.

One can come to similar conclusions by following how the triunity is presented by Willenborg (2022) who polemicizes with Mooney. He claims that the first Council of Constantinople held that the Persons ‘have a single Godhead and power and substance’. He cites the Second Council of Constantinople, which ‘anathematizes anyone who “will not confess that the Father, Son and Holy Spirit have one nature or substance, that they have one power and authority, that there is a consubstantial Trinity, one Deity to be adored in three subsistences or persons”’. He states that there is one nature, substance, divinity, essence, Godhead and there are three Persons, hypostases, subsistences. Finally he suggests ‘we take these statements as expressions of what it is for God to be triune’ (Willenborg 2022, 457). It seems that a proponent of the solution currently under discussion can agree with all the above claims, and at the same time not feel obliged to acknowledge that there is a feature of triunity possessed by God. The contradiction can therefore be avoided by appropriately paraphrasing the statement ‘God is triune’.

Both of the above ways of answering the TP deny that God is triune in Mooney’s sense. Is this a problem? Mooney argues that it is. He writes (2018, 6): ‘it seems obvious, trivial, even platitudinous that God – that is, the one and only God that Christians confess – is divine. But clearly God – the one God – is not a member of a trinity. Rather, God is triune, and only each individual divine person is a member of a trinity.’ Mooney seems to be assuming here that there is something (the Trinity?) that is God, yet is not identical to any of the divine Persons. For him it seems clear and obvious but in fact such an assumption is deeply problematic. First, such an assumption seems to contradict at least some of the writings of the Church Fathers and the claims of many contemporary theologians, so it cannot be treated as evidently belonging to the Christian doctrine (Branson 2022). Second, the problem of the ‘four Gods’ arises. Father is divine, Son is divine, Holy Spirit is divine. God is divine. So now we have four divine beings. Certainly too many. What can be done?¹¹ One can deny that the Persons have the full divine nature, but this claim seems problematic (it was discussed in the previous section). Another option is to introduce two ways of being divine, one for the Persons and one for God. This move may also seem problematic to many (e.g. Leftow refers to this view on the Trinity as ‘Plantingian Arianism’ (2009, 66)). So it turns out that denying that there is a God distinct from each of the Persons, and in particular denying that the Trinity is God, is no more problematic than the alternatives of accepting two different senses of being God or denying the fullness of divinity to the Persons.

Solution C: equivocation

A third way to avoid contradiction in solving the LPT is to introduce an equivocation on ‘is God’: to recognize that the sentence ‘There is one God’ refers to a God of some other kind than the sentences ‘The Father is God’, ‘The Son is God’, and ‘The Holy Spirit is God’. This move also allows for an easy solution to the TP: triunity will be linked to only one of the two properties of being God. The formalization proposed by a proponent of this solution should be as follows:

(TP-CI)   ∀(x) God₂(x) → Triune(x) (TP-CI)   ∼Triune(son) (TP-CIII)   God₁(son)

In this view, being the one God entails triunity, while being a divine Person does not. Thus, the contradiction does not arise.

For this solution the following doubt can be raised. It is usually assumed that if something is God it should possess all perfections. It seems that if there are two senses of being God, realizing either of them should entail these perfections. Mooney argues that triunity in his sense is a perfection.

If loving communities are highly valuable – more so than states of isolation (ceteris paribus) – then it seems that a triune being that contained that sort of value within its own borders would be a greater, more valuable being than an otherwise similar unitarian being. In other words, triunity is a great-making property (Mooney 2018, 4–5).

So being God in any sense should entail triunity. Whereas, according to this position, only the second sense of being God entails it. Moreover, this problem cannot be answered by redefining trinitarianism as ‘being a member of the Trinity’, because then only the first sense of being God will entail it, not both.

There are two possible answers to this argument. One can either argue that not only being three-personed but also being a member of a community is a way of realizing the perfection in question or deny that any similar feature is a perfection.

If one chooses the first option one can start by pointing out that Mooney’s argument is very similar to the well-known one given by Richard of Saint Victor and later developed by Swinburne (1994, 177–178). The premise of the argument is similar – perfection requires perfect love, and perfect love requires relationships, mutual bestowal of all the best, and cooperation in outward giving. Divine being is perfect. But for Swinburne the conclusion is not that divine being is a loving community, but that there is a loving community to which each divine being belongs. This does not seem less convincing than Mooney’s version of the argument.¹² So, perhaps we should conclude that the perfection in question can be realized in two ways – by being a community or by belonging to a community.

The second possible answer to the perfect being argument is to deny that being a community or belonging to the community is a perfection and thus a property included in the divine nature. First, there are religions (e.g. Judaism, Christian unitarianism, or Islam) in which God is considered perfect, although he does not form anything like a divine community. This suggests that, at the very least, it is not obvious whether such a quality is a perfection. Second, even Christian philosophers and theologians engaged in perfect being theology often do not list triunity among the attributes of God that can be discovered by examining His nature by reason. The doctrine of the Trinity is often regarded as revealed and otherwise inaccessible to the human mind. For example, Thomas Aquinas argues that the argument of Richard of Saint Victor can only confirm the existence of the Trinity if one already believes in it. This confirmation consists in showing the consistency of the whole doctrine – God’s perfect love agrees with his existence in the Trinity. However, Aquinas does not exclude the possibility that God’s perfect love could be realized in other ways (ST I, q. 32, a. 1).¹³

Solution D: not counting by classical identity

Accounts of the Trinity using what is known as relative identity avoid the contradiction in solving the LPT by using solution D – by introducing a non-standard way of counting Gods. The number of Gods (one) is determined according to some relation other than classical identity.

A proponent of solving the LPT by means of relative identity can answer the TP in the same way as a proponent of solution B discussed earlier. Being God does not entail being triune in Mooney’s sense – ‘being in some sense three-personed’. God is neither the Trinity as a whole nor the divine nature – nothing but the Persons is God in the strict sense. Consequently, as with solution B, the claim that God is triune in Mooney’s sense must be rejected, and either triunity must be redefined accordingly or the Persons must be denied the attribute altogether. In the case of redefining triunity, the formalization will look exactly the same as the formalization given above for solution B, so I do not repeat it here.

As might be expected, Mooney found using relative identity problematic as well:

This proposal has a lot to be said for it, but there are also reasons to worry. First, relative identity is not exactly popular; many philosophers reject it as ‘unintuitive, unintelligible, and uninformative’, among other things. Of course, these concerns will not bother the philosophical theologian who already endorses a relative identity model of the Trinity on grounds independent of the Problem of Triunity, but even so, it would be better to have a solution to the Problem of Triunity that is not wedded to such a controversial notion (Mooney 2018, 9).

A defence of relative identity would require a separate article; such defences do, in fact, exist (Barber 2015; Jedwab 2015; Van Inwagen 2022). I would just like to point out that this solution, counter-intuitively, does not at all require the denial that classical identity exists. Nor does it require the use of a logic other than some standard version of predicate logic with identity (although such logics have been constructed; see Garbacz 2002). The last remark: would it really be better to have a solution to the Problem of Triunity that is not wedded to the notion of relative identity? I do not think so. Alternatively it could be wedded to the denial of the full divinity of the persons, to weakening of God’s oneness, or to equivocation. It could also not be wedded to any of these, but – as we want an LPT solution anyway – it would still have to coexist with one of these. So it may be better to decide on this marriage of convenience.

Conclusion

Solutions of the LPT and the TP are closely related. Drawing consequences from the assumptions underlying LPT solutions allow to obtain TP solutions at no additional costs. It is clear that all solutions have problems and it is possible to be dissatisfied with all of them. If it were otherwise, the doctrine would probably be less controversial, so many heresies would not have arisen, and the dispute would not have gone on for two millennia. But if one is convinced that the Trinity is worth believing in, one must choose between the available options. The good news is that if one has already accepted some solution to the LPT, one can get a solution to the TP for free. The bad news is that if one comes up with some new promising solution to the TP, to solve the LPT one will have to pay old costs anyway.