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Is a triune God like a square circle?

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14 minutes to read Yes—if you’re a two-dimensional being who is trying to understand a cylinder.

Long ago, back in the mists of time, I debated an atheist who made the following comment:

The existence of the Trinity is contradictory. It is equivalent to a statement that a circle is a square. Of course, we can believe contradictions, but it is not appropriate to allow them in a discussion about reason, that is itself supposed to be using reason to make a case.

Since I recently discussed Trinitarianism and biblical theology on Andrew Schumacher’s Beginning of Wisdom podcast, and he mentioned my response to this criticism way back when, I decided to break it out of mothballs and post it here.

1. Can we believe contradictions?

If you think we obviously can’t, then you are correct, and can skip to the next section. Unfortunately you a dying breed, so I need to answer this question before moving on. There’s an increasingly popular mindset within the church today that is quite happy to affirm that the Trinity entails a contradiction. Some Christians would go so far as to say that they believe in the Trinity because it is self-contradictory—as if believing things which don’t make sense is deeply spiritual.

But contradictions literally cannot be believed. If you’ve been taught that the Trinity is self-contradictory, and you’re happy to believe this, you’re going to have a really hard time witnessing to anybody with half a brain. They will rightly ask not why they should believe in a triune God, but how.

This is because to believe something means that you think it is true. Now, one of the requirements for truth is non-contradiction. For example, some proposition p—let’s say this paint is wet—can be believed quite readily. So can its negation, not-pthis paint is dry. But imagine a proposition, q, which means “p and not-p”—this paint is both wet and dry. You cannot believe q because it patently violates a condition of being truthful. That isn’t to say that you can’t mistakenly think you believe it. You can say “I believe q” if you haven’t actually taken the time to consider it. But that just makes you uncritical. It doesn’t make you spiritual or clever. It doesn’t make you actually believe q.

So what do you actually believe? Well, not that the paint is both wet and dry. You can’t believe this, because you can’t understand what it means to believe both p and not-p at the same time. It doesn’t make sense. Sure, you can read the letters and sound out the words, and if you are very silly you can say that they are true—but the actual structure of the statement does not mean anything. The latter half of the proposition denies the former half, and vice versa. They cancel each other out, and so to say the paint is wet, and the paint is dry, is really to say nothing at all.

So if you say that you believe it, you’re fibbing. You’re making no more sense than if you say that two minus two doesn’t equal zero. No doubt you believe something, but you don’t actually believe what you’re saying because it doesn’t make sense to be believed. It can’t be believed. In the same way, we can’t say that the Trinity is actually self-contradictory, because we’d really just be admitting that this crucially important doctrine doesn’t mean anything. We’d be saying, in effect, that a core teaching of Christianity is not a teaching at all. That, in order to be saved, you have to be stupid or naïve enough to think you believe something when you don’t. We’d be admitting that salvation is based on a nonsense-statement. If that’s the case, we’re all in a lot of trouble one way or another.

2. The square circle

Now a square circle is obviously a contradiction in terms—at least at first glance. In this way, it is a very apt analogy for talking about the Trinity. It’s very helpful. It’s an analogy we can understand and use. So much so that I’m going to go ahead and argue that the doctrine that God is both one being and three beings is exactly like the doctrine that some geometric object has both one side and four sides—yet without entailing a genuine contradiction. (We could equally talk about one side and three sides, as James Anderson does in Paradox in Christian Theology. [ James Anderson, Paradox in Christian Theology (Paternoster, 2007).] )

Person, being, and essence

If you’re up with your Trinitarian theology you will have noticed that I have formulated my statement about God rather strangely—perhaps even wrongly: that he is both one being and three beings. This is not a typical formulation. Normally theologians use different terms: they distinguish between God as one in essence and three in person. Thus they draw a distinction between the way or the sense in which God is one, and the way in which he is three. This is of great importance, because it establishes that he isn’t both one and three at the same time and in the same sense. If he were, this would violate the law of noncontradiction; the Trinity would then be genuinely irrational and unbelievable. Thus they generally talk about God as one essence and three persons. The essence is God; the persons are the Father, the Son, and the Holy Spirit.

For example, Wayne Grudem in his Systematic Theology formulates the doctrine of the Trinity as follows:

  1. God is three persons.
  2. Each person is fully God.
  3. There is one God. [ Wayne Grudem, Systematic Theology (InterVarsity Press, 2003), 231.]

Yet, for my argument, I’ve said that God is both one being and three beings. Why haven’t I described this in terms of essence and persons? Well, it’s not because I think the idea behind the orthodox formulation is faulty or inadequate. I do affirm that the way in which God is one being is different from the way in which he is three beings. But I want to be sure that the paradox inherent in the Trinity is not obscured behind this terminology of “essence” and “persons.” I want to lay bare the ontology of the Trinity so there is no doubt about how confounding and difficult it really is.

When we talk about God, or when the Bible talks of God, it is referring to a single divine being. More than that, it is referring to a single, personal divine being. When Moses speaks to Yahweh in Exodus, he is not speaking to an impersonal essence, and neither is he speaking to three divine persons. He is speaking to one divine person. So when we talk about God, meaning the Godhead, we are talking about a personal being—yet one who is also somehow three personal beings.

The term “essence” tends to obscure this. It’s good for avoiding the law of noncontradiction, but it’s not so useful when we come to talk about God as God. This is because we don’t have a personal relationship with an essence called God; we have a personal relationship with a person called God. So it turns out that this term “essence” is helpful for clarifying that the way in which God as one being is different from the way in which he is three—but it’s simultaneously quite unhelpful in terms of actually describing what it means for God to be one being and three beings simultaneously but in different ways.

In other words, when I say that God is one being and three beings, I mean the following:

  1. God is one being in one way (call this sense A);
  2. God is three beings in another way (call this sense B);
  3. But we don’t know what it means to draw a distinction between ways of being.

Understanding senses of being

The strength of (iii) shouldn’t be underestimated. Try to imagine someone you know being himself, yet also three beings. The only way we can really conceive of this is to think of multiple personality disorder. Yet this is decidedly contrary to how we know God to be. There isn’t any way that someone with multiple personality disorder can be three beings, mentally speaking, and for those three beings to also share fully in one mental being. We can imagine three mental personalities sharing in one physical being (and in this sense we can perhaps very dimly understand the Trinity by analogy). But we can’t imagine three mental personalities sharing fully in one mental personality. Even if all these personalities were harmonious, they would still only be parts of the whole being. But the Father is not a part of God; he is fully God. Like the Son and the Spirit, he shares fully in all of God’s attributes. Each person of the Trinity is the same being as God.

So it must be admitted that there seems to be a paradox in the doctrine of the Trinity. We just don’t understand what it means to be one being in one way, and three beings in another way. We have no conception of such a thing because we have no experience of it.

However, although we don’t get it, we can see that there is nothing necessarily contradictory about it. Rather, when we put it into noncontradictory language, it just remains baffling to us. But why should it not? All things considered, we can’t really be surprised that God is someone whose nature we do not, and perhaps cannot, fully understand. It comes as no shock to the Christian that God is baffling. There’s an entire doctrine in systematic theology known as the incomprehensibility of God! Being God is certainly a condition none of us will ever experience. And since we understand things primarily in terms of our experience, our understanding of God is necessarily limited. We can understand the concept of God’s mind in terms of our own minds; but where there are differences we are confounded. We can understand God’s love in terms of our own love; but where there are differences we are bemused. And there are things we cannot understand about God because we lack any conceptual basis for them—his timelessness, for example. We grasp it in only the most abstract way.

This does not mean that these things are not explicable in principle—merely that they are not explicable to us. Just as a colorblind person may find the distinction between red and green inexplicable, but can accept it on faith from a normally-sighted person, so we can find different senses of being inexplicable, but accept the possibility on faith from God.

Reconciling the square and the circle

This returns me to the analogy of the circle and the square. Let me draw on James Anderson’s work and extend it a little bit. Here’s an example of how it may be reasonable to believe that the doctrine of the Trinity is resolvable—even if we can’t understand it:

Imagine a two-dimensional world called Flatland, inhabited by two-dimensional people. To these people, three-dimensional objects like spheres or cones or cylinders are simply inexplicable. Since the Flatlanders only have experience of two dimensions, they cannot conceive of three-dimensional shapes. These are beyond their understanding, because the entire conceptual framework of their minds is limited to the horizontal plane.

Now, you are able to communicate with the Flatlanders, and you wish to talk to them about cylinders. How do you do this?

Well, if you’re trying to reveal to them what a cylinder looks like from the side, you might say that it’s a square. If, on the other hand, you’re concerned with revealing something as regards how it looks from above, you might say that it’s a circle. Both of these propositions are true. You, as a three-dimensional being, find it trivial to reconcile them, because you can see that the cylinder is shaped like a square in one way (let’s call it sense A), and shaped like a circle in another way (let’s call it sense B). You can see that neither the square nor the circle are “parts” of the cylinder in the way we usually use the word; and both share fully in its nature. Yet they are distinct.

The Flatlanders are not so fortunate. They don’t know what it means to see something from above or from the side. These terms have no meaning to them; words like vertical don’t correlate to reality as they know it. They can’t conceive of objects with height because they can’t conceive of height itself. They can only conceive of shapes with two dimensions—and in two dimensions a circle cannot be a square. They don’t know, nor can they understand, what it means for something to be shaped in different senses or different ways. They have a conception of the horizontal sense, but not of the vertical sense. So an object which is both a circle and a square appears, at least as far as they can understand these things, to be a contradiction in terms.

Nonetheless, they have reason to believe you when you tell them about cylinders—and so they formulate the following way of talking about them:

  1. A cylinder is one-sided in one way (call this sense A).
  2. A cylinder is four-sided in another way (call this sense B).
  3. But we don’t know what it means to draw a distinction between ways of being sided.

Now the Flatlanders are quite correct to formulate their understanding in this manner. They know that what you have told them is explicable to you; that it is real and true and believable. That is, there’s nothing intrinsically irrational or incoherent about a square circle when it’s configured as a cylinder, and it does not violate the laws of logic—even if they can’t understand how. Therefore, having reason to trust you, they hold that a cylinder is shaped in sense A as a square, and in sense B as a circle—even though they don’t have any idea what it means for there to be different senses of shapedness.

Similarly, we have reason to trust God and so we hold that, as a being in sense A, he is one; as a being in sense B, he is three. We don’t know what it means for there to be different senses of being. But we know there are different senses, because he said so. God is one being, one person, in one sense—and three beings, three persons, in another.

Because we don’t know how to draw a distinction between different senses of being, there tends to be an implicit equivocation in our descriptions of God. This results in the appearance of contradiction, which emerges because our descriptions are limited in accuracy. When it comes to the nature of God, we suffer the same sort of conceptual shortcomings that the Flatlanders do when it comes to the nature of space. Our language describes things with a level of accuracy corresponding only to our own perception; not necessarily to the actual state of things. So a certain distinction in God’s nature goes unstated—unable to be stated. God’s nature is more subtle, more fine than our experience and our language.

Because of our innate lack of precision here, we seem to be contradicting ourselves when we aren’t. There is what James Anderson calls an unarticulated equivocation in our description of God. Trying to describe his being in human terms is perhaps a little like trying to measure the width of a hair with a tape measure, or the hue of a rose with a six-sided color wheel. The tool is too coarse for the job. Thus, the paradox we perceive is a merely apparent contradiction, resulting from an unarticulated equivocation (what Anderson whimsically dubs a MACRUE).

Once we articulate the equivocation—that is, once we explicitly distinguish between senses of being—we see that no real contradiction exists. We just find the solution inexplicable.

Can we believe what we can’t understand?

I argued at the beginning that we cannot believe what we cannot understand. Am I now contradicting myself, since we cannot understand the Trinity; or am I merely apparently contradicting myself, due to an unarticulated equivocation? The latter; so let me articulate.

Logical contradictions are inexplicable in the sense that they are meaningless. Since a contradiction cancels itself out, it means nothing. And we can’t understand something which has no meaning.

The Trinity is inexplicable in a different sense. God’s being is not logically meaningless. Indeed, it is logically meaningful. We can explicate it, as I have above, and we can understand it in logical terms. It doesn’t contain any contradictions. However, this doesn’t imply that the meaning is explicable to us. Something can have objective meaning but remain subjectively inexplicable. Objectively, a contradiction has no meaning; and so subjectively it naturally does not either. But objectively, the Trinity does have meaning. This fact alone doesn’t imply that we must be able to grasp it, but in principle it can be grasped. To a sufficiently enabled mind, the meaning is available. But to us? No, not necessarily. Just as the distinction between red and green can be believed in principle, yet not understood by a color-blind man; and just as the distinction between horizontal and vertical can be believed in principle, yet not understood by the Flatlanders; so the distinction between being and being can be believed in principle, yet not understood by us.

3. How the ambiguity of being affects the law of identity

I have mentioned that God does not have parts: the Father is not a part of God; the Son is not a part of God; the Spirit is not a part of God. They are all fully God. They all share fully in his attributes. That is, each person of the Trinity is the same being as God, but there is an unspoken equivocation in our understanding of being. God is one being in one sense; three in another—but we don’t understand what it means to draw a distinction between ways of being.

It therefore follows by good and necessary consequence that “being” is not a univocal term; it does not (necessarily) have only a single, unambiguous referent. When applied to God, at least, it seems to refer to more than one thing, even though we don’t understand exactly what. When we subject the doctrine of the Trinity to logical analysis, we find that it forces us to formulate a doctrine of being which gives a consistent account of it: the principle of Non-Univocal Being. Following in Anderson’s slightly droll footsteps, I shall dub this NUB.

NUB appears central to Christian metaphysics, and affects it in a larger and fairly significant way, because it has ramifications for the law of identity.

The law of identity is one of the three major logical axioms. Simply put, it is the notion that an entity is the same as itself: A is A. By corollary, an entity is not the same as some other entity: A is not B. If an entity was the same as some other entity, then it would be one and the same with that entity: A is B. The reason this is important is because, if we make this identity statement fully explicit, we find that it is saying that:

A is the same as B with respect to its being

This is an unproblematically clear statement on the face of it. For a non-Christian it’s probably always unproblematically clear. However, for a Christian committed to the thesis of non-univocal being, it is not necessarily clear, despite appearances. For example, if “A” is the Father and “B” is the Son, this statement is both true and false, because it contains an unarticulated equivocation. It is true in one sense for the term “being,” and false in another.

This has obvious ramifications for a certain category of arguments about the nature of God which leverage a key feature of identity: transitivity. Transitivity says that if A is the same as B, and B is the same as C, then (by transitive relationship) A is the same as C.

This is important because we can draw the following kinds of inferences:

  1. The Father is the same as God.
  2. The Son is the same as God.
  3. Therefore, the Father is the same as the Son.

This is a heresy called Sabellianism or modalism. However, because it relies on a univocal understanding of being, a Christian has no reason to accept it. If Christianity entails a theory of non-univocal being (NUB), we can see clearly that the argument only appears to go through because it equivocates.

Now, let me be clear. I am not suggesting that a non-Christian must accept, on his own terms, that this argument equivocates. He is by no means committed to a thesis like NUB. He has no reason to be, because he does not presuppose that the Bible’s testimony regarding the nature of God is in any way authentic. What I am saying here is that a Christian may reject the conclusion of this argument because, on his own grounds, the testimony of Scripture gives him good reason to believe that the argument commits some kind of non-obvious error. Because the charge of self-contradiction is an internal critique of the Trinity, the Christian may bring all of his own religion’s resources to bear in refuting that charge. NUB is at least one way in which the apparent self-contradiction of the Trinity can be resolved, so a Christian has every right to argue that the conclusion of the above argument is false. In fact, he need not even be committed to NUB in order to use it as a means of showing that in principle these sorts of arguments fail to conclusively prove self-contradiction in the Trinity. Even if NUB is not true, it constitutes a defeater to the argument; just as the greater-good defense, even if false, constitutes a defeater to the problem of evil.

In other words, as an internal critique of Christian theology, the above sorts of arguments fail. NUB is sufficient to show that, on Christian grounds, the charge of internal incoherency or contradiction is invalid. The Trinity is indeed like a square circle— but that doesn’t mean it is a contradiction.



Having read your article, I found it quite enjoyable and intellectually honest.

I come from a OnenessPentecostal background, and currently have Oneness leanings still. Having studied trinitarianism, and oneness theology your argument is both satisfactory, but in many ways true to oneness theology also.

Onenss theology holds to Father, Son, and Spirit existing simultaneously.

Oneness theology typically denies the distinct “personhood” of Father, Son and Holy Spirit, at least from the understanding of what it means to be a “Person” today.

After spending time reading the Early Church Fathers… they too never defined “Personhood” in today’s terms either… it is a more recent construct of post reformation trinitarianism… (The Book, “The Quest for the Trinity” by Stephen Holmes argues that modern Trinitarian views are not historically othrodox, but doesn’t argue wether or not they are correct)

This leaves a lot of confusion on the Trinity when it comes to terms and meaning. (Trinitarians like Oneness also are usually more united over LANGUANGE, than they are over MEANING).

The strength of the Oneness argument was to see GOD as a personal Being often equated.

Early Church Father saw God as a Personal Being… because personhood of the members didn’t equate to a separate conscious apart from the other members of the Trinity or God

Modern-day Trinitarians often sees GOD in 2 ways:
1. An exclusive reference to God the Father based on context
II. as a community/corporation/unit…. and the members of trinity being the personal beings that make up this unit. (Though never 1/3 of God.)

All that to say, I believe you captured the nuance of the scriptures that both speak of God in terms of 3, but also in terms of 1… (It’s how I teach people on the nature of God) , especially your third statement, that the line between “Being” is one we do not know where it ends or begins.


Great article! Some years ago, I read the novel /Flatland/ and it allowed me to understand why I can’t comprehend the non-contradictory nature of the Trinity, but can accept its coherence by analogy. Your essay has helped to formalize these ideas for me. Thanks!