Is the Trinity Logical?
Is the doctrine of the Trinity necessarily logically contradictory? To answer the question requires having both a statement and interpretation of the doctrine. So let us start.
According to the classical formula, the Trinity is one in ousia (substantia) and three in hypostases (persona). I purposely leave these terms in what are to me foreign languages so as not to assume to much about their meanings, as I take these meanings to be intentionally vague in the classical doctrine. It was, after all, a doctrine created by a committee with the goal of satisfying what were doubtless varying different interpretations.
At this point, there is no logical problem. The Trinity is three in one sense, and one in another sense. There are many things that are both plural and unitary in some way. A committee is both a singular entity and composed of multiple members. An egg may be yolk, white, and shell, and yet still one egg.
Yet, this does not seem to say quite enough. The doctrine of the trinity attempts to avoid the claim that there could be three separate gods. What does this add to the problem? Well, it depends how we construe “god.” What is essential to being a god, and what separation would make one god separate from another? Unfortunately, there is very little agreement on this. The Christian can retort that whatever it is that is essential to being a god is what is captured by the term “ousia,” while what is not is captured by the term “hypostases.” Then, they could sort qualities between the two as needed to arrive at their desired conclusion. There is, at least no necessary logical problem in doing so.
I tend to hold a rather minimal doctrine of the Trinity. So, this kind of solution seems fine to me. But some wish to go further. Some, with the Athanasian creed like to add some further apparently relevant grammar, saying that one must be able to claim that (1) The Father is God, (2) The Son is God, (3) The Holy Spirit is God. Is it possible to square this with the claim that God is the Trinity?
Well, if taken as referring to “God” in exactly the same sense in each clause, the answer seems clearly to be “No.” The Father is not the Trinity. The Son is not the Trinity. The Holy Spirit is not the Trinity. God is not dependent on anything outside of God. But the persons of the Trinity are dependent on one another.
At this point, the Christian might take one of two routes. First, they might throw their hands up and claim that the trinity is what I will call a “logical mystery.”* That is to say that the trinity is logically incoherent and yet true. This appears to be a position taken by some, for instance, Lutherans who are not terribly impressed by logic in any case.
There are, however, very good reasons not to take this route. For one, if we throw out logic, it hardly seems that claims about God can be meaningful. If God can be logically incoherent God might be both good and evil. So, claiming that God is good would be emptied of all cognitive content. This seems to me far too high a cost for discourse about God.
Another route would be to claim that the way “God” is used to describe the Father, the Son, and the Holy Spirit is not the same as the way that it is used to describe the Trinity. This would not be without precedent. If I have three glasses of water, I might say that what is in glass 1 is water, what is in glass 2 is water, what is in glass three is water. Yet I would not at any point be claiming that any one of these has exhausted the category “water” in a way that excludes the others. This analogy has the benefit of working with colloquial meanings of the English equivalent of “substantia” the three glasses are filled with the same substance. But they are yet differentiated by other qualities.
But let us add another qualification. What if we add that the Trinity must be in some sense one “self” as some wish to stipulate. Is it yet possible to have three hypostases (Father, Son and Holy Spirit) and yet one self? Again, we would need a robust account of selfhood to sort the question out in the abstract. But the philosopher Brian Leftow has provided us with an analogy that suggests that there is at least one sense on which the situation does not lead to any necessary logical conflict.
Imagine that Marty McFly has a time machine and wants to start a band. He has no friends. So Marty decides to constitute the band himself. He picks up a guitar and plays. Then hops in the time machine and comes back to play the drums along with himself. Finally, he comes back to sing vocals. There is a sense in which, watching the stage, we would say that there is Marty 1, Marty 2, and Marty 3. Yet, there is another sense in which we would say that there is only one “self” Marty. Assuming we can avoid bootstrap paradoxes and the like, there is no logical incoherence in the scenario.
Of course, no one is claiming that God is a time traveling McFly. We need not posit that this is how God is constituted. The point was only to point out that there is no necessary logical contradiction in the set of claims put forward. If there is at least one scenario where the claims can cohere, it must be possible for the claims to cohere. Beyond that, we are free to claim that the trinity is an epistemic mystery* without facing any necessary logical problem.
In short, my own position is that there is no Logical Problem of the Trinity writ large. The doctrine is just to vague for that kind of thing. There certainly are logical problems for particular models of the Trinity advocated by particular theologians. But those are separate from the broader doctrine all by itself.
* Being logically mysterious is different from being epistemically mysterious. A logical mystery is logically incoherent yet true. An epistemic mystery is something that is unknown. The nature of the trinity may be epistemically mysterious without being logically mysterious. I.e. It may just be that we acknowledge that don’t know how the trinity is constituted in a logically consistent way without accepting that it is necessarily not constituted in a logically consistent way.