Hammered this Trinity definition out with Copilot. Theologically sound?
One triadic category of Being (Yellow, Father),
non-empty because their identity pole is the Father,
their predicate/quality pole is the Son/Logos (Red),
and their instantiation/action pole is the Spirit (Blue)
is the Trinity (God) subsisting as three irreducible persons.
The Trinity was a crucial topic of debates in the first Councils, from the one in Nicea till the one in Constantinople. Every phrase in the final Nicene Creed was a long discussed matter. The simplest example is the large debate between the words ομοούσιος (did not exist before) and ομοιούσιος (existant word at the time), which both mean same substance (Son and Father). The Church Fathers finally decided to keep the first.
So, with regard to Trinity, modern philosophical interpretations try to resolve modern time uncertainties on what the first Christians implied by this term.
Well, what do you mean by that? Copilot itself—by which I mean its “Think deeper” model, of course—tells me:
“A theologically sound claim or teaching is one that is accurate, coherent, and spiritually healthy according to the standards of the religious tradition in question”.
So, which religious tradition are you referring to? To some trinitarian tradition, evidently, but which trinitarian tradition exactly?
And: what does it mean for philosophy if a definition is accurate, coherent, and spiritually healthy according to the standards of some religious tradition or other?
…what does Copilot tell you?
I sense bias. waggles eyebrows
Its “short takeaway”—at the end of its long answer—says:
“Maryann’s language most closely tracks classical Nicene Trinitarianism. If philosophy accepts theological standards from that tradition, it becomes a different kind of inquiry”.
Exactly. It means nothing for philosophy, for if philosophy accepts theological standards from a religious tradition, it becomes a different kind of inquiry altogether…
Since when did Philosophy become a person?
…only if the Trinity exists.
You and your “persons”… 
“Good to see you, Copilot. Can you check this? The category/ground of all being is triadic, rather than three different beings, so the category is non-empty (the Father), and its predicate/quality is the Son/Logos, and their instantiation/action is the Spirit—three persons sharing being. Did I say it well?”
I’m reminded:
“‘These voices,’ I said appreciatively, ‘these voices—they’re a kind of bridge back to the human world’. […] What those Buddhist monks did for the dying […], might not the modem psychiatrist do for the insane? Let there be a voice to assure them […] that in spite of all the terror, all the bewilderment and confusion, the ultimate Reality remains unshakably itself and is of the same substance as the inner light of even the most cruelly tormented mind. By means of such devices as recorders, clock-controlled switches, public address systems and pillow speakers it should be very easy to keep the inmates of even an understaffed institution constantly reminded of this”. (Aldous Huxley, The Doors of Perception.)
It truly is a brave new world… AI as a God Who shall, if not answer, then at least reply to prayers! 
So you admit that you are a lifeless binary processing biological machine then….no different to AI.
The problem is if you key crp into AI you get crp out and how are you going to give life to this machine which merely exists because it needs to exist to claim that it doesn’t exist?
How are you going to give life to this representation of reality (non illusion) which claims that it’s a misrepresentation of reality (an illusion)?
Ah, another obsessive religious fanatic joins the discussion…
A biological machine, yes. Binary processing, only on the scale of classical mechanics. (Quantum computers should be able to do true random, while classical computers can only simulate it.) And lifeless… Well, if I’m lifeless, what does “life” even mean? Then it’s a mere term—and not even a concept—, like “free will” etc.
I’m no religious fanatic my friend…you do a lot of guessing in your religious cult.
If you’re no religious fanatic, then what does “religious fanaticism” even mean?
You exist because you need to exist to claim that you don’t exist.
You claim that you possess life…In what way do you possess life in your binary processing existence?
You claim that good is bad and bad is good hence your half logic philosophy +=- and -=+
How do you know that good is bad and bad is good?
Can you prove it?…..No you can’t.
So what we know about you is that you exist and you claim a lot that you can’t prove.
You claim that you are a psychotic who exists because you need to exist to claim that you don’t exist.You claim that you are a misrepresentation of reality (an illusion) rather than a representation of reality (a non illusion) due to your starting philosophical guess that good is bad and bad is good (which you can’t prove) and you apply your religious fanatic half logic starting philosophical guess +=- and -=+ to everything.This is what we know about you.
And?…you come across as a religious fanatic fool…..so what?
There’s no such thing as the sort of free will that “true random” implies, because there is no true random. Good thing genuine free will doesn’t require true random, or we wouldn’t even be able to have this conversation.
He’s gone…smoke must be coming out of his ears.
“I’m no religious fanatic”, he says—then goes on droning about the same stuff he’s been droning about in every thread he’s replied to or has created (and there are many)…
Who are you even talking to? No one in particular? Anyone who does not believe exactly as you believe?
A representation of reality can be an illusion without being a misrepresentation of reality, by the way: if reality itself is an illusion. And where did I claim to possess life?
I don’t think good is bad and bad is good; I think both are really neutral, because they’re neutralized by one another. So I’m not switching good and bad, if that’s what you mean.
And as for existence, it depends on what you mean. Do I think I’m a fleeting existence that think they’re no eternal existence? Yes.
You claim,in your existence, that everything is a misrepresentation of reality,even your claims!!!
No,you are wrong… you claim to be no religious fanatic and then you drone on and on about how your religious fanatical claims are a misrepresentation of reality.
I suppose though that, if you are talking to me in particular, you might be thinking of something I wrote that goes like this: good is good compared to bad, and bad is bad compared to good; but this means bad is actually what makes the good good, and is thereby itself good; and, likewise, good is what makes the bad bad and is thereby itself bad… But if good and bad are each both good and bad, then either is neither!
I suppose you could if you are a religious fanatic …yes.
Why do you claim in your existence (because you need to exist to claim that you don’t exist) that your claims are a misrepresentation of reality?
It’s hardly a selling point for your religion is it?
It depends what you mean by “represent”. I said a representation of reality could be an illusion without being a misrepresentation of reality. Now I suppose you might say I said I was an illusion. I said I was a fleeting existence, and a fleeting existence is an illusion compared to an eternal existence. Truth is a value; truth is only truth compared to falsehood, and falsehood is only falsehood compared to truth.
Could do what? It’s not clear (to me) what you’re referring to exactly.