Well, I was attempting to adopt Trinitarian vernacular learned from early posts to describe the LDS view. Perhaps I fell short. Help me out here. Given the LDS belief that the Father and the Son have separate spirits, and separate bodies, would the phrase “separate and distinct” work here. And since the Trinity can be described as “three persons, one being”, couldn’t a non-Trinitarian view of the Godhead be “three persons, three beings”?
Ah, okay.
I personally prefer to let each religion define their doctrines based on their own understandings of terms, along with defining what those words mean within that context, because a lot of confusion happens when we try to apply one understanding/framework to another.
However, from a Trinitarian perspective, yes, the LDS Godhead would be separate persons and separate beings, but that does not add to your original argument that that separation of persons and beings somehow makes John 17:22 more intelligible than a Trinitarian view on that verse, especially since your presentation of the implications of the Trinity doctrine on John 17:22 wouldn’t necessarily be how actual Trinitarians interpret that verse.
From the Trinitarian perspective, the LDS position entails not only separate persons but also three separate beings for various reasons. The pertinent part is on the “being”. “Being” is referring to what “is”. This is sometimes referred to as “nature”. For the Trinitarian, it is the nature of “God” to eternally exist as three distinct Persons, Father, Son, and Holy Ghost. These Persons are not each other, and they have eternally existed in this relationship with each other. They are all God, and have the same Divine attributes, and always have. There never was a time (including “before” time) when the Trinity did not exist as such. Because their very existence is intimately and eternally tied together (since it is the nature of their existence to exist as a Trinity), and you cannot have one Person without the other, they are termed “one being”.
In contrast, the LDS view on the Godhead is very different, and points to three separate beings,
from the Trinitarian perspective, for various reasons. Firstly, it is believed that the Son and the Holy Ghost, like all of us, are spiritual children of the Father (and Heavenly Mother). So, there was a time when they just existed as “intelligence”, prior to being spiritually begotten. The Father Himself progressed to Godhood at some point in eternities past (as various LDS prophets have taught, including Joseph Smith). The Father, Son, and Holy Ghost came into a covenant relationship at some point, after the Son and Holy Ghost were spiritually begotten. Therefore, from the Trinitarian perspective, the LDS view is three separate beings because the three Persons do not have it as their one nature/being to eternally exist in relationship with each other
as a Unity (since we clearly see the differences in origin of the Persons), in addition to the notion of progression to Godhood.
Another difference was also mentioned before: for Trinitarians, there is a difference of “nature” or “species”, if you will, between man and God. There is a chasm between man and God, a chasm that was bridged by Christ, but it is there nonetheless. Although we may become children by adoption, we are not of the same nature as God. In contrast, LDS theology teaches that we are all of the same nature or species as God (God the Father Himself being embodied and being a man). The difference is in degree of progression.