In this model, all relations are rooted in the Father, and the Father provides the ground for the entire context of relations. However, in the model of mutuality and interchangeability, it can be very quickly seen that there is no ontological ground for the relations of the three persons. If the Father is mutually dependent on the Son and the Spirit, we are left with no framework for these relationships to exist in. This lack of framework becomes more clear when we ask questions of the state of the existence of the Father, Son, and Spirit. In what mode does the Father exist? In the traditional Model, the Father is self existent and the only ingenerate one (as per Alexander of Alexandria and Athanasius the Great), the Son is begotten from the Father and thus exists within the context and framework of the Father. The ground of the Son’s being is the Father, and thus there can be relations between the Father and the Son. The Spirit, either proceeds only from the Father, and thus has the shared framework of the Father with the Son, but must have all relations with the Son through the Father; or the Spirit processes from both the Father and the Son and thus has mutual accessibility to both by means of being grounded in both ontological sources.
However, if there is strict mutuality in the trinity, the Son’s ontological framework is distinct from the Father’s and Spirit’s. Each person exists as a discrete ontological identity that does not have a rooting in the others, and the mutuality has no framework in which to operate. The world then is such that it must exist in one of these three frameworks, for they can have nothing at all to do with each other, as they have no mutual grounding in a single ontological root. Thus, while at first glance it may seem like we end up with Tri-theism, we in fact end up with strict mono-theism as only one person of the trinity could in fact be the God of this world, and the other two persons could know nothing of it, having no ontological framework from which to share in the world.
An objection might be that the mutuality of the trinity is not one of three discrete persons ontologically distinct, but that they share a mutuality in the divine essence. This essence then creates the shared ontological framework of the trinity that allows for the mutual relations that are being proposed. If by the divine essence, what is meant is an essence proper to one of the persons of the trinity and shared with the other two, then we are back to the traditional understanding and a workable ontology. However, this also introduces the begetting and spirating of the traditional model.
If instead we say that the divine essence does not properly belong to any one of the persons of the trinity but is equally their own, then we come to a problem. Is the divine essence prior to the divine persons? If it is, then it can be something in which they each participate, but then it is not identifiable with the persons themselves, as it is prior to them. It then becomes the source from which they all proceed. The essence, prior to the persons or the relations of persons, is either impersonal or personal. If it is prior to all persons, then it is impersonal, and thus contrary to its manifestation in the Persons of the Trinity. This also brings in the category of person or hypostasis which also must then be a category in which all three members of the Trinity participate, and which must be prior to them. If the divine essence is personal, then there is in fact a divine person in which all members of the trinity participate, and we return once more to the traditional model. As well, taking this particular perspective would be to in fact do what Vladimir Lossky so rightly criticized of western Theological tradition in the Mystcial Theology of the Eastern Church, the priority of essence above persons and their relationship.
If on the other hand, we say that each of the persons properly has what we call divinity, yet do not share a prior essence, then we run up against nonsense. For if there is no prior essence, we may simply describe their shared characteristics as “divine” but that is an epistemological model and not a description of a reality shared by the three persons. We are simply saying, the Logos is Unique, the Spirit is Unique, the Father is Unique, but they each share the exact same attributes, we are immediately contradicting ourselves. As well, even displaying these identical predicates does not form a ground of ontological interaction. Three very alike things cannot interact if they do not have a common ground. Three actors may play Hamlet, but unless they are on the same stage, they do not finish each other’s lines. There is no context for the first to being “What a piece of work is man,” and for the next to say “How noble in reason!” and for the last to continue “How infinite in faculties!”
Thus we come once more to the situation raised above, that of discrete persons without a ground of mutual ontology. In simple terms, there’s no “something” for the persons to interact through. This reveals the wisdom of the ancient teachings of the Church, that the Father, who is His own essence, shares Himself with the Son and they share themselves with the Spirit (to follow the western model). The ground of all “Personness” or Hypostasis and being, even divine being, is the Father, and thus all of reality holds together in one great mutuality of being shared from the tap root, the Father.
This of course does not inherently mean that there must be subordination in the Trinity, for the Father shares the whole Self with the Son, and that Self is clearly a giver of Self. This sharing of divinity, a.k.a. the Father’s own self, brings about mutuality of love, even if it does not bring about mutuality of ontological origin. The Father gives the Father’s self away to the Son and the Spirit and holds nothing back for Himself.
Concerns for subordination in the church, and continued patriarchal structures should be therefore centered on the mutual giving of the Triune life, not with the restructuring of the Trinity. For, as we have seen, the loss of a mutual ontological framework for the Father, Son, and Spirit, divides the Trinity instead of uniting it.