a koinonia of persons
When Migliore uses this expression, he means that God is a fellowship of love shared among three persons. He does not mean that God is just like us, and enjoys a friendship with others.
mutual indwelling or "being in one another"
This is not a communicable attribute. Mercy, love, and justice are communicable attributes.
Gregory the Great
He is not one of the Cappadocian Fathers. Gregory of Nazianzus, Gregory of Nyssa, and Basil of Ceasarea are Cappadocian Fathers.
Deus non est Genere
Thomas Aquinas (and Karl Barth) use this phrase to express that God is utterly unique. God is not a particular instance within a class.
Theologians often employ a strategy of identifying divine attributes by choosing facets of existence that we find to be good and then "extending them out" to the nth degree.
In his article on the Cappadocians, Allison reminds us that it is a mistake to imagine that this word (when translated into English) in the ancient world (especially when used to speak of God) meant personality rather, it meant a capacity for relationship.
Proper trinitarian theology questions the modern understanding of person that grounds personal identity in this.
social nature of the triune God
Migliore warns that our understanding of this should not be a projection of our own ideals of community; to which he adds, we must not forget that God is God and we are creatures.
Karl Barth's retrieval of classical attributes (in dialectical pairs)
According to Migliore, this enables Barth to say that God is "free to be compassionate toward us, free to become vulnerable for our sake, without ceasing to be God."
He believes that the Trinity lays a foundation for a society of brothers and sisters, of equals, in which dialogue and consensus are basic constituents of living together in the world and the church.
Two of the great Cappadocian Fathers, Basil of Ceasarea and Gregory of Nyssa, were taught theology by her.
One of the key implications of speaking of this as the constitutive attribute of God, is the recognition that "God is the one who freely loves, and loves in freedom."