This is how I understand Augustine back when I read his stuff alot more…This should be somewhat correct…hopefully
Each person of the Trinity is distinct from the other, but each Person cannot exist independent of the other, nor independent of the same identical substance
each of which it is. The Father gets His substance from being God which He is, not from His being Father. The Son likewise gets His substance from being God which He is, not from His being Son. (This is the looming contradiction, but I will ignore it and speak of non-accidental, non-essential properites.)
Here’s is why the relation between each Person is said to be both
non-essential and
non-accidental to the Godhead. Each Person gets its own unique property in virtue of
which relation it shares to some other Person in the Trinity; that is, each unique property (father-hood, son-hood, holy-spirit-hood) springs from the very relation it has to the other Person. So it is in virtue of this *very relation *to the other Person each Person is what it is. This is why we say that the Son exists in virtue of his very relation of *origin *and
procession from the Father. And the Father exists in virtue of His relationship He has to His Son.
However, each relation between each person, is a different relation. This is why they are said to b *non-essential *properties of the
one substance,
God, because the relationship the Father and Son share, cannot be predicated as belonging to the relationship, say, the Son and the Holy Spirit share.
Moreover, each relation is said to be *non-accidental *since if you were to remove the relation, say, the Father had towards His Son, He would simply no longer
be the Father, and likewise the Son would no longer
be the Son.
In sum: Yes, those relations of God that are said to be accidental are the
extrinsic relations God has to other entities like the universe or human beings, such that if you annihilated one of the members of the relation, the other member remaining would have its essence unaffected. The relations found within God between the Persons, however, are more like
intrinisic relations since each person is God Himself…In an analogous way, when I say “my legs are longer than my arms,” I am speaking of a relation “longer than” that two parts of me share to one another. But since neither my leg nor my arm is a substance or a “thing” in its own right independent of me since when I severe either the one or the other from my body, the one is no longer a leg and the other is no longer an arm, but just dead matter, so essentialy, I can only be saying that I am
relating myself to myself, rather than relating myself to something else or relating two independently distinct objects. Similar for God, each Person shares a
unique relation to each other Person each of which God
is. So with respect to the Trinity God has both non-essential, non-accidental properties or relations.
This is how I understand Augustine anyway…