God is not “triple, or three by multiplication,” Augustine says (The Trinity). Nor does He get bigger by addition: “the Father alone or the Son alone or the Holy Spirit alone is as great as Father and Son and Holy Spirit together,” in contrast to bodies that “grow by being joined together” (6.2.9).
Augustine is aware of the oddity of this kind of talk: “it is not easy to see how you can talk of the Father alone or the Son alone, since the Father is always and inseparably with the Son and the Son with the Father; not that both are Father or both Son, but that they are always in each other and neither is alone.” We can talk about persons alone in the same way “we say the trinity is God alone, though he is always with the holy spirits and souls; but we say that he is God alone because these others are not God with him.” Similarly, we can speak of the Father alone, even though He always has His Son, because the Father is not the Son.
But this doesn’t get to the heart of the oddity of Augustine’s musings on the Persons alone.
Let’s try to imagine the “Father alone,” as if He were the only God. The first thing we should realize is that the “Father alone” is no longer Father, since He no longer has a Son. He’s just God, or the Unbegotten, because, like the Unbegotten of Arianism, He is inherently un-related. How can we even speak of this “Father” stripped of what identifies Him, that is, His Fatherhood?
And if the “Father” without the Son is no longer Father, then He is something less than He is with His Son. He is all that the Father is, minus the Father bit. He may not be “bigger” with the Son than He is without, but with the Son He is something that He wouldn’t otherwise be, namely, Father.
Augustine’s point is that this “Father alone” would still be the same divine substance with all the same divine attributes that He actually possesses. Each person is “perfect” even without the others. But that doesn’t make any sense, because the Persons are persons only by virtue of relations.
Augustine is no Arian, of course. But it says something about the inner logic of his trinitarian theology that he’s capable of assigning the name “Father” to what must in fact be an un-Father. He doesn’t seem fully to grasp the import of his own contribution – that there are things said of God “relationship-wise” (Hill’s translation) as well as “substance-wise.” And it seems to imply a certain looseness between the Father’s divinity and His Fatherhood, as if the Fatherhood were nearly something that can be stripped away and leave the Father still “perfect” in Himself.