If the personal relations were accidents in God they would be really distinct from his divinity. If they were only conceptual relations then the persons would not be really distinct from each other. And if they were substantial relations the persons would be three really distinct beings, three gods. Thus, the divine personal relations must be subsistentrelations. Such a notion is entirely without counterpart in Aristotelian philosophy. Thomas writes: ‘Now distinction in God is only by relation of origin … while relation in God is not as an accident in a subject, but is the divine essence itself; and so it is subsistent, for the divine essence subsists’.
If the divine relations themselves subsist then it is not possible to conceive of them as existing in another, such as the personal essence of each divine person. Indeed, there is no particular Father-essence, Son-essence or Spirit-essence; there is simply the divine essence subsisting according to three really distinct relations within itself. These three subsistent relations simply are the three persons of God. Clearly, there is a radical difference between the criteria by which creaturely persons (or supposita) are distinguished and those by which divine persons are distinguished. Thomas locates this difference precisely in the fact that creaturely relations are not subsistent (i.e. they are accidents in creatures) while divine relations subsist in virtue of their identity with God's essence:
There cannot be a distinction of suppositum in creatures by means of relations, but only by essential principles; because in creatures relations are not subsistent. But in God relations are subsistent, and so by reason of the opposition between them they distinguish the supposita; and yet the essence is not distinguished, because the relations themselves are not distinguished from each other so far as they are identified with the essence…
...The distinctions between the Father, Son and Holy Spirit are not as those between thing and thing or substance and substance. Neither are they distinct as between accident and accident within a single subject. As far as essence is concerned the divine relations are not really distinct from each other – they are all three the one same God. As fully existing by virtue of the self-same divinity the divine persons cannot be distinguished by anything other than the opposition of their relations. And while those relations wherein they are distinguished cannot be properly ascribed to each person, as befits opposition, everything else about them can. Their distinction lies solely in their relations of opposition. As real, non-accidental and identical with God's essence these relations must themselves be subsistent. Reformed theologian John Owen remarks that ‘a divine person is nothing butthe divine essence … subsisting in an especial manner’. That special manner is as a subsistent relation.
If the divine persons just are the divine relations subsisting in the Godhead then it must be that the Father is identical with the relation of paternity, the Son with filiation and the Spirit with spiration. As subsistent relations these ordinarily abstract terms are predicated of the persons concretely. These are not relations that are superadded to already-constituted subjects in the Godhead, otherwise it would not be the relations that ultimately constitute and distinguish the divine persons after all. Gilles Emery distils the essence of the claim for the simplicity of the divine persons:
[In God] relative property and person designate the same reality, even though their mode of signifying it differs. In the final analysis, this identity of relative property and person rests on the nature of a divine relation, and … divine relations formally possess the being of the divine essence. This applies in full to the three personal relations, that is, to the three relative properties which constitute the persons: paternity, filiation, and procession. These relations or relative properties ‘are the subsisting persons themselves’: paternity is the Father himself, filiation is the Son, and ‘procession’ is the Holy Spirit.
Just as God's simplicity requires the real identity of the divine essence and relations, it also requires that we conceive these relations as subsistent and each of the divine persons as identical with his distinct relation. This identity means that the persons quapersons are non-composite.” [James E. Dolezal, “Trinity, Simplicity and the Status of God’s Personal Relations,” IJST, Vol. 16, issue 1, January 2014.]
Not only is he “simply existence,” but traditional Christian theism has always held that God is “simple existence.” “Simple” here does not mean the opposite of complex (what can be more complex than God?), but rather it affirms that God is not composed of any parts external to himself. Thus, any distinctions we make with respect to God must themselves be identical to him. One way to illustrate this is by way of our understanding of God as triune. By “triune,” we mean that God is one in three. He is one identical essence, and he is also three persons. But this does not in any way mean that God is composed of three parts—Father, Son, and Holy Spirit. Rather, it means that the three persons of the Trinity are each one and all together identical to God. They are….one in essence, three in persons. So, we make distinctions—between Father, Son, and Holy Spirit—and the distinctions do actually tell us that the Father is not the Son, who is not the Spirit, who is not the Father. But those distinctions are in no way “parts” of God. The three are one and the same God.
So also, though not in an identical way, are the attributes of God. They are distinctions that we make with respect to God’s character. But these distinctions with respect to who God is essentially are themselves not parts of God that come together to “compose” who he is. Rather, they just are God. Thus, when we say God is eternal, we do not mean that God partakes of that which is eternal and external to his existence. What we mean is that the eternity of God is itself God. To think otherwise is to make God dependent on something else—in this case eternity—in order to be who he is essentially.” [Scott Oliphint,God With Us, pp. 17-18.]