Objection 1. It would seem that the divine relation is not the same as the divine essence. For Augustine says (De Trin. v) that "not all that is said of God is said of His substance, for we say some things relatively, as Father in respect of the Son: but such things do not refer to the substance." Therefore the relation is not the divine essence.
Objection 2. Further, Augustine says (De Trin. vii) that, "every relative expression is something besides the relation expressed, as master is a man, and slave is a man." Therefore, if relations exist in God, there must be something else besides relation in God. This can only be His essence. Therefore essence differs from relation.
Objection 3. Further, the essence of relation is the being referred to another, as the Philosopher says (Praedic. v). So if relation is the divine essence, it follows that the divine essence is essentially itself a relation to something else; whereas this is repugnant to the perfection of the divine essence, which is supremely absolute and self-subsisting (3, 4). Therefore relation is not the divine essence.
On the contrary, Everything which is not the divine essence is a creature. But relation really belongs to God; and if it is not the divine essence, it is a creature; and it cannot claim the adoration of latria; contrary to what is sung in the Preface: "Let us adore the distinction of the Persons, and the equality of their Majesty."
I answer that, It is reported that Gilbert de la Porree erred on this point, but revoked his error later at the council of Rheims. For he said that the divine relations are assistant, or externally affixed.
To perceive the error here expressed, we must consider that in each of the nine genera of accidents there are two points for remark. One is the nature belonging to each one of them considered as an accident; which commonly applies to each of them as inherent in a subject, for the essence of an accident is to inhere. The other point of remark is the proper nature of each one of these genera. In the genera, apart from that of "relation," as in quantity and quality, even the true idea of the genus itself is derived from a respect to the subject; for quantity is called the measure of substance, and quality is the disposition of substance. But the true idea of relation is not taken from its respect to that in which it is, but from its respect to something outside. So if we consider even in creatures, relations formally as such, in that aspect they are said to be "assistant," and not intrinsically affixed, for, in this way, they signify a respect which affects a thing related and tends from that thing to something else; whereas, if relation is considered as an accident, it inheres in a subject, and has an accidental existence in it. Gilbert de la Porree considered relation in the former mode only.
Now whatever has an accidental existence in creatures, when considered as transferred to God, has a substantial existence; for there is no accident in God; since all in Him is His essence. So, in so far as relation has an accidental existence in creatures, relation really existing in God has the existence of the divine essence in no way distinct therefrom. But in so far as relation implies respect to something else, no respect to the essence is signified, but rather to its opposite term.
Thus it is manifest that relation really existing in God is really the same as His essence and only differs in its mode of intelligibility; as in relation is meant that regard to its opposite which is not expressed in the name of essence. Thus it is clear that in God relation and essence do not differ from each other, but are one and the same.
Reply to Objection 1. These words of Augustine do not imply that paternity or any other relation which is in God is not in its very being the same as the divine essence; but that it is not predicated under the mode of substance, as existing in Him to Whom it is applied; but as a relation. So there are said to be two predicaments only in God, since other predicaments import habitude to that of which they are spoken, both in their generic and in their specific nature; but nothing that exists in God can have any relation to that wherein it exists or of whom it is spoken, except the relation of identity; and this by reason of God's supreme simplicity.
Reply to Objection 2. As the relation which exists in creatures involves not only a regard to another, but also something absolute, so the same applies to God, yet not in the same way. What is contained in the creature above and beyond what is contained in the meaning of relation, is something else besides that relation; whereas in God there is no distinction, but both are one and the same; and this is not perfectly expressed by the word "relation," as if it were comprehended in the ordinary meaning of that term. For it was above explained (13, 2), in treating of the divine names, that more is contained in the perfection of the divine essence than can be signified by any name. Hence it does not follow that there exists in God anything besides relation in reality; but only in the various names imposed by us.
Reply to Objection 3. If the divine perfection contained only what is signified by relative names, it would follow that it is imperfect, being thus related to something else; as in the same way, if nothing more were contained in it than what is signified by the word "wisdom," it would not in that case be a subsistence. But as the perfection of the divine essence is greater than can be included in any name, it does not follow, if a relative term or any other name applied to God signify something imperfect, that the divine essence is in any way imperfect; for the divine essence comprehends within itself the perfection of every genus (4, 2).
Source: Summa Theologica (New Advent)