Objection 1. It would seem that there are no real relations in God. For Boethius says (De Trin. iv), "All possible predicaments used as regards the Godhead refer to the substance; for nothing can be predicated relatively." But whatever really exists in God can be predicated of Him. Therefore no real relation exists in God.
Objection 2. Further, Boethius says (De Trin. iv) that, "Relation in the Trinity of the Father to the Son, and of both to the Holy Ghost, is the relation of the same to the same." But a relation of this kind is only a logical one; for every real relation requires and implies in reality two terms. Therefore the divine relations are not real relations, but are formed only by the mind.
Objection 3. Further, the relation of paternity is the relation of a principle. But to say that God is the principle of creatures does not import any real relation, but only a logical one. Therefore paternity in God is not a real relation; while the same applies for the same reason to the other relations in God.
Objection 4. Further, the divine generation proceeds by way of an intelligible word. But the relations following upon the operation of the intellect are logical relations. Therefore paternity and filiation in God, consequent upon generation, are only logical relations.
On the contrary, The Father is denominated only from paternity; and the Son only from filiation. Therefore, if no real paternity or filiation existed in God, it would follow that God is not really Father or Son, but only in our manner of understanding; and this is the Sabellian heresy.
I answer that, relations exist in God really; in proof whereof we may consider that in relations alone is found something which is only in the apprehension and not in reality. This is not found in any other genus; forasmuch as other genera, as quantity and quality, in their strict and proper meaning, signify something inherent in a subject. But relation in its own proper meaning signifies only what refers to another. Such regard to another exists sometimes in the nature of things, as in those things which by their own very nature are ordered to each other, and have a mutual inclination; and such relations are necessarily real relations; as in a heavy body is found an inclination and order to the centre; and hence there exists in the heavy body a certain respect in regard to the centre and the same applies to other things. Sometimes, however, this regard to another, signified by relation, is to be found only in the apprehension of reason comparing one thing to another, and this is a logical relation only; as, for instance, when reason compares man to animal as the species to the genus. But when something proceeds from a principle of the same nature, then both the one proceeding and the source of procession, agree in the same order; and then they have real relations to each other. Therefore as the divine processions are in the identity of the same nature, as above explained (27, 2, 4), these relations, according to the divine processions, are necessarily real relations.
Reply to Objection 1. Relationship is not predicated of God according to its proper and formal meaning, that is to say, in so far as its proper meaning denotes comparison to that in which relation is inherent, but only as denoting regard to another. Nevertheless Boethius did not wish to exclude relation in God; but he wished to show that it was not to be predicated of Him as regards the mode of inherence in Himself in the strict meaning of relation; but rather by way of relation to another.
Reply to Objection 2. The relation signified by the term "the same" is a logical relation only, if in regard to absolutely the same thing; because such a relation can exist only in a certain order observed by reason as regards the order of anything to itself, according to some two aspects thereof. The case is otherwise, however, when things are called the same, not numerically, but generically or specifically. Thus Boethius likens the divine relations to a relation of identity, not in every respect, but only as regards the fact that the substance is not diversified by these relations, as neither is it by relation of identity.
Reply to Objection 3. As the creature proceeds from God in diversity of nature, God is outside the order of the whole creation, nor does any relation to the creature arise from His nature; for He does not produce the creature by necessity of His nature, but by His intellect and will, as is above explained (14, 3 and 4; 19, 8). Therefore there is no real relation in God to the creature; whereas in creatures there is a real relation to God; because creatures are contained under the divine order, and their very nature entails dependence on God. On the other hand, the divine processions are in one and the same nature. Hence no parallel exists.
Reply to Objection 4. Relations which result from the mental operation alone in the objects understood are logical relations only, inasmuch as reason observes them as existing between two objects perceived by the mind. Those relations, however, which follow the operation of the intellect, and which exist between the word intellectually proceeding and the source whence it proceeds, are not logical relations only, but are real relations; inasmuch as the intellect and the reason are real things, and are really related to that which proceeds from them intelligibly; as a corporeal thing is related to that which proceeds from it corporeally. Thus paternity and filiation are real relations in God.
Source: Summa Theologica (New Advent)