Objection 1. It would seem that the concrete, essential names cannot stand for the person, so that we can truly say "God begot God." For, as the logicians say, "a singular term signifies what it stands for." But this name "God" seems to be a singular term, for it cannot be predicated in the plural, as above explained (3). Therefore, since it signifies the essence, it stands for essence, and not for person.
Objection 2. Further, a term in the subject is not modified by a term in the predicate, as to its signification; but only as to the sense signified in the predicate. But when I say, "God creates," this name "God" stands for the essence. So when we say "God begot," this term "God" cannot by reason of the notional predicate, stand for person.
Objection 3. Further, if this be true, "God begot," because the Father generates; for the same reason this is true, "God does not beget," because the Son does not beget. Therefore there is God who begets, and there is God who does not beget; and thus it follows that there are two Gods.
Objection 4. Further, if "God begot God," He begot either God, that is Himself, or another God. But He did not beget God, that is Himself; for, as Augustine says (De Trin. i, 1), "nothing begets itself." Neither did He beget another God; as there is only one God. Therefore it is false to say, "God begot God."
Objection 5. Further, if "God begot God," He begot either God who is the Father, or God who is not the Father. If God who is the Father, then God the Father was begotten. If God who is not the Father, then there is a God who is not God the Father: which is false. Therefore it cannot be said that "God begot God."
On the contrary, In the Creed it is said, "God of God."
I answer that, Some have said that this name "God" and the like, properly according to their nature, stand for the essence, but by reason of some notional adjunct are made to stand for the Person. This opinion apparently arose from considering the divine simplicity, which requires that in God, He "who possesses" and "what is possessed" be the same. So He who possesses Godhead, which is signified by the name God, is the same as Godhead. But when we consider the proper way of expressing ourselves, the mode of signification must be considered no less than the thing signified. Hence as this word "God" signifies the divine essence as in Him Who possesses it, just as the name "man" signifies humanity in a subject, others more truly have said that this word "God," from its mode of signification, can, in its proper sense, stand for person, as does the word "man." So this word "God" sometimes stands for the essence, as when we say "God creates"; because this predicate is attributed to the subject by reason of the form signified--that is, Godhead. But sometimes it stands for the person, either for only one, as when we say, "God begets," or for two, as when we say, "God spirates"; or for three, as when it is said: "To the King of ages, immortal, invisible, the only God," etc. (1 Timothy 1:17).
Reply to Objection 1. Although this name "God" agrees with singular terms as regards the form signified not being multiplied; nevertheless it agrees also with general terms so far as the form signified is to be found in several "supposita." So it need not always stand for the essence it signifies.
Reply to Objection 2. This holds good against those who say that the word "God" does not naturally stand for person.
Reply to Objection 3. The word "God" stands for the person in a different way from that in which this word "man" does; for since the form signified by this word "man"--that is, humanity--is really divided among its different subjects, it stands of itself for the person, even if there is no adjunct determining it to the person--that is, to a distinct subject. The unity or community of the human nature, however, is not a reality, but is only in the consideration of the mind. Hence this term "man" does not stand for the common nature, unless this is required by some adjunct, as when we say, "man is a species"; whereas the form signified by the name "God"--that is, the divine essence--is really one and common. So of itself it stands for the common nature, but by some adjunct it may be restricted so as to stand for the person. So, when we say, "God generates," by reason of the notional act this name "God" stands for the person of the Father. But when we say, "God does not generate," there is no adjunct to determine this name to the person of the Son, and hence the phrase means that generation is repugnant to the divine nature. If, however, something be added belonging to the person of the Son, this proposition, for instance, "God begotten does not beget," is true. Consequently, it does not follow that there exists a "God generator," and a "God not generator"; unless there be an adjunct pertaining to the persons; as, for instance, if we were to say, "the Father is God the generator" and the "Son is God the non-generator" and so it does not follow that there are many Gods; for the Father and the Son are one God, as was said above (Article 3).
Reply to Objection 4. This is false, "the Father begot God, that is Himself," because the word "Himself," as a reciprocal term, refers to the same "suppositum." Nor is this contrary to what Augustine says (Ep. lxvi ad Maxim.) that "God the Father begot another self [alterum se]," forasmuch as the word "se" is either in the ablative case, and then it means "He begot another from Himself," or it indicates a single relation, and thus points to identity of nature. This is, however, either a figurative or an emphatic way of speaking, so that it would really mean, "He begot another most like to Himself." Likewise also it is false to say, "He begot another God," because although the Son is another than the Father, as above explained (31, 2), nevertheless it cannot be said that He is "another God"; forasmuch as this adjective "another" would be understood to apply to the substantive God; and thus the meaning would be that there is a distinction of Godhead. Yet this proposition "He begot another God" is tolerated by some, provided that "another" be taken as a substantive, and the word "God" be construed in apposition with it. This, however, is an inexact way of speaking, and to be avoided, for fear of giving occasion to error.
Reply to Objection 5. To say, "God begot God Who is God the Father," is wrong, because since the word "Father" is construed in apposition to "God," the word "God" is restricted to the person of the Father; so that it would mean, "He begot God, Who is Himself the Father"; and then the Father would be spoken of as begotten, which is false. Wherefore the negative of the proposition is true, "He begot God Who is not God the Father." If however, we understand these words not to be in apposition, and require something to be added, then, on the contrary, the affirmative proposition is true, and the negative is false; so that the meaning would be, "He begot God Who is God Who is the Father." Such a rendering however appears to be forced, so that it is better to say simply that the affirmative proposition is false, and the negative is true. Yet Prepositivus said that both the negative and affirmative are false, because this relative "Who" in the affirmative proposition can be referred to the "suppositum"; whereas in the negative it denotes both the thing signified and the "suppositum." Whence, in the affirmative the sense is that "to be God the Father" is befitting to the person of the Son; and in the negative sense is that "to be God the Father," is to be removed from the Son's divinity as well as from His personality. This, however, appears to be irrational; since, according to the Philosopher (Peri Herm. ii), what is open to affirmation, is open also to negation.
Source: Summa Theologica (New Advent)