I answer that, The name "Trinity" in God signifies the determinate number of persons. And so the plurality of persons in God requires that we should use the word trinity; because what is indeterminately signified by plurality, is signified by trinity in a determinate manner.
Reply Obj. 1: In its etymological sense, this word "Trinity" seems to signify the one essence of the three persons, according as trinity may mean trine-unity. But in the strict meaning of the term it rather signifies the number of persons of one essence; and on this account we cannot say that the Father is the Trinity, as He is not three persons. Yet it does not mean the relations themselves of the Persons, but rather the number of persons related to each other; and hence it is that the word in itself does not express regard to another.
Reply Obj. 2: Two things are implied in a collective term, plurality of the supposita, and a unity of some kind of order. For "people" is a multitude of men comprehended under a certain order. In the first sense, this word "trinity" is like other collective words; but in the second sense it differs from them, because in the divine Trinity not only is there unity of order, but also with this there is unity of essence.
Reply Obj. 3: "Trinity" is taken in an absolute sense; for it signifies the threefold number of persons. "Triplicity" signifies a proportion of inequality; for it is a species of unequal proportion, according to Boethius (Arithm. i, 23). Therefore in God there is not triplicity, but Trinity.
Reply Obj. 4: In the divine Trinity is to be understood both number and the persons numbered. So when we say, "Trinity in Unity," we do not place number in the unity of the essence, as if we meant three times one; but we place the Persons numbered in the unity of nature; as the supposita of a nature are said to exist in that nature. On the other hand, we say "Unity in Trinity"; meaning that the nature is in its supposita.
Reply Obj. 5: When we say, "Trinity is trine," by reason of the number implied, we signify the multiplication of that number by itself; since the word trine imports a distinction in the supposita of which it is spoken. Therefore it cannot be said that the Trinity is trine; otherwise it follows that, if the Trinity be trine, there would be three supposita of the Trinity; as when we say, "God is trine," it follows that there are three supposita of the Godhead. _______________________
SECOND ARTICLE [I, Q. 31, Art. 2]
Whether the Son Is Other Than the Father?
Objection 1: It would seem that the Son is not other than the Father. For "other" is a relative term implying diversity of substance. If, then, the Son is other than the Father, He must be different from the Father; which is contrary to what Augustine says (De Trin. vii), that when we speak of three persons, "we do not mean to imply diversity."
Obj. 2: Further, whosoever are other from one another, differ in some way from one another. Therefore, if the Son is other than the Father, it follows that He differs from the Father; which is against what Ambrose says (De Fide i), that "the Father and the Son are one in Godhead; nor is there any difference in substance between them, nor any diversity."