Objection 1. It would seem that this word "person," as applied to God, does not signify relation, but substance. For Augustine says (De Trin. vii, 6): "When we speak of the person of the Father, we mean nothing else but the substance of the Father, for person is said in regard to Himself, and not in regard to the Son."
Objection 2. Further, the interrogation "What?" refers to essence. But, as Augustine says: "When we say there are three who bear witness in heaven, the Father, the Word, and the Holy Ghost, and it is asked, Three what? the answer is, Three persons." Therefore person signifies essence.
Objection 3. According to the Philosopher (Metaph. iv), the meaning of a word is its definition. But the definition of "person" is this: "The individual substance of the rational nature," as above stated. Therefore "person" signifies substance.
Objection 4. Further, person in men and angels does not signify relation, but something absolute. Therefore, if in God it signified relation, it would bear an equivocal meaning in God, in man, and in angels.
On the contrary, Boethius says (De Trin.) that "every word that refers to the persons signifies relation." But no word belongs to person more strictly than the very word "person" itself. Therefore this word "person" signifies relation.
I answer that, A difficulty arises concerning the meaning of this word "person" in God, from the fact that it is predicated plurally of the Three in contrast to the nature of the names belonging to the essence; nor does it in itself refer to another, as do the words which express relation.
Hence some have thought that this word "person" of itself expresses absolutely the divine essence; as this name "God" and this word "Wise"; but that to meet heretical attack, it was ordained by conciliar decree that it was to be taken in a relative sense, and especially in the plural, or with the addition of a distinguishing adjective; as when we say, "Three persons," or, "one is the person of the Father, another of the Son," etc. Used, however, in the singular, it may be either absolute or relative. But this does not seem to be a satisfactory explanation; for, if this word "person," by force of its own signification, expresses the divine essence only, it follows that forasmuch as we speak of "three persons," so far from the heretics being silenced, they had still more reason to argue. Seeing this, others maintained that this word "person" in God signifies both the essence and the relation. Some of these said that it signifies directly the essence, and relation indirectly, forasmuch as "person" means as it were "by itself one" [per se una]; and unity belongs to the essence. And what is "by itself" implies relation indirectly; for the Father is understood to exist "by Himself," as relatively distinct from the Son. Others, however, said, on the contrary, that it signifies relation directly; and essence indirectly; forasmuch as in the definition of "person" the term nature is mentioned indirectly; and these come nearer to the truth.
To determine the question, we must consider that something may be included in the meaning of a less common term, which is not included in the more common term; as "rational" is included in the meaning of "man," and not in the meaning of "animal." So that it is one thing to ask the meaning of the word animal, and another to ask its meaning when the animal in question is man. Also, it is one thing to ask the meaning of this word "person" in general; and another to ask the meaning of "person" as applied to God. For "person" in general signifies the individual substance of a rational figure. The individual in itself is undivided, but is distinct from others. Therefore "person" in any nature signifies what is distinct in that nature: thus in human nature it signifies this flesh, these bones, and this soul, which are the individuating principles of a man, and which, though not belonging to "person" in general, nevertheless do belong to the meaning of a particular human person.
Now distinction in God is only by relation of origin, as stated above (28, 2, 3), 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. Therefore, as the Godhead is God so the divine paternity is God the Father, Who is a divine person. Therefore a divine person signifies a relation as subsisting. And this is to signify relation by way of substance, and such a relation is a hypostasis subsisting in the divine nature, although in truth that which subsists in the divine nature is the divine nature itself. Thus it is true to say that the name "person" signifies relation directly, and the essence indirectly; not, however, the relation as such, but as expressed by way of a hypostasis. So likewise it signifies directly the essence, and indirectly the relation, inasmuch as the essence is the same as the hypostasis: while in God the hypostasis is expressed as distinct by the relation: and thus relation, as such, enters into the notion of the person indirectly. Thus we can say that this signification of the word "person" was not clearly perceived before it was attacked by heretics. Hence, this word "person" was used just as any other absolute term. But afterwards it was applied to express relation, as it lent itself to that signification, so that this word "person" means relation not only by use and custom, according to the first opinion, but also by force of its own proper signification.
Reply to Objection 1. This word "person" is said in respect to itself, not to another; forasmuch as it signifies relation not as such, but by way of a substance--which is a hypostasis. In that sense Augustine says that it signifies the essence, inasmuch as in God essence is the same as the hypostasis, because in God what He is, and whereby He is are the same.
Reply to Objection 2. The term "what" refers sometimes to the nature expressed by the definition, as when we ask; What is man? and we answer: A mortal rational animal. Sometimes it refers to the "suppositum," as when we ask, What swims in the sea? and answer, A fish. So to those who ask, Three what? we answer, Three persons.
Reply to Objection 3. In God the individual--i.e. distinct and incommunicable substance--includes the idea of relation, as above explained.
Reply to Objection 4. The different sense of the less common term does not produce equivocation in the more common. Although a horse and an ass have their own proper definitions, nevertheless they agree univocally in animal, because the common definition of animal applies to both. So it does not follow that, although relation is contained in the signification of divine person, but not in that of an angelic or of a human person, the word "person" is used in an equivocal sense. Though neither is it applied univocally, since nothing can be said univocally of God and creatures (13, 5).
Source: Summa Theologica (New Advent)