Objection 1. It would seem that the name "person" should not be said of God. For Dionysius says (Div. Nom.): "No one should ever dare to say or think anything of the supersubstantial and hidden Divinity, beyond what has been divinely expressed to us by the oracles." But the name "person" is not expressed to us in the Old or New Testament. Therefore "person" is not to be applied to God.
Objection 2. Further, Boethius says (De Duab. Nat.): "The word person seems to be taken from those persons who represented men in comedies and tragedies. For person comes from sounding through [personando], since a greater volume of sound is produced through the cavity in the mask. These "persons" or masks the Greeks called prosopa, as they were placed on the face and covered the features before the eyes." This, however, can apply to God only in a metaphorical sense. Therefore the word "person" is only applied to God metaphorically.
Objection 3. Further, every person is a hypostasis. But the word "hypostasis" does not apply to God, since, as Boethius says (De Duab. Nat.), it signifies what is the subject of accidents, which do not exist in God. Jerome also says (Ep. ad Damas.) that, "in this word hypostasis, poison lurks in honey." Therefore the word "person" should not be said of God.
Objection 4. Further, if a definition is denied of anything, the thing defined is also denied of it. But the definition of "person," as given above, does not apply to God. Both because reason implies a discursive knowledge, which does not apply to God, as we proved above (14, 1); and thus God cannot be said to have "a rational nature." And also because God cannot be called an individual substance, since the principle of individuation is matter; while God is immaterial: nor is He the subject of accidents, so as to be called a substance. Therefore the word "person" ought not to be attributed to God.
On the contrary, In the Creed of Athanasius we say: "One is the person of the Father, another of the Son, another of the Holy Ghost."
I answer that, "Person" signifies what is most perfect in all nature--that is, a subsistent individual of a rational nature. Hence, since everything that is perfect must be attributed to God, forasmuch as His essence contains every perfection, this name "person" is fittingly applied to God; not, however, as it is applied to creatures, but in a more excellent way; as other names also, which, while giving them to creatures, we attribute to God; as we showed above when treating of the names of God (13, 2).
Reply to Objection 1. Although the word "person" is not found applied to God in Scripture, either in the Old or New Testament, nevertheless what the word signifies is found to be affirmed of God in many places of Scripture; as that He is the supreme self-subsisting being, and the most perfectly intelligent being. If we could speak of God only in the very terms themselves of Scripture, it would follow that no one could speak about God in any but the original language of the Old or New Testament. The urgency of confuting heretics made it necessary to find new words to express the ancient faith about God. Nor is such a kind of novelty to be shunned; since it is by no means profane, for it does not lead us astray from the sense of Scripture. The Apostle warns us to avoid "profane novelties of words" (1 Timothy 6:20).
Reply to Objection 2. Although this name "person" may not belong to God as regards the origin of the term, nevertheless it excellently belongs to God in its objective meaning. For as famous men were represented in comedies and tragedies, the name "person" was given to signify those who held high dignity. Hence, those who held high rank in the Church came to be called "persons." Thence by some the definition of person is given as "hypostasis distinct by reason of dignity." And because subsistence in a rational nature is of high dignity, therefore every individual of the rational nature is called a "person." Now the dignity of the divine nature excels every other dignity; and thus the name "person" pre-eminently belongs to God.
Reply to Objection 3. The word "hypostasis" does not apply to God as regards its source of origin, since He does not underlie accidents; but it applies to Him in its objective sense, for it is imposed to signify the subsistence. Jerome said that "poison lurks in this word," forasmuch as before it was fully understood by the Latins, the heretics used this term to deceive the simple, to make people profess many essences as they profess several hypostases, inasmuch as the word "substance," which corresponds to hypostasis in Greek, is commonly taken amongst us to mean essence.
Reply to Objection 4. It may be said that God has a rational "nature," if reason be taken to mean, not discursive thought, but in a general sense, an intelligent nature. But God cannot be called an "individual" in the sense that His individuality comes from matter; but only in the sense which implies incommunicability. "Substance" can be applied to God in the sense of signifying self-subsistence. There are some, however, who say that the definition of Boethius, quoted above (Article 1), is not a definition of person in the sense we use when speaking of persons in God. Therefore Richard of St. Victor amends this definition by adding that "Person" in God is "the incommunicable existence of the divine nature."
Source: Summa Theologica (New Advent)