Sources quoted from:
http://www.newadvent.org/cathen/15047a.htm
In Scripture there is as yet no single term by which the Three Divine Persons are denoted together. The word trias (of which the Latin trinitas is a translation) is first found in Theophilus of Antioch about A.D. 180. He speaks of "the Trinity of God [the Father], His Word and His Wisdom (To Autolycus II.15).
The term may, of course, have been in use before his time. Afterwards it appears in its Latin form of trinitas in Tertullian (On Pudicity 21). In the next century the word is in general use. It is found in many passages of Origen ("In Ps. xvii", 15). The first creed in which it appears is that of Origen's pupil, Gregory Thaumaturgus. In his Ekthesis tes pisteos composed between 260 and 270, he writes:
There is therefore nothing created, nothing subject to another in the Trinity: nor is there anything that has been added as though it once had not existed, but had entered afterwards: therefore the Father has never been without the Son, nor the Son without the Spirit: and this same Trinity is immutable and unalterable forever (P.G., X, 986).
It is manifest that a dogma so mysterious presupposes a Divine revelation. When the fact of revelation, understood in its full sense as the speech of God to man, is no longer admitted, the rejection of the doctrine follows as a necessary consequence. For this reason it has no place in the Liberal Protestantism of today. The writers of this school contend that the doctrine of the Trinity, as professed by the Church, is not contained in the New Testament, but that it was first formulated in the second century and received final approbation in the fourth, as the result of the Arian and Macedonian controversies. In view of this assertion it is necessary to consider in some detail the evidence afforded by Holy Scripture. Attempts have been made recently to apply the more extreme theories of comparative religion to the doctrine of the Trinity, and to account for it by an imaginary law of nature compelling men to group the objects of their worship in threes. It seems needless to give more than a reference to these extravagant views, which serious thinkers of every school reject as destitute of foundation.
Proof of doctrine from Scripture
New Testament
The evidence from the Gospels culminates in the baptismal commission of Matthew 28:20. It is manifest from the narratives of the Evangelists that Christ only made the great truth known to the Twelve step by step.
First He taught them to recognize in Himself the Eternal Son of God. When His ministry was drawing to a close, He promised that the Father would send another Divine Person, the Holy Spirit, in His place. Finally after His resurrection, He revealed the doctrine in explicit terms, bidding them "go and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost" (Matthew 28:18). The force of this passage is decisive. That "the Father" and "the Son" are distinct Persons follows from the terms themselves, which are mutually exclusive. The mention of the Holy Spirit in the same series, the names being connected one with the other by the conjunctions "and . . . and" is evidence that we have here a Third Person co-ordinate with the Father and the Son, and excludes altogether the supposition that the Apostles understood the Holy Spirit not as a distinct Person, but as God viewed in His action on creatures.
The phrase "in the name" (eis to onoma) affirms alike the Godhead of the Persons and their unity of nature. Among the Jews and in the Apostolic Church the Divine name was representative of God. He who had a right to use it was invested with vast authority: for he wielded the supernatural powers of Him whose name he employed. It is incredible that the phrase "in the name" should be here employed, were not all the Persons mentioned equally Divine. Moreover, the use of the singular, "name," and not the plural, shows that these Three Persons are that One Omnipotent God in whom the Apostles believed. Indeed the unity of God is so fundamental a tenet alike of the Hebrew and of the Christian religion, and is affirmed in such countless passages of the Old and New Testaments, that any explanation inconsistent with this doctrine would be altogether inadmissible.
The supernatural appearance at the baptism of Christ is often cited as an explicit revelation of Trinitarian doctrine, given at the very commencement of the Ministry. This, it seems to us, is a mistake. The Evangelists, it is true, see in it a manifestation of the Three Divine Persons. Yet, apart from Christ's subsequent teaching, the dogmatic meaning of the scene would hardly have been understood. Moreover, the Gospel narratives appear to signify that none but Christ and the Baptist were privileged to see the Mystic Dove, and hear the words attesting the Divine sonship of the Messias.
Besides these passages there are many others in the Gospels which refer to one or other of the Three Persons in particular and clearly express the separate personality and Divinity of each. In regard to the First Person it will not be necessary to give special citations: those which declare that Jesus Christ is God the Son, affirm thereby also the separate personality of the Father. The Divinity of Christ is amply attested not merely by St. John, but by the Synoptists. As this point is treated elsewhere (see JESUS CHRIST), it will be sufficient here to enumerate a few of the more important messages from the Synoptists, in which Christ bears witness to His Divine Nature.
He declares that He will come to be the judge of all men (Matthew 25:31). In Jewish theology the judgment of the world was a distinctively Divine, and not a Messianic, prerogative.
In the parable of the wicked husbandmen, He describes Himself as the son of the householder, while the Prophets, one and all, are represented as the servants (Matthew 21:33 sqq.).
He is the Lord of Angels, who execute His command (Matthew 24:31).
He approves the confession of Peter when he recognizes Him, not as Messias — a step long since taken by all the Apostles — but explicitly as the Son of God: and He declares the knowledge due to a special revelation from the Father (Matthew 16:16-17).
Finally, before Caiphas He not merely declares Himself to be the Messias, but in reply to a second and distinct question affirms His claim to be the Son of God. He is instantly declared by the high priest to be guilty of blasphemy, an offense which could not have been attached to the claim to be simply the Messias (Luke 22:66-71).
St. John's testimony is yet more explicit than that of the Synoptists. He expressly asserts that the very purpose of his Gospel is to establish the Divinity of Jesus Christ (John 20:31). In the prologue he identifies Him with the Word, the only-begotten of the Father, Who from all eternity exists with God, Who is God (John 1:1-18). The immanence of the Son in the Father and of the Father in the Son is declared in Christ's words to St. Philip: "Do you not believe, that I am in the Father, and the Father in Me?" (14:10), and in other passages no less explicit (14:7; 16:15; 17:21). The oneness of Their power and Their action is affirmed: "Whatever he [the Father] does, the Son also does in like manner" (5:19, cf. 10:38); and to the Son no less than to the Father belongs the Divine attribute of conferring life on whom He will (5:21). In 10:29, Christ expressly teaches His unity of essence with the Father: "That which my Father hath given me, is greater than all . . . I and the Father are one." The words, "That which my Father hath given me," can, having regard to the context, have no other meaning than the Divine Name, possessed in its fullness by the Son as by the Father.
Rationalist critics lay great stress upon the text: "The Father is greater than I" (14:28). They argue that this suffices to establish that the author of the Gospel held subordinationist views, and they expound in this sense certain texts in which the Son declares His dependence on the Father (5:19; 8:28). In point of fact the doctrine of the Incarnation involves that, in regard of His Human Nature, the Son should be less than the Father. No argument against Catholic doctrine can, therefore, be drawn from this text. So too, the passages referring to the dependence of the Son upon the Father do but express what is essential to Trinitarian dogma, namely, that the Father is the supreme source from Whom the Divine Nature and perfections flow to the Son. (On the essential difference between St. John's doctrine as to the Person of Christ and the Logos doctrine of the Alexandrine Philo, to which many Rationalists have attempted to trace it, see LOGOS.)
In regard to the Third Person of the Blessed Trinity, the passages which can be cited from the Synoptists as attesting His distinct personality are few. The words of Gabriel (Luke 1:35), having regard to the use of the term, "the Spirit," in the Old Testament, to signify God as operative in His creatures, can hardly be said to contain a definite revelation of the doctrine. For the same reason it is dubious whether Christ's warning to the Pharisees as regards blasphemy against the Holy Spirit (Matthew 12:31) can be brought forward as proof. But in Luke 12:12, "The Holy Ghost shall teach you in the same hour what you must say" (Matthew 10:20, and Luke 24:49), His personality is clearly implied. These passages, taken in connection with Matthew 28:19, postulate the existence of such teaching as we find in the discourses in the Cenacle reported by St. John (14, 15, 16). We have in these chapters the necessary preparation for the baptismal commission. In them the Apostles are instructed not only as the personality of the Spirit, but as to His office towards the Church. His work is to teach whatsoever He shall hear (16:13) to bring back their minds the teaching of Christ (14:26), to convince the world of sin (16:8). It is evident that, were the Spirit not a Person, Christ could not have spoken of His presence with the Apostles as comparable to His own presence with them (14:16). Again, were He not a Divine Person it could not have been expedient for the Apostles that Christ should leave them, and the Paraclete take His place (16:7). Moreover, notwithstanding the neuter form of the word (pneuma), the pronoun used in His regard is the masculine ekeinos. The distinction of the Holy Spirit from the Father and from the Son is involved in the express statements that He proceeds from the Father and is sent by the Son (15:26; cf. 14:16, 14:26). Nevertheless, He is one with Them: His presence with the Disciples is at the same time the presence of the Son (14:17-18), while the presence of the Son is the presence of the Father (14:23).
In the remaining New Testament writings numerous passages attest how clear and definite was the belief of the Apostolic Church in the three Divine Persons. In certain texts the coordination of Father, Son, and Spirit leaves no possible doubt as to the meaning of the writer. Thus in 2 Corinthians 13:13, St. Paul writes: "The grace of our Lord Jesus Christ, and the charity of God, and the communication of the Holy Ghost be with you all." Here the construction shows that the Apostle is speaking of three distinct Persons. Moreover, since the names God and Holy Ghost are alike Divine names, it follows that Jesus Christ is also regarded as a Divine Person. So also, in 1 Corinthians 12:4-11: "There are diversities of graces, but the same Spirit; and there are diversities of ministries, but the same Lord: and there are diversities of operations, but the same God, who worketh all [of them] in all [persons]." (Cf. also Ephesians 4:4-6; 1 Peter 1:2-3)
But apart from passages such as these, where there is express mention of the Three Persons, the teaching of the New Testament regarding Christ and the Holy Spirit is free from all ambiguity. In regard to Christ, the Apostles employ modes of speech which, to men brought up in the Hebrew faith, necessarily signified belief in His Divinity. Such, for instance, is the use of the Doxology in reference to Him. The Doxology, "To Him be glory for ever and ever" (cf. 1 Chronicles 16:38; 29:11; Psalm 103:31; 28:2), is an expression of praise offered to God alone. In the New Testament we find it addressed not alone to God the Father, but to Jesus Christ (2 Timothy 4:18; 2 Peter 3:18; Revelation 1:6; Hebrews 13:20-21), and to God the Father and Christ in conjunction (Revelations 5:13, 7:10).
Not less convincing is the use of the title Lord (Kyrios). This term represents the Hebrew Adonai, just as God (Theos) represents Elohim. The two are equally Divine names (cf. 1 Corinthians 8:4). In the Apostolic writings Theos may almost be said to be treated as a proper name of God the Father, and Kyrios of the Son (see, for example, 1 Corinthians 12:5-6); in only a few passages do we find Kyrios used of the Father (1 Corinthians 3:5; 7:17) or Theos of Christ. The Apostles from time to time apply to Christ passages of the Old Testament in which Kyrios is used, for example, 1 Corinthians 10:9 (Numbers 21:7), Hebrews 1:10-12 (Psalm 101:26-28); and they use such expressions as "the fear of the Lord" (Acts 9:31; 2 Corinthians 5:11; Ephesians 5:21), "call upon the name of the Lord," indifferently of God the Father and of Christ (Acts 2:21; 9:14; Romans 10:13). The profession that "Jesus is the Lord" (Kyrion Iesoun, Romans 10:9; Kyrios Iesous, 1 Corinthians 12:3) is the acknowledgment of Jesus as Jahweh. The texts in which St. Paul affirms that in Christ dwells the plenitude of the Godhead (Colossians 2:9), that before His Incarnation He possessed the essential nature of God (Philippians 2:6), that He "is over all things, God blessed for ever" (Romans 9:5) tell us nothing that is not implied in many other passages of his Epistles.
The doctrine as to the Holy Spirit is equally clear. That His distinct personality was fully recognized is shown by many passages. Thus He reveals His commands to the Church's ministers: "As they were ministering to the Lord and fasting, the Holy Ghost said to them: Separate me Saul and Barnabas . . ." (Acts 13:2). He directs the missionary journey of the Apostles: "They attempted to go into Bithynia, and the Spirit of Jesus suffered them not" (Acts 16:7; cf. Acts 5:3; 15:28; Romans 15:30). Divine attributes are affirmed of Him.
He possesses omniscience and reveals to the Church mysteries known only to God (1 Corinthians 2:10);
it is He who distributes charismata (1 Corinthians 12:11);
He is the giver of supernatural life (2 Corinthians 3:8);
He dwells in the Church and in the souls of individual men, as in His temple (Romans 8:9-11; 1 Corinthians 3:16, 6:19).
The work of justification and sanctification is attributed to Him (1 Corinthians 6:11; Romans 15:16), just as in other passages the same operations are attributed to Christ (1 Corinthians 1:2; Galatians 2:17).
To sum up: the various elements of the Trinitarian doctrine are all expressly taught in the New Testament. The Divinity of the Three Persons is asserted or implied in passages too numerous to count. The unity of essence is not merely postulated by the strict monotheism of men nurtured in the religion of Israel, to whom "subordinate deities" would have been unthinkable; but it is, as we have seen, involved in the baptismal commission of Matthew 28:19, and, in regard to the Father and the Son, expressly asserted in John 10:38. That the Persons are co-eternal and coequal is a mere corollary from this. In regard to the Divine processions, the doctrine of the first procession is contained in the very terms Father and Son: the procession of the Holy Spirit from the Father and Son is taught in the discourse of the Lord reported by St. John (14-17) (see HOLY GHOST).
Old Testament
The early Fathers were persuaded that indications of the doctrine of the Trinity must exist in the Old Testament and they found such indications in not a few passages. Many of them not merely believed that the Prophets had testified of it, they held that it had been made known even to the Patriarchs. They regarded it as certain that the Divine messenger of Genesis 16:7, 16:18, 21:17, 31:11; Exodus 3:2, was God the Son; for reasons to be mentioned below (III. B.) they considered it evident that God the Father could not have thus manifested Himself (cf. Justin, Dialogue with Trypho 60; Irenaeus, Against Heresies IV.20.7-11; Tertullian, Against Praxeas 15-16; Theophilus, To Autolycus II.22; Novatian, On the Trinity 18, 25, etc.). They held that, when the inspired writers speak of "the Spirit of the Lord", the reference was to the Third Person of the Trinity; and one or two (Irenaeus, Against Heresies II.30.9; Theophilus, To Autolycus II.15; Hippolytus, Against Noetus 10) interpret the hypostatic Wisdom of the Sapiential books, not, with St. Paul, of the Son (Hebrews 1:3; cf. Wisdom 7:25-26), but of the Holy Spirit. But in others of the Fathers is found what would appear to be the sounder view, that no distinct intimation of the doctrine was given under the Old Covenant. (Cf. Gregory Nazianzen, Fifth Theological Oration 31; Epiphanius, "Ancor." 73, "Haer.", 74; Basil, Against Eunomius II.22; Cyril of Alexandria, "In Joan.", xii, 20.)
Some of these, however, admitted that a knowledge of the mystery was granted to the Prophets and saints of the Old Dispensation (Epiphanius, "Haer.", viii, 5; Cyril of Alexandria, "Con. Julian., " I). It may be readily conceded that the way is prepared for the revelation in some of the prophecies. The names Emmanuel (Isaiah 7:14) and God the Mighty (Isaiah 9:6) affirmed of the Messias make mention of the Divine Nature of the promised deliverer. Yet it seems that the Gospel revelation was needed to render the full meaning of the passages clear. Even these exalted titles did not lead the Jews to recognize that the Saviour to come was to be none other than God Himself. The Septuagint translators do not even venture to render the words God the Mighty literally, but give us, in their place, "the angel of great counsel."
A still higher stage of preparation is found in the doctrine of the Sapiential books regarding the Divine Wisdom. In Proverbs 8, Wisdom appears personified, and in a manner which suggests that the sacred author was not employing a mere metaphor, but had before his mind a real person (cf. verses 22, 23). Similar teaching occurs in Ecclesiasticus 24, in a discourse which Wisdom is declared to utter in "the assembly of the Most High", i.e. in the presence of the angels. This phrase certainly supposes Wisdom to be conceived as person. The nature of the personality is left obscure; but we are told that the whole earth is Wisdom's Kingdom, that she finds her delight in all the works of God, but that Israel is in a special manner her portion and her inheritance (Ecclesiasticus 24:8-13).
In the Book of the Wisdom of Solomon we find a still further advance. Here Wisdom is clearly distinguished from Jehovah: "She is . . . a certain pure emanation of the glory of the almighty God. . .the brightness of eternal light, and the unspotted mirror of God's majesty, and the image of his goodness" (Wisdom 7:25-26. Cf. Hebrews 1:3). She is, moreover, described as "the worker of all things" (panton technitis, 7:21), an expression indicating that the creation is in some manner attributable to her. Yet in later Judaism this exalted doctrine suffered eclipse, and seems to have passed into oblivion. Nor indeed can it be said that the passage, even though it manifests some knowledge of a second personality in the Godhead, constitutes a revelation of the Trinity. For nowhere in the Old Testament do we find any clear indication of a Third Person. Mention is often made of the Spirit of the Lord, but there is nothing to show that the Spirit was viewed as distinct from Jahweh Himself. The term is always employed to signify God considered in His working, whether in the universe or in the soul of man. The matter seems to be correctly summed up by Epiphanius, when he says: "The One Godhead is above all declared by Moses, and the twofold personality (of Father and Son) is strenuously asserted by the Prophets. The Trinity is made known by the Gospel" ("Haer.", lxxiv).