These are not three persons in the ordinary sense of the word; they are not three individuals, but rather three modes or forms in which the Divine Being exists.
At the same time they are of such a nature that they can enter into personal relations. The Father can speak to the Son and vice versa, and both can send forth the Spirit.
The real mystery of the Trinity consists in this that each one of the Persons possesses the whole of the divine essence, and that this has no existence outside of and apart from the Persons. The three are not subordinate in being the one to the other, though it may be said that in order of existence the Father is first, the Son second, and the Holy Spirit third, an order which is also reflected in their work.
2. Scripture Proof for the Trinity. The Old Testament contains some indications of more than one Person in God. God speaks of Himself in the plural, Gen. 1:26; 11:7; the Angel of Jehovah is represented as a divine Person, Gen. 16:7-13; 18:1-21; 19:1-22; and the Spirit is spoken of as a distinct Person, Isa. 48:16; 63:10. Moreover, there are some passages in which the Messiah is speaking and mentions two other Persons, Isa. 48:16; 61:6; 63:9, 10. Due to the progress of revelation, the New Testament contains clearer proofs. The strongest proof is found in the facts of redemption.
The Father sends the Son into the world, and the Son sends the Holy Spirit. Moreover, there are several passages in which the three Persons are expressly mentioned, such as the great commission, Matt. 28:19, and the apostolic blessing, II Cor. 13:13. Cf. also Luke 3:21, 22; 1:35; I Cor. 12:4-6; I Pet. 1:2. This doctrine was denied by the Socinians in the days of the Reformation, and is rejected also by the Unitarians and the Modernists of our own day. If they speak of the Trinity at all, they represent it as consisting of the Father, the man Jesus, and a divine influence which is called the Spirit of God.
3. The Father. The name ‘Father’ is frequently applied in Scripture to the triune God, as the creator of all things, I Cor. 8:6; Heb. 12:9; Jas. 1:17; as the Father of Israel, Deut. 32:6; Isa. 63:16; and as the Father of believers, Matt. 5:45; 6:6, 9, 14; Rom. 8:15. In a deeper sense, however, it is applied to the First Person of the Trinity, to express His relation to the Second Person, John 1:14, 18; 8:54; 14:12, 13.
This is the original Fatherhood, of which all earthly fatherhood is but a faint reflection. The distinctive characteristic of the Father is that He generates the Son from all eternity. The works particularly ascribed to Him are those of planning the work of redemption, creation and providence, and representing the Trinity in the Counsel of Redemption.
4. The Son. The second person in the Trinity is called ‘Son’ or ‘Son of God.’ He bears this name, however, not only as the only begotten of the Father, John 1:14, 18; 3:16, 18; Gal. 4:4, but also as the Messiah chosen of God, Matt. 8:29; 26:63; John 1:49; 11:27, and in virtue of His special birth through the operation of the Holy Spirit, Luke 1:32, 35.
His special characteristic as the Second Person of the Trinity is that He is eternally begotten of the Father, Ps. 2:7; Acts 13:33; Heb. 1:5. By means of eternal generation the Father is the cause of the personal existence of the Son within the Divine Being. The works more particularly ascribed to Him are works of mediation. He mediated the work of creation, John 1:3, 10; Heb. 1:2, 3, and mediates the work of redemption, Eph. 1:3-14.
5. The Holy Spirit. Though Socinians, Unitarians, and present day Modernists speak of the Holy Spirit merely as a power or an influence of God, He clearly stands out on the pages of the Bible as a Person, John 14:16, 17, 26; 15:26; 16:1-15; Rom. 8:26. He has intelligence, John 14:26, feeling, Isa. 68:10; Eph. 4:30, and will, Acts 16:7; I Cor. 12:11. Scripture represents Him as speaking, searching, testifying, commanding, revealing, striving, and making intercession.
Moreover, He is clearly distinguished from His own power in Luke 1:35; 4:14; Acts 10:38; I Cor. 2:4. His special characteristic is that He proceeds from the Father and the Son by spiration, John 15:26; 16:7; Rom. 8:9; Gal. 4:6. In general it may be said that it is His task to bring things to completion both in creation and redemption, Gen. 1:3; Job 26:13; Luke 1:35; John 3:34; I Cor. 12:4-11; Eph. 2:22.
To memorize. Passages to prove:
a. The Trinity:Isa. 61:1. “The Spirit of the Lord Jehovah is upon Me” (the Messiah), cf. Luke 4:17, 18.
Matt. 28:19. “Go ye therefore and make disciples of all the nations, baptizing them into the name of the Father and of the Son and of the Holy Spirit.”
II Cor. 13:14. “The grace of the Lord Jesus Christ, and the love of God; and the communion of the Holy Spirit, be with you all.”
b. Eternal generation:
Ps. 2:7. “I will tell of the decree: Jehovah said unto me, Thou art my Son; this day have I begotten Thee.”
John 1:14, “And the Word became flesh, and dwelt among us (and we beheld His glory, glory as of the only begotten from the Father), full of grace and truth.”
e. Procession of the Holy Spirit:
John 15:26. “But when the Comforter is come, whom I will send unto you from the Father, even the Spirit of truth, which proceedeth from the Father, He shall bear witness of Me.”
For Further Study:
a. In what sense can we speak of a general Fatherhood of God? I Cor. 8:6; Eph. 3:14, 15; Heb. 12:9; Jas. 1:17. Cf. also Num. 16:22.b. Can you prove the deity of the incarnate Son? John 1:1; 20:28; Phil. 2:6; Tit. 2:13; Jer. 28:5, 6; Isa. 9:6; John 1:3; Rev. 1:8; Col. 1:17; John 14:1; II Cor. 13:14.
c. How do the following passages prove the personality of the Holy Spirit? Gen. 1:2; 6:3; Luke 12:12; John 14:26; 15:26; 16:8; Acts 8:29; 13:2; Rom. 8:11; I Cor. 2:10, 11.
d. What works are ascribed to the Spirit in Ps. 33:6; 104:30; Ex, 28:3; II Pet. 1:21; I Cor. 3:16; 12:4 ff.?
 Louis Berkhof. Summary of Christian Doctrine (Kindle Locations 520-569). Monergism Books.