God's intention in writing the Gospel of John is altogether intrinsic. We have to pray and look to the Lord very much that He would show us the intrinsic significance of John 1 through 16. The first four chapters unveil the flowing God in His divine processed Trinity. In John 4:14b the Lord said, "The water that I will give him will become in him a fountain of water gushing up [springing up] into eternal life." God the Father is the fountain emerging in God the Son as a spring gushing up to be a river, signifying God the Spirit. The Triune God flows into eternal life, and the eternal life has its totality. Our human life also has its totality. A living person is the totality of the human life. The totality of the divine life is the New Jerusalem, which is the destination of the flowing Triune God.
Then John 6 and 7 reveal Christ as the Feast of Passover and the Feast of Tabernacles. These feasts are the enjoyment of the flowing, triune, processed God. Our enjoyment of such a flowing, triune, processed God brings us into the incorporation of the Triune God with us, His redeemed people. This incorporation is the Triune God as the Father, the Son, and the Spirit coinhering with us. They are in us, and we are in Them. As the second Comforter, Christ is the Spirit of reality who comes not only to be with us but also to be in us, the redeemed ones of God (John 14:17). Then the Son in whom we believe is in the Father and we are in Him and He is in us (v. 20). These four ins show the Triune God coinhering with us. This coinhering is a blending, a mingling, and an incorporation. The Triune God is incorporated with His redeemed and transformed people to be one entity.
The issue of this incorporation is the Father's house in John 14, the Son's vine in John 15, and the Spirit's new child to grow up as the new man in John 16. The house is for the Father, the vine is for the Son, and the new man is for the Spirit. The house is for the Father, as the source of the Divine Trinity, to rest and be satisfied. Without a house, we could not have rest; we would be homeless wanderers. Without rest, there is no satisfaction. The Father can rest and be satisfied because He has a house. The vine is for the Triune God in the Son to have an organism for His spreading and multiplication. The all-inclusive and all-extensive Triune God is unlimited. He wants to spread and be multiplied. The vine tree is for fruit-bearing, and fruit-bearing is for the spreading and multiplication of the vine tree. Furthermore, the Triune God needs a man. The Spirit is always for God's moving and acting to carry out His economy. This Spirit needs a man to carry out God's eternal purpose. This man was born as a new child, and this new child is growing. First Peter 2:2 says that as newborn babes we need to desire the milk of the word that we may grow into manhood to be a full-grown man for the fulfilling and carrying out of God's eternal economy which will be consummated in the New Jerusalem. Thus, the issue of the processed and consummated Triune God incorporated with His redeemed and transformed elect is the Father's house for God the Father's rest and satisfaction, the Son's vine as the organism of the Triune God in the Son for His spreading and multiplication, and the Spirit's new child to grow up to be the new man to carry out God's economy in the Spirit. This is the intrinsic view of the first sixteen chapters of John.