The doctrine of the Trinity is based on two basic biblical teachings:
(1) There is one and only one God.
The biblical, theological, and historical evidence for God's absolute oneness has been established in scripture and history. We shall now address the second biblical teaching...
(2) There are three distinct persons who are God: The Father, the Son, and the Holy Spirit.
In addition to declaring God to be one in nature or essence, the scriptures affirm that there are three distinct persons who are God. All are called God, and all have the essential characteristics of a person. Personhood is traditionally understood as one who has intellect, feelings, and will.
All three of these characteristics are attributed to all three members of the Trinity in Scripture. Essentially, personhood refers to an "I," a "who," or a subject. Each "I" in the Trinity possesses (by virtue of its one common nature) the power to think, feel, and choose. Personhood itself is its I-ness or who-ness.
All members of the Trinity are equal in essence, but they do not have the same roles. In brief, the Father is the Planner, the Son is the Accomplisher, and the Holy Spirit is the Applier of salvation to believers.
What scripture plainly teaches is that God has one and only one essence (nature) and that it is not contradictory to have three persons in one essence.
All members of the Trinity are equal in essence, but they do not have the same roles. It is a heresy (called subordinationism) to affirm that there is an ontological subordination of one member of the Trinity to another, since they are identical in essence.
Nonetheless, it is clear that there is a finctional subordination; that is, not only does each member have a different function or role, but some functions are also subordinate to others.
God the Father, God the Son, and God the Holy Spirit all share the same essence of God in an equal manner unsubordinate to each other; however, each member have different functions or roles with some functions being subordinate to others.
By His very title of "Father" and His label of "the first person of the Trinity," it is manifest that His function is superior to that of the Son and the Holy Spirit. The Father, for example, is presented as the Source, Sender, and Planner of salvation.
The Son, on the other hand, is the Means, Sent One, and Achiever of salvation. The Father sent, and the Son came to save us; the Father planned it, but the Son accomplished it on the cross. This is why it is a heresy (called patripassianism) to claim that the Father suffered on the cross only the son suffered and died. Further, the Son is eternally "begotten" or "generated" from the Father, but the Father is never said to be "begotten" or "generated from anyone.
According to orthodox Western theology, the Holy Spirit proceeds both from the Father and the Son (see John 15:26). Jesus said, "When the Counselor comes, whom I will sent to you from the Father, the Spirit of truth who goes out from the Father, He will testify about me" (John 15:26).
Their functional roles are as follows: the Father is the Planner, the Son is the Accomplisher, and the Holy Spirit is the Applier of salvation to believers. However, they are all equal in essence as God.
Jesus, as God, in his role as God the son the accomplisher of our salvation makes intercession for us just as the Bible says that He does in Hebrews 5 as our perfect high priest (e.g. a functional role).
Except for a few cults asserting a false theology (e.g. heresy) and a false church history (note that the heretics were excommunicated), this has always been the position of authentic and historical Christianity.
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