> St. Gregory

This link doesn't address different functions or activities, but rather different natures, which I was not claiming.

> Creator

You gave a false reply. Presumably you didn't carefully read my post. God the Father is the creator, I said, but God the Son is the agent of creation, which explains texts like Col. 1.16; Jn. 1.1; Heb. 1.3. And the texts you quoted about the Spirit doesn't involve Him as an agent of creation. Rather, the Spirit hovered over the waters; He is not playing an agency role in creation. Job 26.13 is an allusion to God's conquering of the forces of chaos, not of the Spirit's role in creation.

> You cannot say the Father alone is Creator.

I never said the Father alone is Creator. I said the Father was the creator and the Son was the agent of creation.

> you cannot say the Father alone is YHWH, the "I am".

I never said the Father alone is YHWH. Jesus also identifies as YHWH. They share a unified essence, though they differ in their roles.

> ** Redeemer **

As redeemer, Jesus is the one who died on the cross to redeem of from our sins. It is the blood of Christ, not the blood of the Father or of the Spirit, that redeems us. It is role the son fulfills that is not a function of either the Father or the Spirit. Jesus is the only one who was slain.

> you cannot assign "Indweller" as a unique operation or role of the Spirit alone

I did not assign it to the Spirit alone, as you mentioned the reference in John et al. But the Spirit is the Paraclete, a role the Father doesn't have. The Spirit intercedes for us with the Father, a role the Father doesn't have.

> The true doctrine does not differentiate the Persons by their activity

I believe you are wrong, by the evidence of the Scriptures.

> These distinctions are eternal and immutable

I agree that the distinctions are eternal and immutable, but not as you have outlined and understood them.

If you posit different activities in the Godhead, then you posit different persons, per St. Gregory Nazianzus, "On Not Three Gods" [url]https://www.newadvent.org/fathers/2905.htm[/url].

Creator

You cannot say that the Father is the Creator distinctly, as though this does not apply also to the Son or the Spirit, since of the Son it is written, "For by him were all things created...all things were created by him, and for him." (Col 1:16) And again, "He was in the world, and the world was made by him..." (John 1:10), and again, "He [that is, the Father] spoke [here we see the Word] and they came to be, He commanded, and they were created." (Psalm 33:9 BST)

Nor was the Spirit absent from the one act of Creation, for even in the beginning, "the Spirit of God moved upon the face of the waters" (Gen. 1:2) And again, "By his spirit he hath garnished the heavens" (Job 26:13), and, "The Spirit of God hath made me, and the breath of the Almighty hath given me life." (Job 33:4) And, "Thou sendest forth thy spirit, they are created: and thou renewest the face of the earth." (Ps. 104:30)

So the Creation is one act, and the actor is one, because the Power is one, and the energy, and the result -- all one. Therefore, the whole Godhead is the Creator: the Father is Creator, the Son is Creator, and the Spirit is Creator. You cannot say the Father alone is Creator.

I AM / YHWH

Likewise, you cannot say the Father alone is YHWH, the "I am". You yourself say that by this you mean, "existence is core to his nature. He just is." Yet if this is a property of nature, you must admit that this is shared among the Three, for it is the community of nature that indicates the unity. If you divide the nature, you divide the Godhead into three gods. But let's not only examine it logically; let's listen also to the Holy Scripture. In it, we hear the Son say of Himself, "Verily, verily, I say unto you, Before Abraham was, I am." (John 8:58) And, more than the name, the concept: "For as the Father hath life in himself; so hath he given to the Son to have life in himself." (John 5:26)

** Redeemer **

Furthermore, you cannot say of the Son, that He is the Redeemer, if by this you intend to differentiate His Person from the Father and the Spirit. For the Father is also the Redeemer, and the Holy Spirit as well. "And they remembered that God was their rock, and the high God their redeemer." (Ps. 78:35) And again, "Thou, O LORD, art our father, our redeemer..." (Is. 63:16) Neither is the redemption of Christ without the Spirit, for, "thou wast slain, and hast redeemed us to God by thy blood" (Rev. 5:9) -- that is, "the blood of Christ, who through the eternal Spirit offered himself without spot to God..." And again, "...grieve not the holy Spirit of God, whereby ye are sealed unto the day of redemption" (Eph. 4:30). So the work being one, and accomplished by the entire Godhead, "Redeemer" cannot be a differentiator amongst the Persons.

** Indweller **

Furthermore, you cannot assign "Indweller" as a unique operation or role of the Spirit alone, since the Son says, "If a man love me, he will keep my words: and my Father will love him, and we will come unto him, and make our abode with him" (John 14:23). St. Paul confirms: "That Christ may dwell in your hearts by faith..." (Eph. 3:17) St. John also confirms this word, saying (of the Father specifically): "And he that keepeth his commandments dwelleth in him, and he in him." (1 John 3:24) So then it is not only the Spirit, but the Father and the Son as well, who indwell. This cannot be a distinguishing mark, then, of only one of them.

** True Doctrine **

The true doctrine does not differentiate the Persons by their activity, which is one; nor by the results, which are one; nor by the energy, which is one; nor by the will, which is one; nor by the mind, which is one. Rather, we have learned to differentiate the Persons by their mode of existence only. Namely, that the Father is without cause, the Son is begotten of the Father, and the Spirit proceeds from the Father.

These distinctions are eternal and immutable, and without reference to Creation, since the Father is eternally the Father of the Son (else He would not be called "father"); the Son is eternally "the Son" because He is begotten of the Father; and the Spirit is the Spirit of Life from the proceeding from the Father and resting in the Son, which the Father gives to the Son "without measure". There is no time when the Son was not, and therefore there is no time when the Spirit was not proceeding from the Father to the Son.

They all exist necessarily, and all are uncaused. They are identical in essence, they are distinct in roles. It's not like they manifest themselves in different ways, but that they each have their role within the one monotheistic Godhead.

The Father is the Creator. He is YHWH, the "I am," meaning existence is core to his nature. He just is. No one or nothing was before Him, and nothing caused His existence. The Father is the Person we pray to. He is the sender: He sent Jesus, and He sent the Holy Spirit.

The Son is the Sent One. The Father sent Him. He was the agent of creation. He came to Earth in the flesh and died for our sins. He is the Redeemer.

The Holy Spirit is also a sent one. He is the Indweller—the One who lives in us. He guides us into truth, convicts us of sin, and makes us holy unto God.

In what sense are the persons of the trinity distinct from one another? In virtue of what are they not identical?