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Thank you so very much, dear brother in Christ, for posting this new thread to discuss the Trinity!

My favorite Trinity passages from Scripture with emphasis:

But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his. - Romans 8:9

For unto us a child is born, unto us a son is given: and the government shall be upon his shoulder: and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace. – Isaiah 9:6

Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost: - Matthew 28:19

In my view, the problem arises whenever we mere mortals attempt to apply the Law of Identity (A=A and not B) to God. Indeed, the LDS doctrine does precisely that and the Trinity is rejected by that religion. And others reject the Trinity on those very logical grounds.

But man is not the measure of God!

The Laws of Logic are part of the creation, not a property or restriction on the Creator of them. We must lay them aside in our meditations on the Names of God.

And again, the Law of Identity does not apply to God.

If ye had known me, ye should have known my Father also: and from henceforth ye know him, and have seen him.

Philip saith unto him, Lord, shew us the Father, and it sufficeth us.

Jesus saith unto him, Have I been so long time with you, and yet hast thou not known me, Philip? he that hath seen me hath seen the Father; and how sayest thou [then], Shew us the Father?

Believest thou not that I am in the Father, and the Father in me? the words that I speak unto you I speak not of myself: but the Father that dwelleth in me, he doeth the works.

Believe me that I [am] in the Father, and the Father in me: or else believe me for the very works' sake. - John 14:7-11

And again,

The Revelation of Jesus Christ, which God gave unto him, to shew unto his servants things which must shortly come to pass; and he sent and signified [it] by his angel unto his servant John: Who bare record of the word of God, and of the testimony of Jesus Christ, and of all things that he saw. Blessed [is] he that readeth, and they that hear the words of this prophecy, and keep those things which are written therein: for the time [is] at hand.

John to the seven churches which are in Asia: Grace [be] unto you, and peace, from him which is, and which was, and which is to come; and from the seven Spirits which are before his throne; And from Jesus Christ, [who is] the faithful witness, [and] the first begotten of the dead, and the prince of the kings of the earth. Unto him that loved us, and washed us from our sins in his own blood, And hath made us kings and priests unto God and his Father; to him [be] glory and dominion for ever and ever. Amen.

Behold, he cometh with clouds; and every eye shall see him, and they [also] which pierced him: and all kindreds of the earth shall wail because of him. Even so, Amen.

I am Alpha and Omega, the beginning and the ending, saith the Lord, which is, and which was, and which is to come, the Almighty. - Revelation 1:1-8

And again,

Wherefore I give you to understand, that no man speaking by the Spirit of God calleth Jesus accursed: and [that] no man can say that Jesus is the Lord, but by the Holy Ghost. –I Corinthians 12:3

God's Name is I AM.