How do Trinitarians explain that the Logos is a person?

In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. Through him all things were made; without him nothing was made that has been made. In him was life, and that life was the light of all mankind. The light shines in the darkness, and the darkness has not overcome it.

There was a man sent from God whose name was John. He came as a witness to testify concerning that light, so that through him all might believe. He himself was not the light; he came only as a witness to the light.

The true light that gives light to everyone was coming into the world. He was in the world, and though the world was made through him, the world did not recognize him. He came to that which was his own, but his own did not receive him. Yet to all who did receive him, to those who believed in his name, he gave the right to become children of God— children born not of natural descent, nor of human decision or a husband’s will, but born of God.

The Word became flesh and made his dwelling among us. We have seen his glory, the glory of the one and only Son, who came from the Father, full of grace and truth. (John 1:1-14, NIV)

Trinitarians would say that the Logos is a person because of these highlighted phrases:

1. The Word/Logos is God. Christians believe in a personal God, so if the Logos is God then it is a person too.
2. The Word made everything. Impersonal things don't make stuff.
3. The Word became flesh and dwelt on the earth. Impersonal words don't become flesh and live on the earth.

The Author's Argument

If we read carefully, the author is arguing that "the Word" (ο λογος) in John 1:1-3 does not refer to the person of Jesus Christ because that was not what John intended the reader to understand. The rest of the argument in the video consists in support for believing that this was not John's intent.

This is an interesting argument in that an implicit premise is that whatever John intended to express in writing the Gospel was true. Perhaps this is a subtle point, but it indicates that the author is appealing to the authority of the Apostle John and not to the authority of the Gospel text itself.

Validity of the Author's Argument

For an argument to be valid, it is impossible for one or more of the argument's premises to be true and for the conclusion to be false. In this case:

(Premise P1) Whatever the Apostle John sought to express in the Gospel account he wrote must be true

(Premise P2) The Apostle John did not seek to express that "the Word" in the beginning of the Gospel referred to the person of Jesus Christ

(Conclusion C) Therefore, "the Word" in the beginning of the Gospel according to John does not refer to the person of Jesus Christ

This is a valid argument. There is no way for the conclusion to be false if both premises are true.

Soundness of the Author's Argument

For an argument to be sound, it must be valid and all of the premises must actually be true. Here, I think, is where the problems lie.

As proof that John did not intend "the Word" to refer to the Person of Jesus Christ, the author offers the following:

(P3) The text does not actually refer to "Jesus", but rather to "the Word"

(P4) The text does not actually refer to "the Son", but rather to "the Word"

(P5) The text does not later say (1:14) that "Jesus" became flesh, but rather that "the Word" became flesh

(P6) The text does not later say that "the Son" became flesh, but rather that "the Word" became flesh

(P7) Although English translations state All things were made by him, etc. (v.3), the Greek pronoun (αὐτός) can also refer to an inanimate object (e.g. "the Word")

(P8) Genesis 1:3 states And God said, Let there be light

(P9) The author of Hebrews states (11:3) The ages were formed by the Word of God

(P10) Psalm 148:5 states He commanded and the heavens were created

(P11) The Apostle Paul states He called things that do not exist into existence (Romans 4:17)

(P12) Psalm 33:9 states He spoke and it was; he commanded and it came to stand

(P13) Psalm 33:6 states By the Word of the Lord the Heavens were made

(P14) The Apostle Peter states (2 Peter 3:5) The heavens and earth came to exist by the word of God

To all of the above, the author asks, "What do you think John has in mind?" He concludes:

John is referring to God's spoken Word

This particular argument, unlike the greater argument, is not valid. Without exception, each of the Scriptures the author cites can be interpreted in exactly the same way in which Trinitarians interpret John 1:1. For example, Psalm 33:6 - By the Word of the Lord the heavens were made - can be understood to mean that the heavens were made by the Son; Genesis 1:3 can be understood to mean that it was Jesus - who is Himself God, co-equal with the Father - who actually said the words, "Let there be light"; etc.

Furthermore, since the author's argument rests solely on the intent of John, we (and he) should really examine the entire corpus of John's works, including the rest of the Gospel, the Book of Revelation, and his epistles (all of which are generally attributed to him). The following passages of attest to John's understanding that Christ, did, in fact, possess equality of divinity and honor with the Father:

And we know that the Son of God is come, and hath given us an understanding, that we may know him that is true, and we are in him that is true, even in his Son Jesus Christ. This is the true God, and eternal life (1 John 5:20).

For as the Father raiseth up the dead, and quickeneth them; even so the Son quickeneth whom he will (John 5:21).

For as the Father hath life in himself; so hath he given to the Son to have life in himself (John 5:26)

That all men should honour the Son, even as they honour the Father. He that honoureth not the Son honoureth not the Father which hath sent him (John 5:23)

I and my Father are one (John 10:30)

Believe me that I am in the Father, and the Father in me (John 14:11; 10:38)

And all mine are thine, and thine are mine; and I am glorified in them (John 17:10)

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 1:8)

And now, O Father, glorify thou me with thine own self with the glory which I had with thee before the world was (John 17:5)

All of these passages debunk any speculation that John somehow considered "the Word" to refer to something other than the second person of the Trinity.

The author's argument is unsound.