I'll reserve judgment about the nature of God, but "from the Biblical point of view", I do see some shortcomings to this basis of reasoning , that the notion of a Trinity is "un-biblical". It would appear that there is not so much a Biblical point of view as there is a point of view imposed on the Bible.
In the book of Genesis, chapter one, the Lord relates the events of the creation in the form of an editorial "we". "Let us make man in our own image and likeness..."
And then in chapter 18 of the same book starting from the first verse:
"Yahweh appeared to (Abraham) at the Oak of Mamre while he was sitting by the entrance of the tent during the hottest part of the day. He looked up and there he saw three men standing near him. As soon as he saw them he ran from the entrance of the tent to greet them and bowed to the ground. "My Lord, if I find favor with you, please do not pass your servant by. Let me have a little water brought...
"They replied, 'Do as you say.'
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That would appear to me as quite clear from a Biblical point of view - and I have sat through hours of arguments that were of much more tenuous nature or connection to text.
Then, of course, there is nearly all the Gospel of John. A man who speaks of God as his Father, in the 8th chapter, 58th verse says that "before Abraham ever was, I am". His audience reportedly sensed the drift of what he was saying because they picked up stones from the Temple courtyard to express their rebuttal.
It is also in the Gospel of John that the Samaritan woman says to Jesus in chapter 4 that "I know that the Messiah is coming and when he comes he will explain everything." Jesus answers that "That is who I am, I who speak to you."
So, it is the contention of many who have replied to this query:
On the matter of a Trinity or even a Duality, how could Christians have ever been confused if they had studied their Bible?
In chapter 5 of John, it's almost as though Jesus laments in the text about the dilemma: "You pore over the scriptures, believing that in them you can find eternal life; it is these scriptures that testify to me, and yet you refuse to come to me to receive life!"
As sceptical as I am about many things I read, I do find it remarkable that this text predicts a Bible as it will someday be construed. For whenever a certain John put the text to scroll, there was a time before that that there was no Gospel of John and a message of a Messiah coming was all that much less clear.
But coming back to the subject, in combination with the citations John gives from Isaiah and other OT texts, as do other apostolic writers, and then the additional passages that they do not connect directly such as the ones I cited above, then you have the basis for a Trinitarian view of God.