Of all the mysteries of the Bible, surely the doctrine of the Trinity is right at the top of the list. How can Father, Son, and Holy Spirit be three distinct persons, yet one God? The first thing I would say is that since God is God, He is incomprehensible — that is, God is greater than our ability to understand Him. I cannot even grasp all of what heaven will be, let alone the God who has provided a way for me to be there. If God is as great as the Bible says, then God is greater than my mind can conceive. Thus, I would expect that there would be difficult things for me to grasp about God, and thus about the Trinity. The Trinity is a word that is not actually found in the Bible, but is the term theologians have chosen to describe the persons and the relationship of the Godhead. We know that Father, Son, and Holy Spirit are all called God. We know that there are these three persons, and yet only one God. Precisely how all this works is beyond us, but we accept these things as true.
The same thing could be said of the Savior’s two natures — for He is both divine and human, fully God and fully man. How this works is a mystery, but we believe it to be true. Thus, I believe that the Son of God came to the earth in human flesh (Philippians 2:5-8), and in submission to the Father’s will died in the sinner’s place.
I think you have attempted to deal very logically with this matter, and that is to be commended. The problem that I see is that logic probably won’t take us as far as we would like. It may even get us into more troubles. (This is not meant as an excuse for sloppy thinking, but only to acknowledge the limits of our intellect.)
Unfortunately, when I did the series on the Attributes of God (“Let Me See Thy Glory”) which is available on the BSF Website, I did not include a chapter on the Trinity. I’m almost certain that J. I. Packer’s book, Knowing God, deals with the Trinity.
Hampton Keathley has an article on the Trinity on the Biblical Studies Foundation Website. The address is: