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Muslims deny the Christian doctrine of the Trinity. They are so strict in their monotheism that no plurality within God can possibly exist. Many of them erringly assert that the Trinity is really a deceptive doctrine of three gods. Of course it is not, but that does not stop them from claiming it is not rational nor does it stop them from misrepresenting it.
Muslims often appeal to logic as a verification for their theological systems. They claim that Islam is true and Christianity false and that the Trinity simply doesn't make sense. In spite of their claims, the doctrine of the Trinity is not illogical at all. In fact, most people believe in trinities without even knowing it.
As a painter reveals part of himself, his style, what he is, etc., in his painting, so too, God has revealed part of Himself, His style, and what He is in His creation. Creation reflects, to a large degree, the qualities of God Himself. Let's take a look.
The universe is ordered; therefore, we know that God is a God of order.
The universe operates on laws; therefore, God is a God of law.
The universe has a beginning; therefore, God is the creator.
In mathematics, there is an infinity of numbers. In the universe there is an infinity of distance; Therefore, God the creator of the universe, is infinite.
Absolute truths exist in creation, (i.e., something can not be both itself and not itself at the same time); therefore, God is absolute truth.
The universe is comprised of three primary aspects: Space, Time, and Matter.
Space is comprised of height, width, and depth - a trinity - but each aspect is by nature space.
Time is comprised of past, present, and future - a trinity - but each aspect is by nature time.
Matter is comprised of solid, liquid, and gas - a trinity - but each aspect is by nature matter.
Therefore, we can conclude from looking at the universe, and God as its creator, that it is possible for God to have a trinitarian aspect to His nature since we see it in nature.
If it is fair to say that God may indeed be trinitarian in some aspect of His nature,
then God could easily be trinitarian in nature and still be the one and only God.
God could easily be a plurality and all aspects of this plurality, being of God, would be divine by nature.
Since God is self-aware, has a will, can speak, etc., then it follows that the plural aspects of God could share, in some way, those same qualities.
If this is possible, then why cannot part of God, since God is a plurality, become a man and add human nature to itself?
We can see that there are trinities in nature. So, why can't God be a trinity as well and creation simply be a reflection, in part, of His greatness? It is certainly possible. If the Trinity were illogical, then the possibility would not exist. There is no logical reason why the trinity can not be a reality. It is up to the Muslim to demonstrate a logical contradiction regarding the doctrine of one God in three persons. Simply stating it isn't logical or that it isn't possible proves nothing at all.
The Bible has declared that God is indeed a Trinity and that Jesus is both God and man (John 1:1, 14; Col. 2:9; etc.). Christians have a living redeemer. Christians have God as their savior.