If the doctrine of Trinity is illogical, then by the same logic, everything else is illogical.
Now, there are some who consider it to be an evidently foolish thing to believe in the reality of God as One and yet three persons. They say, 1+1+1=3 in every case, or else mathematics is absurd. But, let me show you by an ancient argument, once again, that mathematics can’t explain reality as it is. I will adapt only one argument from the many that a Greek philosopher of the 5th century BC, Zeno of Elea, used in order to defeat the then philosophers of mathematics, the Pythogoreans. The argument is commonly referred to as The Dichotomy.
Suppose a runner is standing at point A and must reach point B in order to finish the race. The only way he can reach point B is by reaching the halfway point, say A1, between A and B, before reaching B. But then the only way he can reach halfway point A1 is by reaching the halfway point, say A2, between A and A1, and so on ad infinitum in order to finish the course. Thus in order for the runner to reach point B, he will have to traverse an infinite number of points in a finite time, which is impossible, because space becomes infinitely divisible and one has to keep on reaching half-ways before reaching any other point, infinitely; thus, reaching nowhere. Therefore, though empirically apparent, logically, motion is absurd.
Well, but if motion is absurd, then the entire universe, all phenomena, is absurd. If so, what is logical after all?
Conclusion: If logic can’t logically explain empirical realities such as continuity of identity in change, unity in plurality, and abstracts in concrete, how can it even begin to understand God who is Spirit? Reason is certainly not above faith. But, as far as the limits of reason exist, faith is certainly expected to not be irrational.