When I was a visiting professor in Turkey I occasionally got into discussions with my fellow faculty members, all of them Muslims, about differences between Islam and Christianity. The Trinity was always a sticking point. They wanted to know what was the logic behind it. The problem is, there is no logic behind it. It's a brute fact, no more the consequence of reason than any other brute fact. Again, we know it not because we can deduce it, but because it was revealed to us.
Yes, exactly. For a Christian the relation between Father and Son and between Father, Son, and Spirit are revealed facts (and lived realities) to be experienced and affirmed, serving as premises for deduction rather than as conclusion to an argument. However once the revealed premises are accepted in faith, the relation between the divine Persons can be expressed to human understanding in terms of analogy to the human psyche’s internal self-communication between different faculties of the same psyche, as Augustine developed in “On the Holy Trinity” Book 10 and Aquinas later elaborated.