I still think you misrepresent Calvinism, and I see a difference between reasoning in general and logic, a difference I think you don't perceive. Logic is the most basic form of truth. Either a premise is true or false, there is no middle ground. If a premise is true, then it is true, if it is false, then it is not true. That is logic. It's so basic, and fundamental that it is necessarily true. You shouldn't concede contradiction where it might be that you just don't comprehend the solution.
The trinity is not a logical paradox, There is a difference between the concepts of God and Person, so the fact that one God is revealed in 3 Persons is not a paradox. if it was one God and three Gods, then that would be a paradox. I don't claim to fully understand it, but I can see that it is not self refuting. If any being is consistent, it would have to be God. you've heard the phrase: inconsistency is the sign of a failed argument?
If you say that the trinity is a paradox, you are making a very specific claim about it, that it is unreasonable, inconsistent, illogical.. Why make such a bold claim about something so mysterious if you don't have scriptural support to say that it is a logical paradox rather than just a mystery?