Does a doctrine have to be logical to be true?

I have recently seen it stated that a doctrine does not have to be logical to be true. That would mean that a doctrine can be true even though it is illogical. I'm interested in teasing apart what this might mean. What would a doctrine look like if it was illogical? First, we need to define the term "logical". I understand the term "logical" to mean 'conforming to or consistent with the rules of logic'. That's really helpful! What does it mean for something to conform to or be consistent with the rules of logic? Logic is defined by the Encyclopaedia Britannica Dictionary as 'a science that deals with the rules and tests of sound thinking and proof by reasoning.' According to this definition, the heart of logic is 'sound thinking'. The rules and tests of logic are rules and tests that tell us whether or not our thinking is sound or not. For something to be illogical, then, it would mean that something fails one or more rules or tests for sound thinking. Applied to a doctrine: to say that a doctrine might be true but illogical is to say that a doctrine might be true but fail one or more rules for sound thinking. If a doctrine can be true but fail one or more rules for sound thinking, then any doctrine stated in any way could be true. It would mean that sound thinking is not a reliable way to test the truth of a doctrine. But what else is there? If we give up the requirement of sound thinking for a doctrine to be true, then we collapse into complete relativism without the ability to discern between doctrinal assertions. Therefore, I conclude that a doctrine must be logical to be true.