Logician –
Not sure what you mean by a weak perception of self. That one plus one equals two is more real to me than something I see with my own eyes, simply because the fact is my eyes are fallible. Now, it is true that my whole perception of logic may be false, but within my perception, logic is of a higher level than anything else, and my perception is all I can go with, because it is all I perceive.
I understand that we are not capable of comprehending things such as God and the world coexisting but not being able to comprehend something does not indicate a contradiction. Moreover, we cannot fathom God’s existence so essentially it is not possible for this to be a logical problem.