The Great God Logic

THE GREAT GOD LOGIC

I have an idol. I worship a false god. I put my trust in the great god: Logic.
I have known Logic since I was a child. In college, I took Logic courses in the Philosophy department, the Mathematics department, and the Computer Science department — at the same time! I have learned so much about Logic, from propositional Logic to nonmonotonic Logic. And Logic is true. Logic is right. It never misleads me or deceives me. I have complete trust in Logic.
This is a problem, because I also want to worship the great God: The Lord. So the contradictions in the Bible trouble me. If the Bible really was written by God, then how can it say things that Logic declares to be impossible? Should I trust in Logic or God? How can I choose?
It seems to me that most Christians are not very good at Logic. For example, one of the claims I hear Christians say a lot is “If there is one thing in the Bible that is wrong, it might as well all be wrong.” This is flawed Logic. It essentially says:
∃[ F(x) ] ⇒ ∀[ F(x) ]
x∈B                                    x∈B
where B is the Bible, and F(x) means “x is false”. This is not a valid statement. These Christians are confused.

I believed that for a long time...

But then I realized that, in a Christian’s mind, there are no errors in the Bible. So,
¬∃[ F(x) ]
    x∈B
is true for them. That means that the above implication has a false premise, which makes the implication true. Oh my goodness!
Logic has deceived me. Logic has led me astray. I really can’t trust in Logic.
But I can trust in God. Everything God says is true... by definition. If God says it, then that makes it true. If God says 1 = 2, then it is true. If He says 1 ≠ 2, then that is true. And if He says both of them, then both of them are true. If God and Logic disagree, then God is right and Logic is wrong.
All I need is faith...