Your argument is bogus since everyone has to use logic to understand language including the language used in the Scriptures.
Since words would have no meaning without logic, words or language presupposes logic. The rules of thought or words such as the law of contradiction or non-contradiction indicate that a word must mean one thing in a certain context and not its contradiction. Without logic, all words would be no more than the chattering of monkeys. Logic is not an axiom prior to or independent of God because all true reason depends on God's thinking and His revelation to man.