The Greatest logic against God, these days, is Evolution. It is Evolution vs. God. The key to evolution is mutation. And mutation is random.
It follows no logic, no laws of the physical world. There is no science in mutation. It is an error in genetic replication.
It has a mind of its own. And it keeps changing. No patterns.
Patterns is what make this world logical. Anything that has no patterns is illogical.
Mutation has no logic, no patterns. Thus unscientific. Therefore Divine.