kurt godel came out with a theorem which in essence proposed that logic could not explain the whole truth - as logic is a system that can be improved continuously, it is impossible for such system to explain the complete truth. if God completes truth then logic could never explain God. although it is possible to use logic when arguing about the existence of God, it may not be complete, as the system of God is complete whereas system of logic isn't.
as an example. think of the biggest number possible. infinity? what about infinity to the power of infinity. no? see. you can't... because there is no end to it.
without logic then one can only rely on guts - which can be wrong.
this is where i picked my nose.