Logic can be used to deduce that there is a God, so we need to avoid saying things like "logic will inevitably lead to atheism" (I know you didn't say this, but I feel this is what you're getting at. Please correct me if I'm wrong). There is much more at work here than just a simple gathering of facts. There are fallacies that logic can fall into:
Cheese wheels are round and yellow.
The moon is round and yellow.
The moon is made of cheese.
There needs to be a modicum of reason behind the use of logic.
Cheese wheels are round and yellow.
The moon is round and yellow.
The moon is made of cheese.
There needs to be a modicum of reason behind the use of logic.
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