Since you cannot prove that errors in reasoning do not undermine all logical thought, then they must undermine it, correct?

For example, if I falsely conclude that I am a squirrel because I am mortal, I still cannot prove that I have undermined all logical thought. Simply put, logical though will still exist even though I believe that I am a squirrel. Therefore my error in thinking undermined logical thought?

Since you cannot prove that errors in reasoning do not undermine all logical thought, then they must undermine it, correct?
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