The narrator suggests that the main purpose in telling the story is to "unburthen [his] soul." He suggests that it would be impossible for anyone to believe his story and that even he would be unable to accept it had he not experienced it and felt it and heard it and seen it. He is writing the story the night before he expects to be executed.
He also suggests that perhaps someone with a clear intellect and better understanding of things can read the story and figure out how one thing easily led to another. To him the story does seem extraordinary and unbelievable but maybe, he writes, someone "more calm, more logical, and far less excitable" can read the story and find a logical progression from one thing to the next.
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