In the theist-atheist discussion, how do you personally understand the difference and/or value of these perspectives: “absence of evidence isn’t evidence of absence” and “extraordinary claims require extraordinary evidence”?

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I personally see one of these claims as stretches of the ability of reason to comprehend things it just can’t understand, and the other as self-evident. Let’s take them in turn. Absence of evidence isn’t evidence of absence would appear to be the more palatable of logical assertions to the believer.