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1. Proof (by your meaning) emphatically does NOT equal belief.
2. No proof or evidence or anything else is irrefutable, in fact, irrefutability is a hallmark of being unscientific.
3. Proof. Is. Strictly. A. Mathematical. Concept.
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Perhaps I wasn't clear, but what I meant by 'proof' is something that makes you go "Hey, that makes a lot of sense." Proof is the little bit of puzzle that fits in to complete the picture... or at least, make it more complete than it already is.