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Vladimir_Nesov comments on The Importance of Self-Doubt - Less Wrong
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Your observations (of people claiming to having seen an angel, or a kangaroo) are distinct from hypotheses formed to explain those observations. If in a given case, you don't have reason to expect statements people make to be related to facts, then the statements people make taken verbatim have no special place as hypotheses.
"You don't have reason to expect statements people make to be related to facts" doesn't mean that you have 100% certainty that they are not, which you would need in order to invoke privileging the hypothesis.
Why do you have at most 99.999999999% certainty that they are not? Where does that number one-minus-a-billionth come from?
The burden of proof is on the one claiming a greater certainty (although I will justify this later in any case.)
Now you are appealing to impossibility of absolute certainty, refuting my argument as not being that particular kind of proof. If hypothesis X is a little bit more probable than many others, you still don't have any reason to focus on it (and correlation could be negative!).
In principle the correlation could be negative but this is extremely unlikely and requires some very strange conditions (for example if the person is more likely to say that Islam is true if he knows it is false than if he knows it is true).