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paper-machine comments on The Dilemma: Science or Bayes? - Less Wrong
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So when you said what I quoted in the great-grandparent, that is, "[10^6 cases aren't] going to be accepted as ... particularly valid evidence", you meant that it would be accepted as evidence, that is, it belongs to your second tier of belief? That's what's bothering me.
Sorry, I guess at that point I was just thinking of the first tier of belief when making that comment.
But I think it's also true that most notable conjectures have, in addition to verification of some cases, some sort of handwavy reason why we would believe them, such as a sketch of a proof but with many holes in it, and this is at least important as the other kind of evidence.