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.
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.