Strong enough evidence can overcome a very low prior, yes. And this doesn’t have to take very many observations.
But more instances do not necessarily stack like that. That can only happen to the degree they are independent sources. For example, suppose you write a dubious claim in a book, then you make nine more copies of the book. Does that make the claim ten times more likely to be true? What if it’s a hundred thousand copies? Did that help?
Of course it doesn’t! You’re re-counting the same evidence. The contribution of the nine books is completely screened off by the first; the new books have no new information.
I think the cases of miracle reports like weeping icons are similarly not independent enough. A thousand weeping icons is barely more evidence than one. It just means that the hoaxers copied each other’s scam.
Furthermore, we already know that some similar instances of miracles were hoaxes. Shouldn’t every new hoax report lower my prior that miracles are real?
″ but (say) ten times almost nothing is still almost nothing”
Ok, cool. So if your prior will be one millionnth I will need just six miracles :)
Strong enough evidence can overcome a very low prior, yes. And this doesn’t have to take very many observations.
But more instances do not necessarily stack like that. That can only happen to the degree they are independent sources. For example, suppose you write a dubious claim in a book, then you make nine more copies of the book. Does that make the claim ten times more likely to be true? What if it’s a hundred thousand copies? Did that help?
Of course it doesn’t! You’re re-counting the same evidence. The contribution of the nine books is completely screened off by the first; the new books have no new information.
I think the cases of miracle reports like weeping icons are similarly not independent enough. A thousand weeping icons is barely more evidence than one. It just means that the hoaxers copied each other’s scam.
Furthermore, we already know that some similar instances of miracles were hoaxes. Shouldn’t every new hoax report lower my prior that miracles are real?