A million people is certainly more persuasive than one. But when we’re talking about a claim that has no other evidence supporting it, a far greater degree of incredulity is warranted. (By contrast, “I saw an brown dog” has LOADS of evidence supporting it to begin with, such as the fact that you’ve seen hundreds of dogs so you know they exist and are common, and that people see them from time to time).
More to the point, in this case, we don’t have a million people saying “I saw God.” We have millions of people saying “our parents said their parents said their parents said their parents heard from their parents that a while ago 1.5 million people saw God.” When you have millions of people sharing and retelling a story over the course of generations, I believe it is more likely that story gets distorted over time rather than remains constant. This was my point, not that I should ignore 1.5 people who claim to have witnessed an event.
Gwern commented because you said something technically wrong, even though it was essentially right. You denied that “having a large number of people telling a story makes it more likely the story is true”. But having a large number tell the story does make it more likely to be true. After all, conditioning on the story’s being false makes it less likely that a large number would be telling it (out of all possible false stories).
But your primary point remains: Often, even after conditioning on a story’s being told by millions, the probability of the story’s being true remains vanishingly small.
A million people is certainly more persuasive than one. But when we’re talking about a claim that has no other evidence supporting it, a far greater degree of incredulity is warranted. (By contrast, “I saw an brown dog” has LOADS of evidence supporting it to begin with, such as the fact that you’ve seen hundreds of dogs so you know they exist and are common, and that people see them from time to time).
More to the point, in this case, we don’t have a million people saying “I saw God.” We have millions of people saying “our parents said their parents said their parents said their parents heard from their parents that a while ago 1.5 million people saw God.” When you have millions of people sharing and retelling a story over the course of generations, I believe it is more likely that story gets distorted over time rather than remains constant. This was my point, not that I should ignore 1.5 people who claim to have witnessed an event.
Gwern commented because you said something technically wrong, even though it was essentially right. You denied that “having a large number of people telling a story makes it more likely the story is true”. But having a large number tell the story does make it more likely to be true. After all, conditioning on the story’s being false makes it less likely that a large number would be telling it (out of all possible false stories).
But your primary point remains: Often, even after conditioning on a story’s being told by millions, the probability of the story’s being true remains vanishingly small.