Funny, my gut reaction is that this is extremely true.
If 1 or a million people tell me some thing, there are exactly 3 options available to me:
increase my belief in that thing by some amount
leave my belief unchanged
decrease my belief
Suppose my 50 neighbors—all nice normal folks—tell me in passing that they saw my brown dog loose in the morning. Why would I decrease my belief? Wouldn’t that be incredibly perverse?
And why would I ignore them and leave my belief unchanged? I don’t discriminate against any other information source. If my eyes tell me 50 times that my brown dog is loose, I don’t go ‘phsaw, who cares what you guys think’. I increase my belief that my dog is loose.
About any proposition in general, the more people tell you it, the more you believe it. Let’s generalize this even more: the more data you have telling you to believe some proposition, the more you believe that proposition. (What a shocking conclusion.)
Now, sometimes there are conspiracies, but they are extremely rare and unlikely and require involved explanations (like explaining the existence of religious belief in general does). Those Jews are right that the more testimony the greater the likelihood, but this truth does not prove the things they want it to prove.
tl;dr: your post is ill-founded and you need to explain why the Bayesian solution to the raven paradox is wrong.
No. That link is about a highly specific tiny statement with tons of more germane evidence to take into account, which drowns the epsilon evidence. I am not talking about any specific point.
Likewise, the raven paradox has tons of more germane evidence which outweighs the logical point of observing a non-raven if you deliberately miss the point.
I feel like I’m trying to discuss the trolley paradox, and everyone is going, ‘no, toss over your backpack instead of pushing the fat man or letting them die! Isn’t it obvious there are tons of other things you could do?’
(Someone help me out here, we must have an article about how people love to finesse logical or philosophical arguments in this sort of way. Oh wait, I guess we do: The Least Convenient Possible World.)
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.
Funny, my gut reaction is that this is extremely true.
If 1 or a million people tell me some thing, there are exactly 3 options available to me:
increase my belief in that thing by some amount
leave my belief unchanged
decrease my belief
Suppose my 50 neighbors—all nice normal folks—tell me in passing that they saw my brown dog loose in the morning. Why would I decrease my belief? Wouldn’t that be incredibly perverse?
And why would I ignore them and leave my belief unchanged? I don’t discriminate against any other information source. If my eyes tell me 50 times that my brown dog is loose, I don’t go ‘phsaw, who cares what you guys think’. I increase my belief that my dog is loose.
About any proposition in general, the more people tell you it, the more you believe it. Let’s generalize this even more: the more data you have telling you to believe some proposition, the more you believe that proposition. (What a shocking conclusion.)
Now, sometimes there are conspiracies, but they are extremely rare and unlikely and require involved explanations (like explaining the existence of religious belief in general does). Those Jews are right that the more testimony the greater the likelihood, but this truth does not prove the things they want it to prove.
tl;dr: your post is ill-founded and you need to explain why the Bayesian solution to the raven paradox is wrong.
Which is very poor practice if they were all convinced by each other.
Tell me, of the millions of things that you have been told, have more than half been about things where they were all convinced by each other?
Second question: do you not understand the relevance of the raven paradox? Epsilon evidence is still non-zero evidence. Bite that tiny bullet!
There’s still a chance, right?
No. That link is about a highly specific tiny statement with tons of more germane evidence to take into account, which drowns the epsilon evidence. I am not talking about any specific point.
Likewise, the raven paradox has tons of more germane evidence which outweighs the logical point of observing a non-raven if you deliberately miss the point.
I feel like I’m trying to discuss the trolley paradox, and everyone is going, ‘no, toss over your backpack instead of pushing the fat man or letting them die! Isn’t it obvious there are tons of other things you could do?’
(Someone help me out here, we must have an article about how people love to finesse logical or philosophical arguments in this sort of way. Oh wait, I guess we do: The Least Convenient Possible World.)
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.