The reason why Bob should be much more skeptical when Alice says “I just got HHHHHHHHHHHHHHHHHHHH” than when she says “I just got HTHHTHHTTHTTHTHHHH” is that there are specific other highish-probability hypotheses that explain Alice’s first claim, and there aren’t for her second. (Unless, e.g., it turns out that Alice had previously made a bet with someone else that she would get HTHHTHHTTHTTHTHHHH, at which point we should suddenly get more skeptical again.)
Bob’s perfectly within his rights to be skeptical, of course, and if the number of coin flips is large enough then even a perfectly honest Alice is quite likely to have made at least one error. But he isn’t entitled to say, e.g., that Pr(Alice actually got HTHHTHHTTHTTHTHHHH | Alice said she got HTHHTHHTTHTTHTHHHH) = Pr(Alice actually got HTHHTHHTTHTTHTHHHH) = 2^-20 because Alice’s testimony provides non-negligible evidence, because empirically when people report things they have no particular reason to get wrong they’re quite often right.
(But, again: if Bob learns that Alice had a specific reason to want it thought she got that exact sequence of flips, he should get more skeptical again.)
So, now suppose Alice says “I just won the lottery” and Amanda says “I just saw a ghost”. What should Bob’s probability estimates be in the two cases?
Empirically, so far as I can tell, a good fraction of people who claim to have won the lottery actually did so. Of course people sometimes lie, but you have to weigh “most people don’t win the lottery on any given occasion” against “most people don’t falsely claim to have won the lottery on any given occasion”. I guess Bob’s posterior Pr(Alice won the lottery) should be somewhere in the vicinity of 1⁄2. Enough to be decently convinced by a modest amount of further evidence, unless some other hypothesis—e.g., Alice is trying to scam him somehow, or she’s being seriously hoaxed—gets enough evidence to be taken seriously (e.g., Alice, having allegedly won the lottery, asks Bob for a loan to be repaid with exorbitant interest).
On the other hand, there are lots and lots of tales of ghosts and (at best) very few well verified ones. It looks as if many people who claim to have seen ghosts probably haven’t. Further, there are reasons to think it very unlikely that there are ghosts at all (e.g., it seems clear that human thinking is done by human brains, and by definition a ghost’s brain is no longer functioning) and those reasons seem quite robust—they aren’t, e.g., dependent on details of our current theories of quantum physics or evolutionary biology. So we should set Pr(ghosts are real) extremely small, and Pr(Amanda reports a ghost | Amanda hasn’t really seen a ghost) not terribly small, which means Pr(Amanda has seen a ghost | Amanda reports a ghost) is still small.
Bob’s last comparison (claims of seeing ghosts, against actual wins of big lottery prizes) is of course nonsensical, and as long as one of it’s of the form “more claims of ghosts than X” it actually goes the wrong way for his purposes. What he wants is more actual sightings of ghosts and fewer claims of ghosts.
There’s a nonzero probability that the lottery is a complete scam, and the winners are entirely fictional. (The lottery in 1984 worked like this, but I’m not paranoid enough to believe this is true in real life.)
Sure, but a small enough one that I don’t think it makes much difference to anything here. I might be missing something, though; if you disagree, would you like to say why?
Slightly more seriously: yeah, I agree that human thinking could happen on other substrates besides human brains, but no instances of that have been reported so far, and we don’t know of any plausible mechanism that would make it happen after the brain the thinking started off in has died, and in any case you’re just yanking my chain so I’ll shut up.
The reason why Bob should be much more skeptical when Alice says “I just got HHHHHHHHHHHHHHHHHHHH” than when she says “I just got HTHHTHHTTHTTHTHHHH” is that there are specific other highish-probability hypotheses that explain Alice’s first claim, and there aren’t for her second. (Unless, e.g., it turns out that Alice had previously made a bet with someone else that she would get HTHHTHHTTHTTHTHHHH, at which point we should suddenly get more skeptical again.)
Bob’s perfectly within his rights to be skeptical, of course, and if the number of coin flips is large enough then even a perfectly honest Alice is quite likely to have made at least one error. But he isn’t entitled to say, e.g., that Pr(Alice actually got HTHHTHHTTHTTHTHHHH | Alice said she got HTHHTHHTTHTTHTHHHH) = Pr(Alice actually got HTHHTHHTTHTTHTHHHH) = 2^-20 because Alice’s testimony provides non-negligible evidence, because empirically when people report things they have no particular reason to get wrong they’re quite often right.
(But, again: if Bob learns that Alice had a specific reason to want it thought she got that exact sequence of flips, he should get more skeptical again.)
So, now suppose Alice says “I just won the lottery” and Amanda says “I just saw a ghost”. What should Bob’s probability estimates be in the two cases?
Empirically, so far as I can tell, a good fraction of people who claim to have won the lottery actually did so. Of course people sometimes lie, but you have to weigh “most people don’t win the lottery on any given occasion” against “most people don’t falsely claim to have won the lottery on any given occasion”. I guess Bob’s posterior Pr(Alice won the lottery) should be somewhere in the vicinity of 1⁄2. Enough to be decently convinced by a modest amount of further evidence, unless some other hypothesis—e.g., Alice is trying to scam him somehow, or she’s being seriously hoaxed—gets enough evidence to be taken seriously (e.g., Alice, having allegedly won the lottery, asks Bob for a loan to be repaid with exorbitant interest).
On the other hand, there are lots and lots of tales of ghosts and (at best) very few well verified ones. It looks as if many people who claim to have seen ghosts probably haven’t. Further, there are reasons to think it very unlikely that there are ghosts at all (e.g., it seems clear that human thinking is done by human brains, and by definition a ghost’s brain is no longer functioning) and those reasons seem quite robust—they aren’t, e.g., dependent on details of our current theories of quantum physics or evolutionary biology. So we should set Pr(ghosts are real) extremely small, and Pr(Amanda reports a ghost | Amanda hasn’t really seen a ghost) not terribly small, which means Pr(Amanda has seen a ghost | Amanda reports a ghost) is still small.
Bob’s last comparison (claims of seeing ghosts, against actual wins of big lottery prizes) is of course nonsensical, and as long as one of it’s of the form “more claims of ghosts than X” it actually goes the wrong way for his purposes. What he wants is more actual sightings of ghosts and fewer claims of ghosts.
There’s a nonzero probability that the lottery is a complete scam, and the winners are entirely fictional. (The lottery in 1984 worked like this, but I’m not paranoid enough to believe this is true in real life.)
Sure, but a small enough one that I don’t think it makes much difference to anything here. I might be missing something, though; if you disagree, would you like to say why?
There are definitions about ghost brains..? 8-0
By definition, a ghost is of someone who has (bodily) died. By definition, to be bodily dead means to have a brain that is no longer functioning.
No love for uploads, I see :-D
They’ve never yet been known to leave ghosts.
Slightly more seriously: yeah, I agree that human thinking could happen on other substrates besides human brains, but no instances of that have been reported so far, and we don’t know of any plausible mechanism that would make it happen after the brain the thinking started off in has died, and in any case you’re just yanking my chain so I’ll shut up.
You didn’t even address the elderly vampires. Did you not read the post?
I don’t know whether Bob’s trolling, but I’m pretty sure you are.
[EDITED to add: I see someone downvoted you; it wasn’t me.]
Just joking, homie.
gjm is a good old chap, not a homie :-P
What is the probability of someone not reading the post and posting a comment which happens to use exactly the same cca 2500 characters as this?
Assuming at least 4 bits per character, the probability is at most 2^10000. Quite unlikely, if you ask me.
I hope I have addressed your concerns sufficiently.