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Ok, I admit that science is hard. But about you ? How do you, personally, know what's a subversion of the natural order and what isn't ?
Which possibility do you think is more likely in this case: genuine miracle, or mass confirmation bias ? That's why I'd like you to clarify this:
Well, can you put a ballpark figure on it ? Do miracles happen (on average) once a year ? Once a century ? Once a millennium ? Once per the lifetime of our Universe ?
I think this is another difference between our methods; and I must confess that I find your approach quite weird. This doesn't automatically mean that it's wrong, of course; in fact, many theists (including C.S.Lewis) advocate it, so there might be something to it. I just don't see what.
The big difference between your approach and mine is that you seem to be entirely discounting empirical evidence; or, if not discounting it, then trivializing it at the very least. So, for example, if a trusted friend told you that he was fishing in the pond behind his house and caught a Great White shark; and if all of your friends confirmed this; then you'd accept that as true. I, on the other hand, would ask to see the shark.
The reason for this is not that I'm some sort of a hateful, un-trusting person (or rather, that's not the only reason, heh); but because we have mountains and mountains of data on sharks, and all of it tells us that they are incredibly unlikely to show up in ponds, and are also quite strong and thus nearly impossible to catch using an ordinary fishing line. Compared to this overwhelming pile of evidence, the testimony of a few people does not suffice to turn the tide of my belief.
So, is there a reason why you value empirical evidence as little as you do ? Alternatively, did I completely misunderstand your position ?
I have at least as much difficulty as the hypothetical scientist. Possibly slightly more difficulty, because the hypothetical scientist will know more science than I do.
Insufficient data for a firm conclusion.
Opposing the mass confirmation bias hypothesis, are the claims that the water on the ground and on people's clothing was dried during the time; also apparently people 'miles away' (and thus unlikely to have been caught up in mass hysteria at the time) also reported having seen it.
Having said that, there is another explanation that occurs to me; the scene was described as the dancing sun appearing after a rainstorm, bursting through the clouds:
If the clouds were thick enough, it may be hard to see the Sun; the bright light could have been... something else sufficiently hot and bright. (I do not know what, but there's room for a number of other hypotheses there).
I am very poorly calibrated on such low frequencies, so take what I say here is highly speculative. (Also, the rate seems very variable, with several a year in the time of the Gospels, for example).
At a rough guess, I'd say possibly somewhere between once a year and once a century. Might be more, might be less.
Let me explain further, then, by means of an analogy. Consider the example you provide, of a trustworthy friend claiming to have found a great white shark in a nearby pond. For the sake of argument, I shall assume a rather large pond, in which a Great White could plausibly survive a day or two, but fed and drained by rivers too small for a Great White to swim along.
I shall further assume that you are aware that all your friends were on the fishing trip together (which you were unable to join due to a prior appointment).
Now, catching a Great White is a noteworthy accomplishment. If your friend were to accomplish this, it is reasonable to assign a high probability that he would tell you. Therefore, I assign the following:
P (Being told | Great White caught) = 0.95
It is also possible that your friends are collaborating on a prank, giving you an implausible story to see if they can convince you. If this is the case, they could have decided to do so while on the fishing trip, and laid out the necessary plans then. Exactly what probability you assign to this depends a lot on your friends; however, for the sake of argument, I shall assume that there's a 20% chance of this scenario.
P (Being told | No great white caught) = 0.2
Now, furthermore, there is no plausible way for a Great White to have ended up in the pond; and no plausible way to catch one with a simple fishing line. There are a variety of implausible but physically possible ways to accomplish both actions, though. So the prior probability of a Great White being caught is very low:
P (Great White caught) = 0.05
(possibly less than that, but let's go with that for the moment).
Thus, P(Being told) = P (Being told | Great White caught) * P(Great White caught) + P (Being told | No great white caught) * P(No great white caught) = (0.95 * 0.05) + (0.2 * 0.95) = 0.2375
Plugging this into Bayes, P(Great White caught | Being told) = P (Being told | Great White caught) * P(Great White caught)/P(Being told) = (0.95 * 0.05)/0.2375 = 0.2
So, given certain assumptions about how trustworthy your friends are, etc., I find that the probability that they have indeed captured a Great White is higher if they tell you that they have than if they do not. Mind you, the prior probability for capturing a Great White is very low to begin with; the end result is still that it is more probable that they are lying than that they have captured a Great White, and you would be perfectly sensible to request further proof, in the form of the shark in question, before believing their claims.
It's not that I completely discard empirical evidence; it's just that empirical evidence, one way or another, is somewhat rare in the case of this particular question, and thus I am forced to rely on what evidence I can find.
I have, on at least one occasion, observed some evidence; but it's the sort of evidence that doesn't communicate well and is rather unconvincing at one remove (I know it happened, because I remember it, but I have no proof other than my unsupported word).
You yourself have said that the prior probability of a miracle occurring on any given day is relatively small, "somewhere between once a year and once a century". You also said that, if a miracle were to occur, you would likely be unable to recognize it as such: "I have at least as much difficulty as the hypothetical scientist. Possibly slightly more difficulty...". You also offered a plausible-sounding natural explanation for the event, and, as you mentioned, many other perfectly natural explanations exist. In addition, we have zero recorded evidence for this miracle, other than people's testimonies; whereas any other spectacular events (such as volcano eruptions or Justin Bieber sightings) are usually accompanied by plenty of recorded data (including news reports, cellphone footage, instrument telemetry, etc. etc.).
Given all of this, I'd argue that the probability of this particular event being a miracle is quite low -- even if we grant that a miracle-causing god of some sort does exist.
Whoa, whoa, wait a minute, 0.05 is huge ! It's about 460 times greater than your odds of dying in a car accident during any given year, assuming you live in the USA. And that's car accidents, which are pretty common events. Given that no recorded evidence of a backyard shark catch exists, I'd estimate its prior to be even lower. After all, meteorite strikes that damage people or property are extremely rare, and yet we do have recorded evidence of them happening, so pond sharks have got to be even more rare than that.
If we estimate the prior at something fairly optimistic, like 1 / 7e6 (meaning that we'd expect this rare event to happen to at least one person on any given day, seeing as there are 7e6 people on Earth), we still get a probability of something like 5.7e-7, which is about the same odds as winning the lottery (though I could be wrong, I don't know much about lotteries).
Wouldn't this drive down the probability ? If I knew that people were catching great whites in ponds all the time, I'd be more likely to believe my friends when they told me they caught one, right ?
What makes you trust the evidence, then ?
If I went fishing in a pond one day, and caught what appears to be at first glance a great white shark, I wouldn't trust my initial impressions. I'd start looking for a hidden camera. And maybe get an MRI, just in case. Those probabilities apply to everyone, including myself. Would you not agree ?
All true.
I would like to point out that, first of all, this occurred in 1917; there were no cellphones to take cellphone footage. And there were news reports at the time (there's a scan of at least one relevant newspaper page on the wikipedia page)
I don't think this detracts all that much from your point, but I felt I should point it out.
I expect that there are significantly more events claimed to be miracles than there are actual miracles. So, given as cursory a look over the available evidence as we've taken in this discussion, it would be sensible to assign a low probability to this incident having been a miracle, yes.
You're right, it is really rather unreasonably large. (All of my assumed priors in my previous posts were multiples of 1/20, a level of granularity perhaps too coarse for this figure). However, I don't believe that detracts from the point I was making at all.
Consider: P(Being told) = P (Being told | Great White caught) * P(Great White caught) + P (Being told | No great white caught) * P(No great white caught)
Taking the previously assumed values of P (Being told | Great White caught) = 0.95 and P (Being told | No great white caught) = 0.2, and taking P(Great White caught) as 1e(-10), that gives P(Being told) = (0.95 * 1e(-10)) + (0.2 * (1 - 1e(-10))) = 0.200000000075
Now, substituting these values in Bayes: P(Great White caught | Being told) = P (Being told | Great White caught) * P(Great White caught)/P(Being told) = (0.95 * 1e(-10))/0.200000000075 = 0.00000000047499999982; or approximately 4.75e-10. While this is minute, it is still over four times larger than the probability that they had caught a Great White had they not yet told you; being told that they had caught a Great White is still evidence in favour of a Great White having been caught. (Though not enough to make it probable that a Great White had actually been caught).
No, because the fact that great whites are not being caught in ponds all the time is evidence. It is very strong evidence for the hypothesis that great whites are not often found, or caught, in ponds.
When I say that empirical evidence is rare, I mean that many things can be adequately explained whether it is true that God exists or not. Therefore, those things do not act as evidence either for or against the hypothesis.
Rather than continue to talk in hypotheticals, I think I'll take a moment to describe the incident in question (and I think you'll see why I say I expect you to be unconvinced by it).
I was waiting outside Church; I had been nearby for some other reason, and it would not be economical to go home before mass (as I would then have had to leave immediately again), but there was still some time to wait. Having planned for this eventuality, I had a book to read with me. (I should perhaps mention, at this point, that I am notorious among my close acquaintances for the difficulty of interrupting me in the middle of a good book).
A little way outside the church, there is a large crucifix set up. While I was reading, a man walked by and knelt at the crucifix in prayer. And, for a brief while, I felt this very strong sense of Presence... strong enough that I found myself unable to continue reading my book until it had gone.
And that's it. After a while, the man got up and walked away; the sense of Presence receded.
So, what makes me trust the evidence? I remember it; and I do not believe there was any way that any human could have faked that experience.
Right, but there were no records of the event itself, just records of people's testimonies. This is somewhat... odd. When e.g. a volcano erupts there is usually tons of footage of the actual event. People can be mistaken, or they can lie; but it's hard to argue with a giant flaming mountain.
Yes, but it's also evidence for any number of other, more likely events: that my friends are pulling a prank, that they are mistaken, that a prank has been pulled on them, etc. etc. We don't need to enumerate them all; what's important here is only the posterior probability. If it is minute, then the reasonable course of action is to say, "until I see that shark, I won't believe that you guys caught it, sorry". There's a huge difference between saying that, and saying, "even though the chances that you caught that shark are even smaller than the chances of a meteorite hitting me in the head anytime soon, I can't come up with a better explanation off the top of my head so I'll believe you, good job !".
You said,
But beliefs do not exist in a vacuum. Instead, they form a Bayesian network: pieces of evidence affect the posterior probabilities of some beliefs; those beliefs change the prior probabilities of other beliefs, and so on. And the problem with the proposition G, which means "a god of some kind exists", is that it's starting to look like for any piece of evidence E, P(G|E) is lower than P(x|E), where x is pretty much any other non-divine explanation; and there is a lot of other evidence that can raise P(x). This is what I was driving at earlier with my hypothetical Alpha-god.
So, is there any piece of evidence E for which P(G|E) is much higher than any alternatives ? Moses, presumably, got exactly such a piece of evidence in the form of a burning bush. We don't have that, however; what we've got is an ancient story about a guy who saw a burning bush, and experience tells us that ancient stories mostly can't be trusted -- or else we'd be forced to believe in Zeus, Shivah, the Jade Emperor, etc., possibly at the same time.
As you have anticipated, I am unconvinced by your report, but the question is, why are you convinced ? You say:
But these aren't the only possibilities. Even if you cannot come up with any others (such as a random brain malfunction, as Jiro points out), why is this experience sufficient to convince you that a miracle occurred -- given that, as you agreed above, the probability of such an event is minute ? Don't you want to see the actual shark, before making your conclusions ?
There appear to have been quite a few pictures - somewhat to my surprise. Most of them appear to be pictures of the crowd, rather than of the Sun... and, as with any google search, some appear to be unrelated.
That is true.
But the posterior probability doesn't just depend on the evidence; it also depends on the prior probability. The prior probability assigned to the shark being caught is substantially lower than the prior probability I'd assigned to the existence of God. The analogy breaks down at the selection of priors.
I suspect that this is a rather severe exaggeration. I can easily propose an infinite number of proposals for 'x' where 'x' is non-divine but where P(G|E)>P(x|E) for almost any E. My method for finding these proposals for 'x' would be to string together a number of randomly selected grammatically correct sentence starting with the word 'because'; this would result in a number of entirely nonsensical proposals. Similarly, I can randomly select evidences E, placing them before the 'because'.
I shall assume you meant, therefore, that "there exists at least one non-divine explanation 'x' for which P(x|E)>P(G|E) for any given evidence E".
You've at least partially answered your own question; Moses saw the evidence in the burning bush. One particular monk saw the evidence in the Miracle of Lanciano. Several thousand people saw the evidence in the Miracle of the Sun. Doubting Thomas saw the evidence in the resurrected Jesus.
Lots of people saw evidence in first-hand observation of miracles.
That's the trouble; as soon as you get to second-hand observation, the evidence is a whole lot less convincing. If you've set the prior for God's existence sufficiently low, then there isn't going to be enough second-hand evidence to alter that.
Because I did see the shark, to extend the metaphor. And then it swam away, on its own business.
Are there any photos (or preferably videos) of the event itself ? I'm looking for something along the lines of this -- although, admittedly, volcano eruptions are relatively mundane events by comparison.
Ah, I see, that is interesting. What is the ballpark prior probability you place on the existence of God (or any other god, for that matter) ?
Yes, good call.
It would be more accurate to say something like, "we have a lot of historical texts that describe people who claim to have seen miracles". The distinction is important, because we have a veritable deluge of such texts regarding all major religions, as well as more modern phenomena such as alien abductions, Bigfoot, etc. The problem with such second- and third-hand accounts are that they -- as you have pointed out -- are notoriously unreliable.
I do not believe that little gray aliens have ever visited Earth, despite the claims of many, many "abductees". Do you ? If not, why not, and what would it take to convince you ? You say:
So, to recap: if someone told you about this shark, you would not believe him. Similarly, you do not believe that your shark story is convincing enough to convert another rational person to your belief. I think we are in agreement on these two points.
One thing I don't understand, though, is why are you convinced ? Do you believe yourself to be that much better -- orders of magnitude better -- at detecting the presence of sharks (or gods) than any other person ? If so, then for what reason ? But if not, then why are you privileging your own perceptions, given that they are no better than anyone else's ?
Think of all the alternative explanations you'd come up with if I told you, "guess what, I was abducted by little gray men from space yesterday". Do not these explanations also apply to yourself ?
There won't be videos; the event in question happened in 1917, and the earliest video cameras were apparently first used in the 1930s. And I'm not sure that anyone can get a halfway reasonable photo of a very bright light source using 1917 camera technology - which doesn't mean that no-one did, of course.
But if it doesn't turn up in a Google search, then I have no idea where else to look for such a picture; should one even exist.
To the existence of an omniscient, omnipotent being, I'd assigned a prior probability of somewhere over 50%.
An excellent point. Very well, then; lots of people claim to have seen evidence in first-hand observation of miracles.
I consider the prior probability that little gray aliens have ever visited Earth to be very small. Despite this, they have become sufficiently mimetic in modern culture that I would consider them a prime choice for hoaxsters; this, in turn, results in me sharply discounting second-hand accounts.
To convince me that aliens have visited Earth will require some piece of physical evidence; perhaps either something made from a material that can be proven not to have come from this planet (and considering what we can make, that might be a tough order) or some piece of technology not merely unavailable to humanity but significantly distant from what is available. I would not necessarily need to hold the evidence in my own hands; I would merely need to be convinced that said evidence exists (e.g. through news reports from reliable sources - 'Scientists Study Alien Technology').
This depends on my prior. For the existence of God, my prior is high enough that I would consider it plausible that he is telling the truth. For finding an actual shark in a lake fed and drained by small streams, my prior is far, far lower.
Yes, this is correct.
Largely because I started with a very high prior. My very high prior was contingent on the word of my parents, and particularly of my father, a wise and intelligent man who is far better than me at telling true from false. He's not infallible, but if he says something is certainly true, then I consider that a good reason to set a high prior for that datum (before updating on any other available evidence, of course).
Many of them do not. I know that I am not making up the story. I know that I am not lying. I know that I was not dreaming. I know that I had not received any major head injuries at around the same time. That covers the majority of the probability with regard to reasons why you might claim to have been abducted by little gray aliens.
As a first-hand observer, I can discount all of those explanations.
Also, my prior for the existence of little gray men from space is fairly low; which would lead to me assigning extra probability to the various 'lying' categories.
The obvious explanation is a brain malfunction, not fakery by another human.
(I also suspect confirmation bias. If you had had the same experience without a man praying nearby, you wouldn't have decided that it proves that such experiences have nothing to do with prayer.)
But even ignoring that, plenty of Muslims and people of other religions have had similar experiences. Yet I doubt you believe that they were real. Since you believe that similar experiences by Muslims are not real, you obviously do believe that there are explanations other than the experience being real. Why not now, too?
Possible; but I consider it an extremely low-probability possibility, for much the same reason as I consider the possibility that a given cloud I see in the sky is a hallucination has very low probability.
No... but I do believe I would still have interpreted it as evidence for the existence of God.
Ah - be careful of assumptions. I see no reason why some of them might not have been real. I'm not sure that the details of what building one goes into for worship, or the wording of the sermons, are what's really important.
Consider Matthew 25:31-46, in which the Final Judgement is directly referenced, and the criteria under which that judgement will take place are given:
There's nothing in there about belonging to a specific religion; it's all about going out there and going good things for people.
So, given that there are Muslims who are good people and do good things, I see no reason why God wouldn't on occasion answer their prayers, on the same criteria (which are hard to find and may take as input information not available without omniscience) as He uses to respond to anyone else.
Hm.
Backing up a little: what's your confidence that an arbitrarily selected perception is the result of processing signals from a distal stimulus that conforms in all significant ways to the perception?
Very very high. Short of strong evidence that a given perception is false (and not merely might be false), I tend to assume that all of my perceptions are caused by a distal stimulus that conforms in all significant ways to the perception in question (possibly filtered by intervening effects, e.g. dimmed if I am wearing sunglasses).
Well, yes, of course very very high.
And, sure, in practice we behave as though all our perceptions are like this, because treating any given one as though it isn't is typically unjustified.
I meant the question somewhat more precisely.
For example, out of 100,000 distinct perceptions, would you estimate the chance that at least one of those perceptions lacks a conforming distal stimulus as ~1? ~.1? ~.01? ~.00001? Other?
Ah. I see.
I'm afraid I can't really give you an answer at the level of precision you're asking for; I'm really not well calibrated for extimating extremely low probabilities. The best I can give you is "small enough as to be near indistinguishable from zero".
And I'm not entirely sure where I should put the upper bound of that category, either.
The possibility that a random cloud is a hallucination is low because clouds are well-studied and there is plenty of evidence for the existence of clouds--evidence of such a nature that anyone can see it. Furthermore, we know something about hallucinations--hallucinations don't cause random people to see random objects under random circumstances. A random cloud in the sky is not the type of thing that hallucinations typically make people see.
Your mystical experience was observable only by yourself, and was of a type which is known to be caused by brain malfunction.
But the more that different religions can do this, the less the meaning of the mystical experience. If God gives those experiences to people of all religions, then those experiences are no longer evidence for any particular religion. For all you know, the Muslim idea of God is the true one, the Christian one is false, and the Muslim God gives experiences to Christians in the same way you think that the Christian one gives experiences to Muslims. Maybe Christianity is really false, the pagans are right that there is a god and a goddess, and they give mystical experiences to Christians. Maybe some form of devil-worship is correct; I assume you believe that the Devil can't hand out mystical experiences, but if you are wrong about just that part, your experience could just as well come from the Devil.
It simply suggests that the criteria that God uses, when deciding when to make His presence known, are not limited to the professed religion of the person in question. Exactly what those criteria are, is not fully clear; but any religion which helped to foster those criteria amongst its adherents would be at least partially correct, in its effects if not necessarily in its dogma.
Why not? We're talking about the what may be second-most powerful entity in existence. (Mind you, there's a big difference between can and will; the existence of the Devil strongly implies the existence of God, and if the Devil is trying to discourage religion, then it would be counterproductive unless some other effects of said experience outweigh that risk.)
That sounds like you're agreeing with me. If God gives people mystical experiences no matter what their religion, mystical experiences are no good in showing that the religion is true. Of course this is a matter of degree. The wider the range of people get the experiences, the worse the experiences are at showing anything.
If beings other than God (such as the Devil) can give out mystical experiences, it's even worse. Mystical experiences not only don't show that the religion is true, they don't even show that "God exists" is true. At this point I don't see why you care that it's not just a brain malfunction, because even if it wasn't, you have no way to tell between an experience sent by God, one sent by the Devil, and there being a sorcerer on every block who occasionally pulls pranks by giving random people mystical experiences.
(As for why the Devil would want to do that? Maybe he knows that people interpret mystical experiences as evidence for their religion being true and he can incite religious conflict by giving people of opposing religions mystical experiences.)
It does not prevent said experiences from showing the existence of God, or from hinting at the criteria He finds important.
The devil is defined more-or-less by being in oppostion to God. If the devil exists, then so does God, pretty much.
And humans capable of pulling off a trick like that would almost certainly have been discovered by now if they were common.