Extraordinary claims and extraordinary evidence

[unkleE]

Dec 4, 2015 7:10:24 GMT ignorantianescia said:

This aphorism is by the way a pet peeve of William Lane Craig, who has responded to it several times (usually in relation to the resurrection).

What do you know? WL Craig is smarter than I am! I hadn't thought of the evidence for the resurrection in that way before. I guess I won't challenge him in a debate!!

Thanks for that.

[ignorantianescia]

Dec 5, 2015 2:18:19 GMT mcc1789 said:

I'd be more surprised if he liked the aphorism. However, I'm not familiar with Bayes' Theorem or probability in general. So how does one calculate that? A resurrection seems pretty improbable from any common-sense standard, more improbable than having a number drawn from the lottery. We know random numbers are selected from lotteries very commonly. Resurrections, however, appear to be rare claims even according to believers. I'm not sure what amount of evidence would make that more or less improbable.

Well, I don't intend to hijack the topic into a debate about the resurrection. It just happened to be that all instances that I found where Craig criticises the adage also concern the resurrection. So maybe it's best to focus on the implications of the lottery analogy for belief in the aphorism, not for belief in the resurrection. And I don't think Craig's analogy (which is a functional analogy, not an argument by analogy) requires the priors of a lottery win and a resurrection to be about equal.

Bayes's Theorem basically entails that any fact with a non-zero prior probability might become the most probable given that the available evidence sufficiently supports the initially less likely fact. (It also has many other implications but we're not concerned with those right now.)

Where does that leave our catchy factoid? Again it presents us with questions about the meaning of "extraordinary evidence". Is extraordinary evidence anything that makes a fact with the lowest prior the one with the highest final probability? Possibly, though that is a very broad and modest definition.

[mcc1789]

Yes I do, of course. But I find it difficult to believe that a religion God started (i.e. factually true) would be totally unsuccessful.

I guess then the question would be: if Christianity were not the most popular religion, would that make it untrue? I don't think it would tell us either way.

If you're referring to "I believe, help my unbelief", then its Mark9:24 as already said.

I didn't know the particular passage before now.

If the matter being referenced is complex, the aphorism can hardly fail to be simplistic. But I guess some aphorisms will be both snappy (as this one surely is) and actually true.

Yes, it's just determining if they really are true that's the tricky bit.

The difficulty, I think, is that the naturalist will always believe that a natural explanation is to be preferred, even if none is currently available. Take Intelligent Design. Suppose it is true that God didn't just start the universe off, but that he interferes in it from time to time to help evolution along (e.g. abiogenesis, the eye, the disappearance of dinosaurs and the beginning of primates able to develop language). I don't believe this myself, but let's say it was true. The ID-ers could never really prove that God did any of these because his actions would not be observable or measurable, so the effects of his actions cannot be linked to him by observing cause and effect. ID could say that there is no other explanation, but I doubt they can prove there cannot possibly be any natural explanation. And the naturalists will keep saying there is an explanation there, even though we haven't yet found it (abiogenesis is an example of them trying many explanations but none of them have been proven yet, as far as I know.) So the situation remains a stalemate.

Well, obviously the sine qua non of naturalism would be preferring natural explanations. However as to God leaving a signature, I'm not sure that's true. The irreducible complexity concept claims the structure of the eye is itself evidence, for instance. Similar claims are made regarding DNA as information. This is pretty vague, however. If a god really wished to be known, I'm sure it could do so in direct ways. You have mentioned Christianity's success, for instance. Very good evidence would be if the idea had been found in areas before missionaries came to them. If we ever meet any extraterrestrials, their being Christians would also be quite telling.

If we could run the experiment over and over again (which we can't do with evolution, but we can do with, say divine healings) then we may resolve the question by testing how often prayer led to healing and didn't, and how often no prayer led to healing (i.e. spontaneous remission) or didn't. It would take a lot of data, and would be muddied by questions like How do we know no-one outside the experiment is praying? and Which God are they praying to? and Maybe God doesn't answer prayers from that person? and Are all healings equally probable?, but in the end we would have enough data to use Bayes Theorem. But short of that, it is pretty difficult.

From what I've read, the efficacy of prayer has been tested. So far I believe the results are negative. Of course, it's difficult to test I'm sure.

Bayes Theorem takes a hypothesis with an assigned prior probability and modifies that probability in the light of new information. The new information is evaluated by asking two questions: 1. How likely is this information to have occurred if the hypothesis is true? and 2. How likely is this information to have occurred if the hypothesis is false? If the information is more likely if the hypothesis is true, the hypothesis is thereby made more likely and a new probability can be calculated.

In the case of divine healing, we might say the prior probability (before evidence) of the hypothesis that God exists and heals is 1 in a hundred (just to pick a number). Suppose we found that of a thousand people prayed for, 50 were healed and 950 were not, whereas of the 1000 not prayed for, 1 fully recovered and 999 did not (that is the new information). Then, if we assume that the second figure (0.001) is the probability of a person being healed if God doesn't exist (i.e. by natural means) and the first figure (0.050) is the probability of a person being healed if God does exist and answers prayers, we can calculate a new probability for the hypothesis that God heals. In this case, if my maths is correct, the probability that God exists has moved from 1 in 100 to 1 in 3 (0.336). Obviously a different prior probability and different experimental results would give different answers.

The matter is further complicated by the fact that the same data could be used to test the hypothesis that prayer has a natural effect, like a placebo or some other psychological effect. The prior probability might be different, but a new probability could be calculated in the same way, but it would be assigned to a different hypothesis. This shows that the supernatural is hard to test. A reasonable person is left to decide what they think without the greater "certainty" of "proof".

Craig hasn't (I presume) tried to put numbers to his resurrection argument, but the logic is the same. If the evidence he refers to, which is accepted by the majority of NT scholars, christian or not, is more likely to have occurred if Jesus was resurrected than if he wasn't, then that evidence increases the probability that Jesus really was resurrected. How much it increases it depends on the assumptions we make about probabilities.

Yes, it does seem to leave us hanging as usual.

[mcc1789]

Well, I don't intend to hijack the topic into a debate about the resurrection. It just happened to be that all instances that I found where Craig criticises the adage also concern the resurrection. So maybe it's best to focus on the implications of the lottery analogy for belief in the aphorism, not for belief in the resurrection. And I don't think Craig's analogy (which is a functional analogy, not an argument by analogy) requires the priors of a lottery win and a resurrection to be about equal.

Yes, sorry, I got off track a bit.

Bayes's Theorem basically entails that any fact with a non-zero prior probability might become the most probable given that the available evidence sufficiently supports the initially less likely fact. (It also has many other implications but we're not concerned with those right now.)

Where does that leave our catchy factoid? Again it presents us with questions about the meaning of "extraordinary evidence". Is extraordinary evidence anything that makes a fact with the lowest prior the one with the highest final probability? Possibly, though that is a very broad and modest definition.

Yes, I'm not sure where it's left now at all.

[ignorantianescia]

Dec 5, 2015 19:17:28 GMT mcc1789 said:

Yes, sorry, I got off track a bit.

You don't need to apologise at all. If anything it was the content of my post that consolidated the gradual 'topic hijack'. But on another level, it's in line with expectations that a discussion about extraordinary claims and extraordinary evidence on fora heavily populated by Christians gravitates to discussion of the resurrection.

Dec 5, 2015 19:17:28 GMT mcc1789 said:

Yes, I'm not sure where it's left now at all.

I'd say in the outer ring of internet Hell: semantic debates.

[mcc1789]

You don't need to apologise at all. If anything it was the content of my post that consolidated the gradual 'topic hijack'. But on another level, it's in line with expectations that a discussion about extraordinary claims and extraordinary evidence on fora heavily populated by Christians gravitates to discussion of the resurrection.

Well that seems natural.

I'd say in the outer ring of internet Hell: semantic debates.

Yep, it seems that way. Both of your inputs have been helpful in unpacking it.

[unkleE]

Dec 5, 2015 19:13:50 GMT mcc1789 said:

I guess then the question would be: if Christianity were not the most popular religion, would that make it untrue? I don't think it would tell us either way.

I think it's a flasification test, not a verification test. I didn't say it would have to be the most popular, and I didn't say it proves christianity is true. What I said is that if it wasn't at least reasonably successful, that would suggest to me that maybe it wasn't from God.

Well, obviously the sine qua non of naturalism would be preferring natural explanations. However as to God leaving a signature, I'm not sure that's true. The Irreducible complexity concept claims the structure of the eye is itself evidence, for instance. Similar claims are made regarding DNA as information. This is pretty vague, however.

That is my point, it is difficult if not impossible either way.

Very good evidence would be if the idea had been found in areas before missionaries came to them, for instance.

Something like this has actually occurred, many times, though not to the level you would probably want to count as evidence. But missiologist Don Richardson has documented many stories of what he calls "redemptive analogies" where missionaries found some analogies to christianity in tribes, and/or stories in their legends of someone coming with a message with details that the missionaries somehow fulfilled. The first analogy that gave him the idea was two warring tribes who valued clever deceit, and so admired Judas rather than Jesus. But when a conflict was at its height, a leader from each village offered one of their children to be brought up by the other. As long as this "peace child" was not harmed, no-one would fight the other. Suddenly Jesus was seen as God's peace child, Judas was no longer a hero, and killing Jesus was killing the peace child. Like I said, it's not strong enough to satisfy your requirements, but all of examples he has researched, taken together, bear some resemblance to what you said.

From what I've read, the efficacy of prayer has been tested. So far I believe the results are negative. Of course, it's difficult to test I'm sure.

I'm not sure what you've read, but there is some misinformation on this being repeated. Basically there are two sorts of studies - (1) prayer as a medical therapy and (2) prayer as the action of a personal God. Of course they are both very different, and they require different methodologies.

The first uses a medical methodology because that is what it is testing. Sceptics often quote the largest such study, by Benson et al, which gives a negative result, and is I'm sure what you have probably read about. But there are many more studies, including a number of meta studies that look at the results of many studies. I have found 26 studies that I could review, and they were 17:9 positive towards the effects of prayer. The meta studies cover 64 separate studies in total, so we have about 80+ studies giving a 2:1 approx positive effect. But somehow people on the internet don't quote them all.

But I don't these studies are very useful for what we are talking about. Prayer is treated as just another therapy, the people praying are not necessarily very committed to the task, the people or even to God, the improvements are modest and the whole thing is nothing like what happens when christians pray. So the results slightly favour prayer, but I don't put any store in them.

The second type of study looks at real prayer by christians who are really praying for healing. Unlike the first type, these studies don't try to estimate the percentage of "successes", but instead look at whether an unexpected recovery has a likely natural explanation or can only easily be explained by divine healing. Most studies are after the event and so the experimental design cannot easily be scientific - and anyway, a personal God answering prayer, or not, is never going to be the same as a scientific effect. I have seen some good analyses that show that some really spectacular recoveries occurred after christian prayer. I find them convincing, but a sceptic can always say the experiment isn't scientific enough.

Prof Candy Gunther Brown has recognised the weaknesses in both approaches, and has developed an approach of measuring before and after at a healing meeting. She did it once, as a trial, for a small sample of people seeking hearing or eyesight healing, and obtained quite positive results for the success of prayer, but again sceptics can always criticise her for something.

But my conclusion is that the evidence seems to point to some healings being unexplained, and with an estimated 300 million people claiming to have experienced or observed a miraculous healing, it only requires a small percentage to be inexplicable and the evidence mounts up.

[mcc1789]

I think it's a flasification test, not a verification test. I didn't say it would have to be the most popular, and I didn't say it proves christianity is true. What I said is that if it wasn't at least reasonably successful, that would suggest to me that maybe it wasn't from God.

Okay, fair point.

That is my point, it is difficult if not impossible either way.

Examples can be thought of. If the world worked exactly as a literal interpretation of the Bible says, that would be great evidence, for instance.

Something like this has actually occurred, many times, though not to the level you would probably want to count as evidence. But missiologist Don Richardson has documented many stories of what he calls "redemptive analogies" where missionaries found some analogies to christianity in tribes, and/or stories in their legends of someone coming with a message with details that the missionaries somehow fulfilled. The first analogy that gave him the idea was two warring tribes who valued clever deceit, and so admired Judas rather than Jesus. But when a conflict was at its height, a leader from each village offered one of their children to be brought up by the other. As long as this "peace child" was not harmed, no-one would fight the other. Suddenly Jesus was seen as God's peace child, Judas was no longer a hero, and killing Jesus was killing the peace child. Like I said, it's not strong enough to satisfy your requirements, but all of examples he has researched, taken together, bear some resemblance to what you said.

That's true, I've heard of things similar to that.

I'm not sure what you've read, but there is some misinformation on this being repeated. Basically there are two sorts of studies - (1) prayer as a medical therapy and (2) prayer as the action of a personal God. Of course they are both very different, and they require different methodologies.

The first uses a medical methodology because that is what it is testing. Sceptics often quote the largest such study, by Benson et al, which gives a negative result, and is I'm sure what you have probably read about. But there are many more studies, including a number of meta studies that look at the results of many studies. I have found 26 studies that I could review, and they were 17:9 positive towards the effects of prayer. The meta studies cover 64 separate studies in total, so we have about 80+ studies giving a 2:1 approx positive effect. But somehow people on the internet don't quote them all.

But I don't these studies are very useful for what we are talking about. Prayer is treated as just another therapy, the people praying are not necessarily very committed to the task, the people or even to God, the improvements are modest and the whole thing is nothing like what happens when christians pray. So the results slightly favour prayer, but I don't put any store in them.

The second type of study looks at real prayer by christians who are really praying for healing. Unlike the first type, these studies don't try to estimate the percentage of "successes", but instead look at whether an unexpected recovery has a likely natural explanation or can only easily be explained by divine healing. Most studies are after the event and so the experimental design cannot easily be scientific - and anyway, a personal God answering prayer, or not, is never going to be the same as a scientific effect. I have seen some good analyses that show that some really spectacular recoveries occurred after christian prayer. I find them convincing, but a sceptic can always say the experiment isn't scientific enough.

Prof Candy Gunther Brown has recognised the weaknesses in both approaches, and has developed an approach of measuring before and after at a healing meeting. She did it once, as a trial, for a small sample of people seeking hearing or eyesight healing, and obtained quite positive results for the success of prayer, but again sceptics can always criticise her for something.

But my conclusion is that the evidence seems to point to some healings being unexplained, and with an estimated 300 million people claiming to have experienced or observed a miraculous healing, it only requires a small percentage to be inexplicable and the evidence mounts up.

The one that I've read about involved medical studies. I'm not sure whether it was by Benson et al., but may have been. For the reasons you said, it's probably very difficult to study, because we can't measure sincerity of prayer very well. Of course there can always be criticism, the question would be whether that holds up. There is always the unexplained, we can definitely agree on that.

[ignorantianescia]

mcc1789, these also all treat the resurrection, but I thought you'd find the comments on ECREE interesting.

dangerousidea.blogspot.nl/2011/01/richard-carrier-on-bayes-theorem.html

Victor Reppert:

I see two major issues with respect to the Bayesian analysis of Resurrection history. One has to do with the left side of the theorem. Is there some way of showing that everyone ought to go into the discussion with such a low prior for any miracle that we can virtually guarantee that nothing coming out of the ancient world will be sufficient evidence.

The usual approach to getting that result is via some form of frequentism. There have been 96,100,000,000 persons who have ever lived, there has only been a very few resurrection reports that have so much as surface credibility, so therefore the one in 96.1 billion, and therefore resurrection has to lose even to the swoon theory. But these lead-footed methods don't work for various reasons that have been pointed out quite often. Earman is, I think, the guy you have to get around if you think you can prove something like this about the prior for miracles.

If you say "Extraordinary claims require extraordinary evidence," (which invariably implies evidence that you're never going to be able to get out of the ancient world), then you have to figure out how do define extraordinary in this context. Does it mean historically unique? In that case you have Indian Prince worries, and there's even a problem believing media reports that Obama won the election. If you think it means contrary to the laws of nature, then why do you presume that every event has a natural cause? Doesn't that beg the question from the beginning. Whether a miracle-working God exists is part of what's at issue here. The skeptic needs an account of extraordinariness that doesn't beg the question and pins an unmanageable prior on all miracle claims for everyone.

The other issue looks at the right side of the theorem, and asks if the evidence surrounding the resurrection is more like what we should expect if the miracle happened or more like what we should expect if it didn't happen. My approach on this is to say that prior probabilities on the matter are certainly going to vary, and that nevertheless we can see if the evidence confirms the miracle story of disconfirms it. Unless you have an argument that shows that no one should have a manageable prior for miracles, you can and should ask this question.

Now notice that I have nowhere said that there is some definite conclusion that everyone will come to, that it is 94% likely that the Resurrection happened based on historical evidence. I am interested in whether the case for the Resurrection confirms it, even if many unbelievers fail to find such evidence "extraordinary" enough.

www.is-there-a-god.info/blog/clues/ecree-extraordinary-claims-require-extraordinary-evidence/

[mcc1789]

I wasn't able to see where the quote by Victor Reppert is from, but the discussion in the second link seemed to be about the same as the one here. I'm not sure I agree with how it frames the atheist view, but that seems to be a problem whenever you're presenting a perspective that differs from your own.

[himself]

Friends don't let friends do Bayes Theorem.

Rev. Bayes' Theorem states: P(A|B) = P(A)*P(B|A)/P(B)

P(*|*) is a conditional probability and reads "probability of A, given B." For example, the probability that we see a 12 on the dice, given two, six-sided dice, with each side numbered from 1 to 6, etc.

The flies in the ointment are the simple probabilities P(A) and P(B). There ain't no such critters. Ever. There is no such thing as a probability without some assumed model or evidence. The probability, for example, that the nitrogen content of a heat of steel exceeds 90 ppm will depend on whether a normal model is an adequate approximation of the distribution.

It is difficult enough to do well even in bounded, well-measured situations. Bayes Theorem is not a magic equation into which you can plug ignorance and receive knowledge. In situations where there is literally no data and the "probabilities" are merely SWAGs (Silly Wild-Ass Guesses) it is much like washing garbage.

[ignorantianescia]

Dec 20, 2015 3:45:32 GMT himself said:

Friends don't let friends do Bayes Theorem.

Rev. Bayes' Theorem states: P(A|B) = P(A)*P(B|A)/P(B)

P(*|*) is a conditional probability and reads "probability of A, given B." For example, the probability that we see a 12 on the dice, given two, six-sided dice, with each side numbered from 1 to 6, etc.

The flies in the ointment are the simple probabilities P(A) and P(B). There ain't no such critters. Ever. There is no such thing as a probability without some assumed model or evidence. The probability, for example, that the nitrogen content of a heat of steel exceeds 90 ppm will depend on whether a normal model is an adequate approximation of the distribution.

It is difficult enough to do well even in bounded, well-measured situations. Bayes Theorem is not a magic equation into which you can plug ignorance and receive knowledge. In situations where there is literally no data and the "probabilities" are merely SWAGs (Silly Wild-Ass Guesses) it is much like washing garbage.

About P(A|B) and P(B|A) in the humanities: Would you say that Bayes Theorem is useful in establishing boundaries for qualitative consideration of (conditional) likelihoods, but absolutely useless for quantifying qualitative topics? (Whatever that is even supposed to mean, Carrier is a major culprit in any conceivable sense.)

[jonkon]

The problem with Bayes Theorem lies in what we MEAN by "probability." The absurd conclusions from the use of Bayes Theorem, namely the probability of an event never having been previously observed is 1/2, arise from the use of the Classical, a priori, meaning of "probability," proposed by Laplace, as opposed to the relative frequency meaning, derived from estimating insurance risks. The a priori meaning appears to work in the examples of a coin or die toss because of the symmetry of the problem, leading to the same relative frequency of the various outcomes.

[unkleE]

I don't have the patience, and probably not the mathematics either, to try to follow all the ideas, but this discussion of Bayes Theorem by Luke Barnes may shed light for some.