Prior Probability of the Resurrection is Zero?

That is not what is going on. There is no reason we could not come to agreement on this:

No priors are involved. No burden of proof pushing.

Another question is given strong evidence that a resurrection occurred what is the likely cause.

This was the second resurrection to occur over a short period of time. Lazarus was resurrected by Jesus previously. We know that Jesus caused this event.

The odds are the same regardless of whether God exists, because we have no way of calculating the odds of a god doing a particular thing.

In a court case that hinges on DNA evidence, the prosecution will not say that the DNA matches the subject with 100% certainty, but usually with only some chance of error so miniscule it is for all intents and purposes certain.

Can you explain why defense attorneys don’t respond “But what if there is a God? Now the odds are different.”

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Multiplying words doesn’t remove the basic math error. That number isn’t computed correctly.

Could you show how we compute probabilities if we assume God exists? For instance, what are the odds of a coin coming up heads if there is a god. vs if there isn’t?

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It seems that discussions over probability vs. improbability swing madly from one end of the continuum to the other based upon the topic being discussed. Am I imagining this or not?

We all seem to defend the improbable events in which we believe as probable, and scoff at the others.

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@swamidass, @Faizal_Ali, @Rumraket, @John_Harshman,

I’d like to make a few quick points. First of all, Drs. Tim and Lydia McGrew, in their carefully argued article, The Argument from Miracles: A Cumulative Case for the Resurrection of Jesus of Nazareth, use a slightly different pair of hypotheses from those used by @swamidass (namely, H1 and H2). Their hypotheses are:

R: Jesus of Nazareth rose miraculously from the dead
and
~R: It is not true that Jesus of Nazareth rose miraculously from the dead.

They then invite readers to consider the ratio P(F|R) / P(F|~R), for any fact F which is relevant to the Resurrection. (Once again, this is similar to @swamidass’s ratio P(E | H1) / P(E | H2. He argues that the numerator is relatively high, while the denominator is very low.)

The McGrews then assemble what they consider to be very powerful evidence for the Resurrection - namely, the women’s discovery of the empty tomb, the combined appearances to the apostles and the appearance to Paul - and proceed to argue that this evidence is 10^44 times more likely under hypothesis R than under hypothesis ~R, before concluding:

Sheer multiplication through gives a Bayes factor of 10^44, a weight of evidence that would be sufficient to overcome a prior probability (or rather improbability) of 10^-40 for R and leave us with a posterior probability in excess of .9999…

We have argued above that, given the Bayes factors of the various pieces of evidence, their cumulative impact would overcome a prior probability of R of 10^-40 while leaving us with a posterior probability of approximately .9999. Even an exceptionally low prior may be overcome by extremely strong evidence. That argument deserves to be answered on its own terms, and it illustrates quite handily the fact that there is no such thing as a finite prior probability that is so low as to be “slippery” and hence impossible to overcome by evidence.

Now, supposing purely for argument’s sake that the McGrews’ calculations were correct, @swamidass’s contention that one can argue for the existence of God on the strength of the evidence for the Resurrection would be correct. All that the skeptic needs to grant is that the prior probability of hypothesis R is greater than 10^-40, and we end up with a very high posterior probability for a theistic hypothesis (Jesus of Nazareth rose miraculously from the dead), after considering the evidence.

Crucially, the McGrews treat each apostle who saw Jesus as an independent witness, which then allows us to multiply the individual probabilities of each of them having the same hallucination. For instance, if the probability of one apostle (say, John) seeing, hearing and feeling the same thing as Simon Peter did when they had an apparition of Jesus is (say) only 1 in 1,000, and if there were ten other apostles (barring Judas Iscariot) who experienced the same thing as Peter did when he had an apparition of Jesus, then we can calculate the probability of them all having the same apparition by chance as (1 in 1,000) raised to the power of 10, or 1 in 10^30. That’s the chief booster used by the McGrews, to beef up their ratio P(F|R) / P(F|~R) to 10^44.

The McGrews argue that the apostles must have all independently experienced Jesus, and that each of them must have had the same experience of their risen Master – otherwise, they wouldn’t have all been ready to suffer and die for him. However, this argument relies heavily on a psychological counterfactual about the conditions under which the apostles would have been ready to die for their belief in the Resurrection, coupled with the psychological assumption that the disciples would have all carefully compared notes about the details of their experience after Jesus appeared to them (maybe, but who knows?), plus two more factual assumptions: the historical assumption (which has been called into question by Professor Candida Moss in recent years) that the apostles were continually under threat of being tortured or martyred, and another historical assumption : namely, that the specific reason why they were martyred was that they believed in and preached the message that Jesus had risen from the dead . The McGrews’ case for the Resurrection is a solid one only if all four assumptions are true.

Now, let’s suppose instead that the evidence for the Resurrection is “only” 10^10 times more likely under hypothesis R than under hypothesis ~R. (10^10 is still a pretty high likelihood ratio.) And let’s suppose that one rates the prior probability of R as 1 in 10^11, which is the maximum value that Rumraket is prepared to generously consider. Now the probability of the Resurrection, in the light of the evidence, falls to 1 in 10, roughly.

Given the unreliability of human memory over a period of decades, or even weeks (if it is contaminated by listening to other people’s recollections of the same event), as well as the massive uncertainties regarding (i) who wrote the Gospels and when, (ii) whether the authors of the Gospels interviewed any eyewitnesses, (iii) what the apostles saw when Jesus appeared to them, and where and when they saw him, (iv) whether they were previously expecting a post-mortem divine vindication of Jesus, and (v) the manner of Jesus’ burial, I honestly do not see how one can argue for a likelihood ratio of greater than 10^10.

@swamidass acknowledges that there is no systematic way of defining the ratio of P(H1) to P(H2) - or as the McGrews would say, P( R) to P(~R). But to make his case for the Resurrection, he needs to explain why he thinks it is more than 1 in 100 billion.

I would argue that the prior probability is much closer to 1 given this was the third resurrection that occurred during Jesus ministry and given was prophesied in the OT.

The bible through all 66 books has redundancy for a reason.

On that matter, they furiously fudge the facts themselves:

“The first set of facts that constitutes evidence for the resurrection is the testimony of putative eyewitnesses to the empty tomb and of these same witnesses (the women who claimed to have found the tomb empty)…”

It’s not a set of facts because we don’t have their testimony.

This is not an isolated error:
“We shall argue that the testimony of the women to the empty tomb is evidence for R, and so we are obviously taking it that their testimony is evidence that the tomb was indeed empty.”

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Look, you’re going to have to decide what you are trying to argue. That God exists? That the resurrection took place? You can’t in the same argument both demonstrate the existence of God and that the resurrection took place and that God did it. Or well you can, it’s just that it’s going to become some colossal calculation and it has to start differently from indicated by Swamidass above.

If one is going to use the resurrection as evidence for God’s existence, one first needs to establish the probability that Jesus came back from the dead. That means the analysis has to start with the hypotheses:
H1: Jesus came back alive from being dead.
H2: Jesus did not come back alive from being dead.

To do that you need to start with the prior probability that someone would come back from the dead. That’s part of your background knowledge. How often do resurrections happen? The evidence for the resurrection (the purported testimonies) then feeds into that evaluation to raise the probability that the resurrection took place(presumably).
However, we also need to establish the probability that the testimony is reliable, we can’t just assume it’s genuine accounts and take them at face value. Here’s another problem: The better the evidence that Jesus died on the cross, the more unlikely it becomes that he was later seen alive. That’s how it works and will have to work, always, for anyone ever.
You disagree? Consider this analogy:
If you provide evidence that some person we know is in Australia this moment(maybe we get a broadcast from him where he’s walking around famous places in Sydney, and they show him live on Australian national television where he’s meeting the Australian prime minister), then any claim I make that he’s right next to me here in Denmark implies a conflict, because we have overwhelming evidence that people can’t be in two places at once.
Simply put, given the evidence we have that he’s in australia renders my claim instantly unbelievable, as in extremely unlikely to be true. And that is despite the fact that I am provably contemporaneous with the person, and I claim to be a direct witness delivering my own 1st-hand account. I should simply not be believed. If there were ten others like me, they should not be believed either. We would have to amass evidence other than our mere say-so.

Same way with the resurrection. Dead people stay dead(it is both the case God normally doesn’t seem to want to resurrect them, and they don’t naturally spring back alive), that’s our background knowledge. The better the evidence that Jesus died, the more unbeliavable the testimony of his postmortem appearances. As in they become less and less likely to be true. It should go without saying that unverifiable accounts(some of which are clearly copies and embellished) from millenia ago can’t overcome that, it’s absurd.

Another, further problem here is that the prior for coming back from the dead is between ≥0 and ≤1 in 100 billion. So we end up with a range for the prior, which means we will calculate a range for the posterior.

Once that has been done, the range of probability that Jesus came back from the dead, given the purported testimonial evidence (the reliability of which in turn also has to be established of course, and the better the evidence for his death, the more doubtful contradictory testimonials become, which means we would need extremely good testimonial evidence, meaning lots of verifiably independent 1st-hand accounts by people we have good reason to believe were eye-witnesses to the purported events), can then feed into another evaluation of the hypotheses:
H1A: God exists.
H2A: God does not exist.
We don’t have enough accounts, and we can’t verify their authenticity or independence.

If the probability that Jesus came back from the dead is greater than not it’s evidence for the existence of God, meaning it íncreases the posterior of God’s existence. How good that evidence is depends on how good the evidence for the resurrection is. But the evidence for the Jesus coming back alive is extremely weak, and it’s highly doubtful that it actually overcomes the evidence for Jesus being dead.

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The point of the claim is that Resurrection is not possible if God does not exist. Therefore we do not expect to see Resurrections.

I’ve already explained the math error you are making. There is no way to systematically compute the prior probabilities on these two hypotheses.

Correct.

Not the case. That is not how it works. The 1/100 billion number is totally made up.

I understand, it’s just that it’s wrong to say that. At best you could only say you wouldn’t know how a resurrection could happen without God. But your ignorance is not evidence for it’s impossibility. Other supernatural explanations are conceivable, so are natural explanations.

Therefore we do not expect to see Resurrections.

Even if God exists we don’t expect to see resurrections, because if God existed and wanted to resurrect people frequently, that would happen. So the fact that they don’t seem to happen is evidence that God generally doesn’t want them to happen. He might have wanted to in the case of Jesus, but that is the hypothesis we are trying to calculate the probability of, so we can’t use it as evidence for itself.

I’m sorry but I’m not making any error. If you wish to argue that God exists by appealing to the resurrection as evidence, we have to start with the prior for people coming back from the dead.

Extraordinary claims require extraordinary evidence. The reason the claim that a man came back from the dead is considered an extraordinary claim is because we generally don’t have experience of people doing that. The more infrequently that has happened, the more out of the ordinary is the claim that it nevertheless occurred. When we say it is extraordinary, we are saying it has an extremely low prior, that’s what an extraordinary claim is: One with an extremely low prior.

We have no experience of people ever coming back from being fully dead for several days. So for Jesus coming back from the dead, it has to have a prior below one in all the people who ever lived and didn’t come back from the dead, which is pretty much everyone who ever lived. So the prior must be less than 1 in 100 billion(again, the estimate for everyone who ever lived), and might be zero.

This is where evidence for the resurrection becomes important. If the evidence is good enough, it can overcome an extremely low (though non-zero) prior. That’s why I’m being generous in setting a prior to 1 in everyone who ever lived.

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I’ve given an alternate strategy that avoids this problem and also agreed that this is not definitive. There is no systematic way of setting this prior.

I’ve made my point. You disagree. I accept this. Please refrain from circular arguing on this point going forward.

Yet there were at least 3 documented during Jesus ministry.

We have no way of determining the effect of God’s existence on the odds of resurrections occurring.

Your position is better stated: “If God exists, and the existence of this God makes resurrections possible, then resurrections are possible.”

You have not shown that the italicized part is true.

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Each of which would have to be assessed independently. They can’t be taken at face value as evidence for people coming back alive. They might have even weaker support than the resurrection itself.

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It supports Joshes argument that God is the instrument of resurrections. Three were documented during his time on earth in human form.

No, it doesn’t do that until we have established that:

  1. They are more likely to have occurred than not.
  2. They are more likely to have occurred if God exists, than if God does not exist.

Three were documented during his time on earth in human form.

Yeah those claims are there, and they have to be assessed on their own merits. What is the evidence that those resurrections occurred? Someone says so?

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The support is in the credibility of the document that reveals these events.