Prior Probability of the Resurrection is Zero?

If I said that clouds form through the condensation of water vapor in the air would you reject that explanation because it didn’t include the origin of the universe?

Why not? Randomness produces order all of the time.

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Yea start with the origin of atoms. If you are making to many assumptions you fail Occurs razor.

Explain how without spurious assumptions.

You know you don’t require this for every explanation of of every natural process.

The Sun is a perfect example. The orderliness of its layers and fusion processes is due to random collisions between atoms.

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You don’t explain the origin of the creator. Does he also just exist accidentally, or without a cause or explanation?

So how did God create the universe, what is the explanation?

Also, why do you think something came from nothing? There’s zero evidence that has ever occurred.

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That’s black & white thinking (or binary thinking).

Even if God exists the prior probability of the resurrection is astronomically low. 99.9999999999999999999999999999 percent of people who have died have remained dead. It’s possible that God turns me into a carrot right now. But it’s astronomicalmy unlikely. God doesn’t seem to be in that business. So is the evidence for the resurrection enough to overcome the low prior probability of it happening? I don’t know.

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There haven’t been that many people in the entire history of Homo sapiens.
It could be between 0 in 100 billion (all the people who ever lived weren’t resurrected by God) and 1 in 100 billion (if one person came was resurrected). That would put it between 100% have remained dead, and 99.99999999999% have remained dead.

Maybe God resurrected others we were never told about, like some loner dude living by himself on some island who then later died again. To be really correct, we have to admit that the prior for the resurrection is undetermined as we don’t have a frequency for divine resurrections. That means we can’t actually calculate a posterior for the resurrection, it has to remain an article of faith.

Another issue is, even if we extremely generously grant that God has resurrected one other person in history, then such a generous assumption can’t serve as a premise in a valid argument supposed to appeal to the resurrection as evidence for God’s existence, since God’s existence is assumed when setting the frequency of resurrections by God to at least 1 person.

Even if we could show to a high degree of certainty that Jesus really died, stayed dead for 2 whole days, and came back alive on the third, we’d still be left with the job of having to determine why it happened. It can’t just be assumed that God did it.

Pointing to the case for the resurrection as something that should convince a rational person that God exists is hopeless. It’s faith, it’s believed on faith, and the case does not stand up under scrutiny.

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That is the wrong probability to compute. Basic math error.

You have to compute the probability that ONE person out of 100 billion (or whatever) rose from the dead, given the possibility that God exists.

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I think that is what I said, perhaps I didn’t express myself clearly.

Well that number you calculated in correctly. It is not nearly zero. The method you chose of computing it as 1/ 100 billion is not valid.

How else would you do it? We are trying to come up with a prior for the resurrection. As in a prior probability that the resurrection occurred, and that God did it.

You computed the number that one particular person (chosen at random) was Resurrected given that exactly one person was Resurrected out of 100 billion. This has no conceptual correspondence to the right computation.

As I explained before, the prior is an undefined probability. Though this is not a scientific question, hypothesis testing could help us here. Consider two hypotheses (H1 and H2) and the evidence (E).

H1: The Christian God revealed in the Risen Jesus is real, and he rose Jesus from the dead.
H2: God does not exist or He does and did not raise Jesus from the dead.

These should be perfectly mutually exclusive propositions. With some tweaks, I’m sure we could make them so. Therefore,

P(H1) + P(H2) = 1

What we need to compute is both:

P(E | H1)
P(E | H2)

Note, this does NOT rely upon prior belief of P(H1) or P(H2). Probability of the Resurrection given the evidence, then, becomes:

P(H1 | E ) = \frac{P(E | H1) P(H1) }{ P(E | H1) P(H1) + P(E | H2) P(H2) }

This number is critically dependent on the ratio P(H1) / P(H2). It is essentially undefined, because there is not a systematic way of setting it. Recall however the place we can focus, computing these two numbers:

P(E | H1)
P(E | H2)

The point we have been making is that the second number (to H2), systematically computed, is very low, and the first number (to H1) is relatively high. As for the probability of the resurrection? We don’t have a systematic way of defining priors so we can’t say.

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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.


@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
~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.