Bayesian evaluation for the likelihood of Christ's resurrection (Part 30)

Let us recall our purpose in collecting these non-Christian stories about a "resurrection": we wanted to verify our Bayes' factor for the evidence of Christ's resurrection. My claim is that it's at least 1e54.

The first part of our plan was to find the non-Christian resurrection story with the most evidence behind it. If we make the naturalistic assumption about these stories, we can then say that this level of evidence is approximately what corresponds to a Bayes' factor of 1e9. For by the virtue of having the most evidence, such a resurrection story would have narrowed the field down to itself - one case - from the approximately 1e9 reportable deaths in history.

As it turned out, the "resurrection"s of Krishna and Aristeas had the most evidence behind them, amounting to roughly 1/24th of the evidence for Christ's resurrection. According to our program, this must be assigned a Bayes' factor of roughly 1e9. Then 24 times that amount of evidence would correspond to raising the Bayes' factor to the 24th power - meaning, the evidence for Christ's resurrection has a Bayes' factor of... 1e216.

So yes, that does verify that the Bayes' factor is "at least 1e54". It furthermore demonstrates how much of an underestimate that value is. Recall that, in a slightly different context, I mentioned that the full odds for the resurrection would be far in excess of 1e100, and that our values for the Bayes' factors were drastic underestimates. All that is verified by this completely different methodology, of comparing with non-Christian resurrection stories.

But that's not all. This comparison also provides yet another layer of verification, in that it allows us to check the Bayes' factor of 1e8 for a disciple's testimony about Christ's resurrection. You see, among the non-Christian resurrection stories we've seen, there was not a single case of a person making an earnest, insistent testimony about someone rising from the dead. That says something about the strength and rarity of such testimonies. Granted, we have not investigated every existing non-Christian resurrection story - but if such a testimony really has a Bayes' factor of 1e8, there should be about ten such testimonies for us to find. The fact that we have not found a single one puts a lower bound on the Bayes' factor, of just about 1e8. As usual, there's some nitpicking possible, depending on whether you think there are a hundred or thousands of non-Christian resurrection stories. But it's unlikely for any of that to change the value of 1e8 by more than a couple of orders of magnitude. So our estimate about the strength of the disciples' testimony has now also been verified.

We can now be very confident that Jesus rose from the dead. Our previous calculation which first gave us this confidence has now been verified in multiple ways, using completely different methodologies - by double-checking with the historical background of non-Christian resurrection stories. Everything checks out, and all the numbers are in harmony.

But... all this has been computed under the assumption that there isn't any extreme dependence in the disciple's testimonies. We've already accounted for "normal" dependence, like ordinary social pressure or group conformity. But we have not yet accounted for the possibility that the entire set of testimony about Jesus's resurrection might have been been engineered to be in agreement by some unknown force. That is to say, we've been discounting crackpot theories - like a conspiracy by the disciples to steal Jesus's body, or an alien mind-controlling all the witnesses to the resurrection.

Ignoring such theories is fine and good, as long as both sides of the debate are agreed in dismissing them. Most doubters of the resurrection do not subscribe to these extreme theories, so carrying out our calculations in this way up to this point was still productive. However, they're now facing a double-checked Bayes' factor exceeding 1e54 for the resurrection. This makes the posterior probability against the resurrection so tiny, that the small prior probability assigned to crackpot theories now seem much larger in comparison. Someone set on disbelief can no longer ignore these theories. Indeed they have no other choice: they must fully embrace these crackpot theories.

We will begin to address such theories starting next week.

You may next want to read:
On becoming a good person
Human laws, natural laws, and the Fourth of July
Another post, from the table of contents

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