Theology, philosophy, math, science, and random other things

Bayesian evaluation for the likelihood of Christ's resurrection (Part 42)

Next, consider the factor of 24 that we used, as the ratio between the level of evidence for Jesus's resurrection, and that of the runner-up. This, too, was a very conservative estimate, which favors the skeptic's case.

You'll recall that the runners-up were Aristeas and Krishna, with Apollonius falling not too far behind. In previously reviewing each of these cases, I noted that I was being quite generous in granting them their level of evidence. I felt that there was essentially no evidence, but wanted to express the fact that at least someone had said something - so I somewhat arbitrarily assigned the "some people say..." level of evidence as 1/10th of a single, solid, historic person's sincere testimony. Then, the three people named above then got a multiplier on top of that to account for some additional details.

Of course, this is an overestimate of the "some people say..." level of evidence. Would you believe ten people with "some people say..." stories, over a single person who's giving a sincere, personal testimony? Consider some thought experiments. What would you think of ten people who say, "a friend of a friend whose uncle works for the US government tells me that some people say that the president has been contacted by aliens"? How would that compare with a single witness who sincerely and consistently says "I was there when the aliens contacted the president. It really happened"? If you were a journalist, which source would you cite in your article? If you needed more information, who would you talk to?

Another way to see that the "some people say..." level of evidence is relatively worthless is to observe how common it is. Indeed, this is tied in with the fact that the great number of such evidence throughout history works as evidence FOR the resurrection. We have seen that there is at least 50, and likely hundreds or thousands of such "some people say..." reports for a resurrection. In contrast, none of these non-Christian accounts has even a single, historical person claiming that they personally witnessed the resurrection. This speaks to the relative worth of a single personal testimony over hundreds or thousands of "some people say..." reports.

And remember that this whole time, for the Christian case, we've only been considering the people mentioned in 1 Corinthians 15. This doesn't give many people the full weight their testimonies deserve (John, for example, should be counted more like Peter than just a member of the Twelve), and doesn't take some groups of people (like the women at the cross) into account at all.

All told, the level of evidence for Jesus's resurrection is far greater than 24 times that of the runner up. Using 24 as the factor is a very conservative, pro-skeptical choice.

I've also touched upon the number of "outliers" - the number of resurrection reports with a "some people say..." level of evidence. I've cited 50 such reports, and have used 50 in the calculation as the number of outliers. But as I mentioned, this is a vast underestimate. It comes from a very limited subsample of all the stories in world, reachable by a few minutes with Google in English. The true number of such outliers could easily be in the hundreds or thousands. So this, too, was chosen to favor the skeptical case. In reality, the actual number of outliers would favor the resurrection.

There's still more. Note that, for the "skeptic's distribution", we've integrated out to infinity to get the probability of it explaining the level of evidence for Jesus's resurrection. Strictly speaking, this is an improper way to calculate the Bayesian likelihood. The correct way would be to calculate the probability for the "skeptic's distribution" getting the ACTUAL level of evidence for Jesus's resurrection, rather than calculating the probability of it EXCEEDING that level of evidence. Of course, doing it correctly makes the likelihood smaller, because you're giving up all of that probability out to infinity in the long tail.

The Christian hypothesis must face the same treatment, of course. So its Bayesian likelihood would also drop. But this will not as detrimental as it is for the "skeptic's distribution", because the Christian hypothesis more narrowly focuses the distribution of evidence around the actual value. That is to say, if Jesus did really rise from the dead, it's quite likely for that to have left the amount of evidence that we actually find, while there's good reasons for it to be not that much greater. On the other hand, a long-tailed "skeptic's distribution" would extend on out to infinity - with the consequence that it must pay when the band narrows to the actual amount of evidence we have.

You can argue that the "skeptic's distribution" need not extend on out to infinity - but that just means you're arguing that the "skeptic's distribution" does not follow a power law, instead following another distribution with a stubbier tail. So either the "skeptic's distribution" does worse because it's actually a "stubbier" distribution than a power law, or because it loses its probability mass when we force it to focus around the amount of evidence we actually have in history. In any case, our previous calculation was one that favored the skeptic's case.

Lastly, it's very important to realize that our entire argument about the "skeptic's distribution" only takes the AMOUNT of evidence into account. It argues that no possible effect - not even the ones with a near-total dependence in the evidence (e.g. conspiracy theories) - could falsely generate the amount of evidence for Jesus's resurrection.

Of course, Jesus's resurrection has more than just the sheer AMOUNT of testimonies going for it. We have not yet considered any of the evidence that Christianity has that specifically counters hypotheses like conspiracy theories. These evidence must be considered on top of the mere existence of the numerous testimonies to Jesus's resurrection.

Now, recall that nearly all of the remaining possibility for the skeptic was in crackpot theories like conspiracies. So these evidence against crackpot theories apply nearly their entire weight against the remaining probability for the skeptic. Considering these anti-crackpot evidence would strongly shift the conclusion towards Christianity.

So we see that "even odds" for Jesus's resurrection really is a minimum. It's a value derived by severely discounting and ignoring huge realms of evidence for the resurrection, while granting the skeptic's case every reasonable allowance. The actual odds would be far more favorable towards Christianity.

Next week, we calculate what such "actual odds" may realistically be.

You may next want to read:
Human laws, natural laws, and the Fourth of July
History, moral progress, and moral perfection (part 2)
Another post, from the table of contents

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