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

Bayesian evaluation for the likelihood of Christ's resurrection (Part 10)

Here is another typical attempt to deny Christ's resurrection:

"It may be that some of the disciples were crazy or especially grief-stricken after Jesus's crucifixion. This lead them to see some vivid visions of Jesus, which they related to the other disciples. Some of these other disciples, who had not seen the visions themselves, then spread the story about the 'resurrection' based on the vision of these few crazy people. Then, a few other disciples, who were dissatisfied with Judaism, formed an opportunistic conspiracy to start a new religion based on these budding stories about this 'resurrection', and that's how Christianity started.  

Or, it could have gone another way. A few disciples wanted to start a new religion and formed a conspiracy. After Jesus's death, they suggested to some of the other, more gullible and mentally unstable people that Jesus rose from the dead. With a little faking of evidence, social pressure, and the power of suggestion, they eventually got enough of the other disciples to say that they saw the resurrected Jesus themselves. From there, the resurrection became part of their faith narrative, and that's how Christianity might have started. 

There are dozens of other possibilities like these - it doesn't have to be that everyone was lying or crazy. We just need the right combination of lies, mistakes, and insanity at the right times and situations for Christianity to start. Surely, it is more likely that one of the many possibilities represented here lead to the belief in the resurrection rather than for Jesus to have really come back from the dead."

This is merely an attempt to muddy the waters by complicating the issue.

First, note how weak this argument is, even if we were to grant it everything that it asked for. Remember, the odds for the resurrection are currently at 1e32, so the odds against it are therefore at 1e-32. Now, we'll allow for each independent objection to count as having the full weight of these odds. Never mind that many of these objections contradict one another and therefore reduce the probabilities of the other objections (increasing the probability for 'insanity' decreases the probability for 'conspiracy', because a conspiracy is less likely to succeed with insane people in it). We'll just ignore that. Never mind also that these complex speculations are naturally less likely because of their complexity. We'll also ignore that as well. So, if we can think of a hundred such objections, each of which carries the full weight of the 1e-32 odds for 'no resurrection', the final odds for the resurrection would drop all the way down to... 1e30.

In short, if you're serious about this approach, go ahead and write out a billion independent objections of the kind demonstrated above. That would drop the odds for the resurrection to 1e23, and it might then merit a footnote as something that someone might want to look into sometime.

But more importantly, this kind of objection is simply, fundamentally wrong: it would not fly in any other investigation into a personal testimony, because it completely ignores the rules about how we evaluate evidence in a Bayesian framework.

Imagine, for instance, that your friend claims to have been struck by lightning. You've taken stock of this claim and have decided to assign it a Bayes' factor of 1e8. But then you say, "well, you may be just a little crazy. And you might have had a nightmare about a thunderstorm last night. Then you might have gone to a hypnotist and who had you recall your dream, which you're now confusing with reality. Or maybe it was the hypnotist who planted the suggestion in your mind first and that caused your nightmare. Really, it might have been any of these things - and isn't it more likely that at least one of these possibilities is true, rather than for you to have been actually struck by lightning?"

Should you or your friend then discount the previously assigned Bayes' factor in light of these new possibilities? Absolutely not. The thing to note here is that the Bayes' factor ALREADY includes all of the ways that this claim may be wrong. It is the numerical estimation of the weight of evidence for a human testimony, and as such already inherently includes the possibility that the evidence may be misleading.

Having established its value, it is simply incorrect to further modify it with no evidence, based on enumerating possibilities that were already included in its evaluation. Your friend's proper reply to your wild speculation would be to say, "what makes you think that I had visited a hypnotist or had a nightmare? Of course, anyone might be wrong about anything in any number of ways - but don't you already know how much you trust me? How does a list of ways that I might be wrong, with no evidence behind any of it, make you trust me less?"

Again, this goes back to the "barrage of objections" tactic I mentioned earlier, and why it fails against the resurrection argument presented here. The trap is to get you to think of the many possible objections against the argument, then confuse you into thinking "at least one of them must work!" It requires you to forget that the argument here is fundamentally immune to that line of attack. Once again, my argument is not a deductive argument. It is an order-of-magnitude probability estimation using Bayesian reasoning. It starts with a prior probability, and then it modifies that probability based on the evidence. So, is there any evidence that your friend had a nightmare about a thunderstorm? Then it is proper to include that evidence to re-calculate the probability of the lightning strike. Is there any evidence that a crazy group of disciples reported on the resurrection, which then got hijacked by a conspiratorial group of disciples? Then it would be proper to include that evidence to re-calculate the probability of Christ's resurrection. However, in the absence of such evidence, the mere existence of that possibility should not change our calculations. Such possibilities are already included in the initial calculation.

Let me give an even simpler example. Suppose you flip a coin, then cover it up so that you don't know the outcome. Not having investigated the coin all that carefully, you assume that the probability of it turning up 'heads' is 0.5. Now, someone comes up to you and says, "but consider all the ways that it may turn out to be tails. It might have hit the tabletop, flipped three times after the bounce, landed on its edge, then fallen over to show tails. Or it may have flipped fifteen times before the first bounce then landed flat with the tails side up. In fact, if the coin's leading edge strikes the table at 15 degrees with an angular velocity of 12 rev/s and a downward linear velocity of 2 m/s, it's guaranteed to end up tails. And this is only a small sample of the innumerable ways for you to get tails. Given all these different ways, shouldn't you decrease your 'heads' probability?"

The answer, of course, is that you should not. You should only consider the evidence that you DO have in modifying your probability. You must leave alone any evidence that you MIGHT have. So, in the absence of any evidence, the probability for 'heads' is still 0.5, and the innumerable ways that the coin might turn out to be 'tails' does nothing to change it. Now, it may be that you recorded the first part of the coin flip in slow motion, and it turns out that the coin did indeed strike the table at an angle of 15 degrees for its leading edge, with an angular velocity of 12 rev/s and a downward linear velocity of 2 m/s. That would be evidence. That would cause the probabilities to change. But the mere possibility of this happening, in the absence of the actual evidence, does not change the probability.

Here is the evidence that we DO have: numerous witnesses gave their earnest, personal testimonies, saying that they personally saw the risen Christ. We know how to numerically evaluate such evidence. Earlier in this argument, we have already numerically taken into account the many ways that they may have been wrong, whether through honest mistakes, deception, or insanity. We have no evidence that anything like the speculations of the skeptics have taken place, and the mere possibilities for these speculations cannot change the probabilities. The odds of the resurrection, even with the most conservative estimates, remains 1e32, at a minimum.

We will continue with other parts of the argument next week.

You may next want to read:
Miracles: their definition, properties, and purpose
Sherlock Bayes, logical detective: a murder mystery game
Another post, from the table of contents

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