Blog pages

Bayesian evaluation for the likelihood of Christ's resurrection (Part 9)

After hearing many objections in succession as we just have, it's easy to lose sight of the big picture. For instance, one may fall into the trap of thinking that if even one of these objections has even the slightest chance of being true, the argument would fall apart. But is that really the case? If the disciples had even the slightest chance of being crazy or mistaken or deceptive about the resurrection, would that cause the whole chain of reasoning to break and the case for the resurrection to collapse?

This is where it's useful to remember the big picture. You see, a standard deductive argument does work like that - A and B together lead to C, which lead to D, which then leads to the conclusion. For such an argument, all of its premises must be entirely true and each step of its reasoning must be completely correct. Anything else invalidates the whole argument. That is why a barrage of objections can sometimes succeed against such an argument, or at least cast doubt on its soundness.

But my argument for the resurrection is not a deductive argument. It is an order-of-magnitude probability estimation argument using Bayesian reasoning. The objections against it can take two forms: you must either claim that I'm misusing the mathematical apparatus (that is, Bayes' rule), or disagree with my estimated values for the probabilities.

If you think that I've made a mistake in applying Bayes' rule, then by all means point it out. Otherwise, the objections against it all come down to wrangling over the probability values. The point here is that in such wrangling need not produce absolute certainty. The argument does not depend on it. I do not need to claim, for example, that there is absolutely no chance that the disciples were lying. Having demonstrated that the Bayes' factor for a typical, relatively unconditioned human testimony is around 1e8, I only need to demonstrate that the disciples are not more likely to be liars than such a "typical" person. In fact, anything which suggests that the disciples' honesty exceeded that of the "typical" person actually strengthens the argument beyond its original form, by increasing the Bayes' factor. This is what has actually happened upon the examination of every single objection thus far.

Furthermore, even if one of the objections were to "succeed", it would not be a fatal blow to the argument; we would merely have to re-calculate the final odds. So, for instance, let's say that the objection about the disciples being mistaken somehow "succeeds", and it results in the Bayes' factors from their testimonies dropping from 1e8 to 1e4. In fact, let's say that these objections are so wildly successful that we must take the square root of every single Bayes' factor we used. Such an instance would not cause the whole argument to be simply invalid. Instead, we would just have to recalculate the final odds with the new numbers. We'd find that the final odds dropped from their original value of 1e32 to 1e5 - corresponding to around a 99.999% chance FOR the resurrection still having occurred.

So, let's be clear about the effect of these repeated objections. Our argument is not a deductive argument. If it were, any objection might cause the whole argument to be invalidated if we can't demonstrate with absolute certainty that the objection is false. It is easy to think this way when you hear many objections in succession - that one of them must eventually get through a chink in the armor and deliver the fatal blow. But it simply does not apply to our case.

Rather, our argument is an order-of-magnitude probability estimation using Bayesian reasoning. From the beginning, it is strong enough to survive multiple successful objections against it. We are then fielding objections against this argument. If an objection succeeds, that would decrease the power of the argument - but if it fails it must correspondingly increase the power, by demonstrating that the resurrection witnesses were more honest, correct, and sane than what we had initially assumed. And this latter case is what has happened in every objection thus far.

So, we've started from an incredibly strong original argument, and each of the repeated objections have only strengthened it further. We will continue to look at more opportunities for strengthening next week.

You may next want to read:
A real discussion on the problem of evil and omnipotence.
Isn't the universe too big to have humans as its purpose?