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One possible class of objections would try to argue that the prior probability for the resurrection wasn't small enough. So one may say:

"It's not just that people don't rise from the dead. NO supernatural claim of ANY KIND has EVER been validated in a controlled setting. Therefore the prior probability for the resurrection must be smaller than the value used in the calculation."

Well, let's again just give away everything the this objection asks for. So, take every human to have ever existed (1e11), and say that every single person has made 100 supernatural claims, all of which we have managed to test in "controlled settings" and have proven false. I will just ignore the fact that this level of testing simply hasn't been actually done. So, if I were to grant all that, the upper bound on the probability of the resurrection would drop to... 1e-13, which is 9 orders of magnitude LARGER than 1e-22, the value we actually used.

In fact, to demonstrate just how much we've already given away by setting the prior probability to 1e-22, consider the following scenario. Let's go ahead and say that every single mammal to have ever lived - estimated to be around 1e20 animals - have each made 100 supernatural claims, and that we have tested every single one of these claims and found them all to be false. Now, take a moment to actually imagine what this would entail: a time-travelling bunny would hop up to you and say "A mean old wolf tried to eat me, and I broke my leg while trying to get away - but then I was miraculously healed! And I was also blessed with this carrot!" And you'd respond, "Well, Mr. bunny, do you mind if I go ask Mrs. bunny, Mr. wolf, and your friends the sheep to see if they can verify your story? Because the other 99 times you told me something like this, it turned out to be false." So you would get into the time machine with Mr. bunny and his carrot to see if you can validate this supernatural claim.

It only is at this level of fantasy - with talking animals making supernatural claims, which you attempt to verify with your time-machine - that we finally reach enough of a sample size (1e20 mammals, 1e2 claims each) to reduce the prior probability to 1e-22. At this point, we're far into the realm of the absurd, and more than a dozen orders of magnitude past any semblance of empiricism. So the prior probability of 1e-22 we used is, as I already said, a far smaller value than anything any skeptic can rationally ask for.

Here is another objection along the "prior is too big" line.

"But science says that miracles can't happen; so whatever prior probability value you've set for the resurrection must have been too big to start with. If the conclusion to the calculation is that the resurrection actually happened, we must reduce the prior probability, so that we can arrive at a rational, scientific answer."

One wonders at how anyone can invoke "science" after abandoning empiricism and ignoring mathematical reasoning. This kind of statement betrays a willingness to pay lip service to math, reasoning, and science, while ignoring the conclusions that these fields actually lead to - all for the purpose of clinging to a bankrupt preconceived notion.

For instance, I have seen numerous skeptical arguments about miracles that mention Bayes' theorem and their prior probabilities. I have not seen a single one of these put an actual, numerical value to this prior probability. Among all the ones that I've seen, the argument has ALWAYS been "and since this number is going to be so small, it might as well be zero, although the value isn't actually, absolutely zero". So they claim to acknowledge that the prior probability can't be zero, while the argument functions as if it were zero in all circumstances. They thus pay lip service to probability theory, while ignoring it in practice, to reach their preconceived conclusions.

You must actually do the math. Use Bayes' rule. At the very least, don't just bring it up only to have your biases negate the whole point of using Bayesian reasoning. Ideally, try to assign actual values to the various probabilities and likelihoods, even if they're just order of magnitude estimates. Base these values on some kind of empirical data. And most importantly, don't just reject the conclusion because it didn't agree with your preconceived notions, or fiddle with the numbers to arrive at the conclusion you were looking for.

We'll continue our examination of possible objections next week.