When it becomes apparent that Christians like myself are depending primarily on history for empirical evidence of God’s involvement in history (imagine that!), atheists quite often appeal to probabilities….specifically, Bayesian probability.
Now, Bayesian probability is a complicated subject, but the relevant point here is that the probability of a particular event (or of a particular explanation being true) depends on its prior probability: the base rate of that particular event within the general population of events. Simply put, if a particular event is already known to be extremely rare, this “rareness” needs to be included in evaluating evidence for that event.
Bayes’ Theorem (image by mattbuck)
This becomes particularly important when we’re comparing competing explanations. Even if the evidence seems to point more toward one explanation, that explanation might not be the most probable if it was already very unlikely. For example, hearing a loud thunderous roar outside is good evidence that there’s a thunderstorm….unless, of course, you live in the desert outside Baghdad, where thunderstorms are vanishingly rare and roadside bombs are much more frequent.
It’s important because prior probabilities aren’t always easy to spot. For example, let’s say that you test positive for a very rare type of cancer, and the test is 80% reliable (in other words, 20% of the people who are cancer-free will get a false positive). You might conclude that you have an 80% chance of having the cancer….but you’d be wrong. The cancer is very rare to begin with, so your chances of being cancer-free and having a false positive are higher than your chances of having cancer in the first place.
The atheist argues that it doesn’t matter how improbable a natural explanation of the resurrection account is. The prior probability of a divine miracle is 0, so a naturalistic explanation is more likely no matter what.
Of course, this begs the question, and it’s bad math. An event without precedent doesn’t have a prior probability of zero; it has a prior probability that is undefined. But that doesn’t stop the atheist. As Jeff over at Randal Rauser’s blog argued:
We just don’t have any way of assessing the probability of the miracle option, and so there’s no reason to consider it a live option.
But that’s wrong.
Suppose archeologists uncover a previously undisturbed Mayan ruin next to what appears to be a large meteor impact crater. However, there are no meteor fragments. Mayan glyphs within the ruin say that demons fell from the sky in a great metal coconut and tried to draw the people away from the priests. The demons, it says, were ambushed and killed; their great metal coconut was dragged into the sea.
In among the ruins are carvings of a language unlike any known lexicon on Earth. Some of the symbols are numeric; they describe a series of primes and representations of the first five perfect numbers, along with a representation of pi and depictions of orbital mechanics. Finally, there are carved drawing which appear to depict a Dyson sphere at various stages of development.
Now, it’s entirely possible that all the elements of this discovery are all purely coincidental. Perhaps this branch of the Mayans had more knowledge of advanced mathematics than we had thought, and perhaps the whole “great metal coconut” was a myth that sprang up following a meteor impact that mysteriously left no fragments. Perhaps the depictions of a Dyson sphere are coincidences as well. It’s wildly unlikely, but it’s theoretically possible.
Yet this is what the skeptical atheist must maintain. Why? Well, we don’t have any past instances of alien landings on Earth, so we have no way of assessing the probability of the alien option. Clearly, then, there’s no reason to consider it a live option. No matter how strong the evidence for an alien landing was, the stubborn misapplication of prior probability would lead the atheist to insist that it was not an alien landing.
This is ridiculous, and it’s not at all the way we actually view reality. We don’t start life with a set of pre-defined prior probabilities; every event we are exposed to (personally or by someone else’s testimony) builds prior probability over time. If we had to know prior probability in order to evaluate ANY evidence, we wouldn’t be able to know anything at all.
More simply put: if you can’t believe in something unless you’ve already seen it at least once before, you can’t believe in anything at all. There’s a first time for everything.
Ultimately, the appeal to undefined prior probability is just a complicated way of neatly veiling unfalsifiability. If prior probability of a particular option is undefined, that doesn’t mean you can just throw the option out. It means purely Bayesian probabilistic analysis just isn’t going to work.