A few months ago, there was a post over at Thinking Christian about the historical accuracy of the Resurrection of Jesus. This got me thinking about the inferences involved in reaching the conclusion that the Resurrection probably happened.
Intuitively, the Resurrection is significant because it is a very unusual event. We have never observed any other resurrections, so scientifically, we can estimate the odds at being around 1 in 10 billion. Or perhaps it's less likely still.
It is this improbability which has to be compared with alternative improbabilities in assessing whether we should infer that the Resurrection happened. For example, would someone write a story saying that it happened if it never occurred? Would the story have been embarrassing to the early church that promulgated it? Well, suppose that we assign a mere 1% chance that the story was fabricated, and another 1% chance that the church would have told a story that was embarrassing. Let's throw in another 1% improbability factor, just for fun. That brings us to 1 in a million odds that the story would have been written if it weren't true.
No help there. The story only becomes plausible when we reach 1 in 10 billion odds. After canceling factors, there's still only a 1 in 10,000 chance that the story is true. A rational person must conclude that the event probably didn't happen.
This isn't proof that the Resurrection didn't occur. It may have. It's simply not rational to conclude that it did.
If you're a god, what is the point of demonstrating your power in an unambiguous way to just a few people, when the rest of the world would be irrational to conclude that the witnesses were telling the truth?
What we have discovered here is a trap set by our intuitions. We intuitively think that miracles (highly improbable one-time events) are an appropriate way for a god to verify his status as deity. This intuition is flawed because it only works if the believer fails to be rational. Instead, the god should demonstrate his power in repeatable, scientifically testable ways, so that rational people will have reason to conclude he is at least god-like in capability.