## Friday, December 31, 2010

### Are miracles improbable?

Here's my take on the meaning of the slogan: Extraordinary Claims Require Extraordinary Evidence. (I don't know if other nonbelievers would agree with this.) An extraordinary claim is a claim that an improbable event occurred. An example is a miracle. Since a miracle is a violation of a law of nature it does not happen very often, possibly never. We can estimate a highest possible value for the probability of some miracle occurring e.g one in a billion for a person rising from the dead. (Say if approximately out of every billion people that have died there is one alleged claim of resurrection.) Extraordinary evidence for an extraordinary claim would be evidence which if the claim were not true, then the probability of the evidence itself would be a lot lower than that of the extraordinary claim being true. For example if testimony to a miracle was given and the likelihood of such testimony occurring was say one in a trillion if the miracle did not actually occur. (Thus a believer might argue that approximately out of every trillion false claims made there is at most one which is endorsed by a person willing to die for the claim.) If the probabilities involved cannot be compared then no case can be made.
By Peter Hawkins on The onus of miracles on 12/31/10

Is it improbable that a poker player had five royal flushes in a row? Well, that’s highly improbably if the deck is randomly shuffled. If, on the other hand, the dealer is a card sharp, then it may be highly probable (even inevitable) that the player had five royal flushes in a row.

So you really can’t say, in the abstract, what is probable or improbable. That depends on other variables, known or unknown.

1. One relevant variable is the existence of God, which would make the Resurrection highly probable, as Licona noted.

2. I think the point Peter is making is that there is a sensible Bayesian gloss to give ECREE like this.

If ones prior odds of some claim are very low, one needs very high likelihood ratios to make that claim convincing.

Or ('scuse unformatted maths)

P(C|E)/P(¬C|E) = P(E|C)/P(E|¬C) * P(C)/P(¬C).

If P(C)/P(¬C) is very low - the claim is improbable ('extraordinary'). The likelihood ratio of evidence must be strongly slanted towards the claim to make the claim convincing. I leave it as an exercise to the reader to fill in the numbers Peter provides.

So that "if Christianity is true, the resurrection isn't surprising at all" or "if he was cheating, 5 flushes wouldn't be surprising" was sort of the point he was trying to make.

When saying (for example) that the Gospel accounts are evidence for the resurrection, one is assumedly suggesting that they give a big confirmatory shove to resurrection over it's negation. An ECREE reply following Hawkins could be 'perhaps this data does favour the resurrection hypothesis - however, my prior assignment of the likelihood of any radical breaks in the apparent laws of nature (like a bodily resurrection) is very low indeed. For the gospels to make it reasonable to believe the resurrection occurred they would need to be extraordinarily good evidence - such that the resurrection explains them much better than any other naturalistic counter-offer as to how the Gospel came to be. It is my judgment that the evidence don't reach that bar".

Someone might be mistaken in making assignments as they do, but their practical reasoning is impeccable. Perhaps a slightly more accurate (albeit less snappy) way of putting it is "Claims I take to be extraordinary take evidence I judge as extraordinarily powerful".

Happy new year

3. You haven't justified the negative priors. And it's profoundly unclear how you could even make a stab at doing so. How do you know ahead of time that the deck is stacked or randomized?

4. I would say that drawing 5 royal flushes in a row is pretty good evidence for a highly probable existence of the Card Sharp.

5. Steve: *Shrugs* it's no more (un)justified in principle than having any other sort of priors. And I think someone has fairly good reason to set P(bodily resurrection) extraordinarily low, unless they have some good reason to hold otherwise (like Christianity).

The card dealing case makes it easier. If we see five royal flushes, that seems to be evidence that the guys a (fairly incompetent) cheat: it is far more likely you'd see five royal flushes if the guy was a cheat than if he wasn't. If this guy was Ghandi or similar, though, you might still prefer the hypothesis they just got lucky.

6. thepolemicalmedic said...

"Steve: *Shrugs* it's no more (un)justified in principle than having any other sort of priors."

"Shrugs" is a pretty poor way to justify your priors. And the question at issue is not whether you're justified in having priors, but whether your priors are justified.

I realize the temptation to make this easy on yourself. But you must pay the toll before you cross the bridge.

"And I think someone has fairly good reason to set P(bodily resurrection) extraordinarily low, unless they have some good reason to hold otherwise (like Christianity)."

You *say* they have a good reason without *giving* a good reason.

*Given* Christianity, that no doubt has an affect on our expectations.

But even absent the given, we we’d only be justified in setting a low (must less extraordinarily low) prior probability of the Resurrection if we also knew the pertinent variables, which (ex hypothesi) rendered the Resurrection highly improbable.

How do you know in advance of the fact the pertinent variables which render the prior probability of the Resurrection high or low?

"The card dealing case makes it easier. If we see five royal flushes, that seems to be evidence that the guys a (fairly incompetent) cheat: it is far more likely you'd see five royal flushes if the guy was a cheat than if he wasn't. If this guy was Ghandi or similar, though, you might still prefer the hypothesis they just got lucky."

You're missing the point. I'm not discussing what a witness saw. Rather, I'm asking how you'd be in a position to quantify the in advance of the fact. If you don't know ahead of time whether the deck is stacked or randomized, how can you probabilify the priors?

To quantify the outcome one way or the other, you need additional information. It's not something you can quantify in a vacuum. Therefore, the assignments of prior probabilities would be premature and unwarranted absent further salient information.