The idea at work behind my lottery example is pretty central to the rest of it, so I’ll start there. In essence, the big idea is that lots of technically distinct outcomes are indistinguishable in practice. If Person A that you’ve never heard of wins the lottery, you don’t regard this as being particularly noteworthy, even though it was obviously incredibly unlikely to have happened. This is because, as far as you’re concerned, Person A is exactly like almost everyone else who bought a ticket. Had Person B won the lottery instead, you would have thought about Person B exactly as you would about Person A. It’s unremarkable that Person A won because, in a sense, somebody that you could label as ‘Person A’ was overwhelmingly likely to win that lottery. It was either going to be ‘Person A’ or someone important to you, and people important to you only bought a dozen tickets all together. Similarly, when you roll a 100-sided die, you don’t feel the need to explain the fact that you rolled a ’23′ despite the tremendous improbability of doing so. This is because ’23′ is only meaningful to you as a number, like any other, and you were guaranteed to roll one.

To make the analogy to modern Christianity more explicit, I think it’s clear that Christianity doesn’t depend on the name ‘Jesus’. What’s important (to greatly oversimplify) is that its central figure was the messiah and that he died and arose. That is, supposing that the story of Jesus had died out rather quickly, while the story of this Simon had caught on, stuck around, and become a powerful religion worldwide, something relevantly like Christianity would exist today. It might be different in any number of particulars (just as one stranger who wins the lottery can be an old housewife in Ohio while another is a coal miner in Nevada), but these particulars aren’t important with respect to addressing the single historical question at stake (whether the messiah died and rose).

I think that the explicit probablistic argument is probably just needlessly confusing, and that the rest follows fairly intuitively. The idea is that a religion relevantly similar to Christianity (that is, one based the messiah resurrecting) could have come about in one of four ways. Prior to this, we were only considering two possibilities. If Jesus actually rose, and his story spread, then that explains Christianity. If Jesus did not rise, and a myth spread about his rising anyway, then that also explains Christianity. There’s some probability that the first possibility occurred, and some possibility that the second occurred.

To choose convenient numbers (and not meaning to imply anything about the actual probabilities involved), say that we concluded that there was a 50% chance of Christianity being the result of Jesus actually rising, and a 50% chance of it being a result of a false myth about Jesus. That means that, from our present observation (that Christianity exists), we conclude that there was a 50% chance that Jesus actually rose. However, because our present observation can’t distinguish in advance between Jesus-Christianity and Simon-Christianity, the survival of Simon’s story has to be considered as well. Now, in addition to our first two possible explanations of our observation that Christianity exists, we also have to consider two similar explanations involving Simon. If we assume that everything else is equal, this gives us a 25% chance of Jesus rising, a 25% chance of a false Jesus myth surviving to the present, a 25% chance of Simon rising, and a 25% chance of a false Simon myth surviving to the present. That Christianity is -actually- about Jesus is unimportant, just as it didn’t matter that you’d actually rolled a ’23′. The fact of the ’23′ was unsurprising -because- there were so many other numbers that were indistinguishable beforehand.

However, no one thinks that Simon could actually have arisen. Christians not only believe that Jesus was the messiah, but that no one else could have been the messiah. Nobody thinks “well, someone else could have risen instead”. So, if we’re discounting that explanation for Christianity, we’re left with only three. Each was equally probable before, so they’re equally probable now (even if we didn’t start from equally probable events, they’d remain proportionally similar), and we now conclude from the fact of modern Christianity that there’s only a 33% chance of someone having risen.

Again, I used those probabilities because they were convenient. If you wanted to use 99% for Jesus having risen and 1% for a false Jesus myth surviving, it would become something close to 98% Jesus rising, 1% false Jesus myth, 1% false Simon myth. The point is merely that one’s certainty has to decrease.

The intuitive take-home of all of the above is merely that as the number or likelihood of possible explanations for something increase, the likelihood of any other explanation being correct decreases. This tablet is at least suggestive of other explanations for our observation that modern Christianity (or something indistinguishable from it beforehand) exists, and so other explanations (including that Jesus actually rose) must be seen as less likely.

The whole thing is tremendously oversimplified, of course. In fact, we have to consider interference effects between the two stories and the possibility that this raises that there were other similar stories going around that we haven’t discovered yet, to name a few things.

I’m still having trouble understanding how the probability that Jesus rose from the dead is reduced if we find out that there was a 1 cent. BC figure named Simon whose disciples claimed that Gabriel said that he (Simon) would rise from the dead.

I had trouble following the lottery argument. Maybe I am just a little slow.

I looked at the Wikipedia article. Looking at the statement of Bayes’ theorem, it looks like the probability of A will only change (that is, P(A|B) will be less than P(A)) if P(B|A) and P(B) are different. So the probability that Simon’s followers claimed that Gabriel said Simon would rise from the dead given that Jesus rose from the dead would have to be different from the probability that Simon’s followers claimed that Gabriel said Simon would rise from the dead. I have no idea why that would be the case. Maybe I have misunderstood the formula.

It’s simply about how we consider testimony. Ames is the lawyer, but it seems to me that a witness who maintains that someone performed a miracle is a whole lot more persuasive by himself than he would be if we’d already heard (and discounted the testimony of) other witnesses making similar claims about other people.

I probably worded that poorly, so let’s consider an analogy to investors. Successful casual stock traders (and some professional ones) suffer horribly from a phenomenon known as survivor bias. They came up with a strategy, followed that strategy, and consistently made pretty good money. They know that this sort of thing doesn’t happen often by random chance, so they assume that there’s something to their strategy. What they’ve overlooked is that lots and lots of people tried something similar and lost money. It’s like winning a lottery and assuming that it was because you had a better number-picking strategy than everyone else did. You absolutely have to look at the whole initial sample, and you have to make sure that a successful result was not just an expected statistical outlier. Someone had to win that lottery, after all.

From our vantage point, we can note that, yes, it was pretty unlikely that this particular person would win this particular lottery. However, when we consider that we would have said that about every person who bought a ticket, we see that our observation was guaranteed beforehand.

Something similar can be done here. Assuming that the story of Jesus is unique, we know that we can represent our probability of knowing of it in the present as P = P(j)P(jl) + P(~j)P(fjl), where P(j) is the probability of the Jesus story being true (whatever that may be), P(jl) the probability of the true Jesus story surviving to the present, P(~j) the probability of the Jesus story not being true, and P(fjl) the probability of the untrue Jesus story surviving to the present.

On the other hand, if the Jesus story is not unique, it’s obvious that we could not distinguish the present situation from one in which another, similar story had survived (this is just like when we noted that one person winning the lottery was indistinguishable from another person in advance). So the probability of our knowing of a story indistinguishable from the Jesus story becomes P = P(j)P(jl) + P(~j)P(fjl) + P(s)P(sl) + P(~s)P(fsl), where the ‘s’ represents this other figure and less the conjunction of two surviving stories (though we can assume that this is unlikely, and it will remain higher than the probability given just one potential figure).

Provided that the above adequately describes the situation, and provided that no one thinks that Simon could possibly have been the messiah, it follows from Bayes’ theorem (see Wikipedia) that this evidence makes it more likely than it was before that no one rose from the dead. I think that Wikipedia does a good job of explaining that last bit, but I’d be glad to take a stab at it if you’d like.

I’m not an expert on Judaism but I had been getting the feeling that Jewish scholars were downplaying the idea that Isaiah 57 referred to the Messiah or that the Messiah would be a suffering servant. Now we’re being told that Judaism already had an idea that the Messiah would die and rise again and that that somehow casts doubt on the Christian faith. Maybe I am missing something. Or maybe the folks seizing on this to question the gospels are.