A Bayesian Argument for the Resurrection of Jesus

I read...a surprisingly large amount of that.

If I understand it right, they are saying that modern scholarship confirms that the Gospels avoid certain obvious failure modes - eg being written hundreds of years after the fact, wildly contradicting each other on important points, and erring on simple points of geography and history - and that someone would've called them on it if they just blatantly made things up - therefore the Gospels can be assumed mostly true. The Gospels say many people saw Jesus die on the Cross and then saw him alive later, and that natural explanations (Jesus survived the crucifixion, everyone was hallucinating, it was Jesus' twin brother - yes, they actually addressed that) are all unconvincing; therefore Jesus really was resurrected. According to the Gospels, this was seen by many witnesses, including luminaries like St. Peter, and none of them later came forward to say "No, we didn't see this at all, shut up". Further, many of them later died an extremely predictable martyr's death, proving that they believed in Christ's resurrection enough to sacrifice their lives for him, something they wouldn't have done if it were all made up (they point out that although some people, like kamikaze pilots, have sacrificed their lives to false philosophies, it is far more unlikely that the Apostles would sacrifice their lives to a false empirical fact, namely that they had seen Jesus rise from the dead).

Multiplying the low probabilities of everyone involved simultaneously having some kind of fit of insanity leading them to sincerely believe Jesus had risen from the dead gives 1 : 10^39 against, and since this is a very small number obviously the argument must be correct.

This argument doesn't quite take the truth of the Gospels as a premise, but it comes close. Although there are some atheist accounts that allow for the truth of the Gospels as written while still casting doubt on Christ's divinity, that's not where the smart money lies - most atheists would deny to one degree or another the validity of the Gospels themselves. Either the entire thing was made up (a theory which the McGrews reject, and I think rightly) or a historical Jesus had various miracles falsely attributed to him by overzealous believers. This leaves the McGrews' objection that the existence of a wider Christian community, many of whom had been personally involved in the events described, would have limited the Gospel writers' ability to make things up even if they had been so inclined.

So instead of basing his argument on the likelihood of people hallucinating resurrected Jesus, the McGrews should have investigated the probability that the Gospel writers would make up miracles and the probability that they would be caught; something like

P(resurrection) ~= P(gospels true) ~= 1 - [P(people make stuff up about Jesus) * P(they don't get called on it)]

So what is the probability that, given some historical tradition of Jesus, it will get embellished with made-up miracles and people will write gospels about it? Approximately 1: both Christians and atheists agree that the vast majority of the few dozen extant Gospels are false, including the infancy gospels, the Gospel of Judas, the Gospel of Peter, et cetera. All of these tend to take the earlier Gospels and stories and then add a bunch of implausible miracles to them. So we know that the temptation to write false Gospels laden with miracles was there. Apologists say that the four canonical Gospels are earlier and more official than the apocryphal Gospels, and I agree, but given the existence of a known tendency for people to make up books, and a set of books that sound made-up, the difference seems more one of degree than of kind.

That leaves the question of whether anyone would notice. The dates of all the Gospels are uncertain, but around 70 - 80 AD for the synoptics seems like a fair guess. The average life expectancy in classical Judaea for those who survived childhood was 40 to 50. That means Jesus' generation would be long gone by the time the first Gospel came out, and even people who were teenagers at the time of Jesus' crucifixion would be dying off. Christian tradition lists all the Apostles except John as dead by 75 AD.

There's also the more general question of argument from silence. Let's say someone did have evidence against something in the Gospels. Most Judeans at the time wouldn't have been literate, especially not in the Greek in which the Gospels were written. Many who were, might not have had the time or interest to pen responses to what seemed a minor cult at the time. If any did, those responses might not have spread in an age when every work had to be laboriously copied by hand. And if by some miracle a refutation did become popular, there's no reason to think we would know about it since many of the popular works of the age have been lost completely.

Matthew mentions that on the day of Jesus' crucifixion, graves opened and the dead walked the earth throughout the city of Jerusalem for several hours. No one else (including the other evangelists!) mentioned the dead walking the earth, either to confirm or refute it, so clearly the 1st century AD Judean skeptical community wasn't exactly on top of its game. That alone casts suspicion on the whole "if this was false, someone would've said so" argument.

All of this makes the Gospel argument relatively uninteresting to me. But it hints at a different problem which is interesting. Twenty years after the death of Christ, we have Paul writing letters to flourishing churches all across the eastern Mediterranean, all of whom seem to have at least a vague tradition of Christ being resurrected and appearing to people. That means Christianity spread really, really fast, presumably by people who were pretty sure they had met the resurrected Christ. At my current, limited level of Biblical scholarship I consider myself still confused on this point and yet to see a satisfactory explanation (people rising from the dead doesn't count as 'satisfactory').

I'm sorry, but you just don't get a Bayes Factor of 10^40 by considering the alleged testimony of people who have been dead for 2000 years. There have to be thousands of things which are many orders of magnitude more likely than this that could have resulted in the testimony being corrupted or simply falsified.

You don't even need to read the article to see that 10^39 is just a silly number, but for those interested, it is obtained by assuming that the probability of each of the disciples believing in the Resurrection is independent of the probabilities for the other disciples. Despite the fact that the independence assumption is clearly nonsense, and they themselves describe it as a "first approximation", they then go on to quote this 10^39 figure throughout the rest of the article, and in the interview.

I'm sorry, but it's this section where the paper just starts to get silly.

One hypothesis that need not detain us for long is that the disciples themselves did not believe what they were proclaiming, that they were neither more nor less than frauds engaging in an elaborate conspiracy.

Well, ok, that does sound pretty unlikely. But is its improbability really even on the order of 10^39? Have the authors actually thought about what 10^39 means?

If you took every single person who has ever lived, and put them in a situation similar to the disciples every second for the entire history of the Universe, you wouldn't even be coming close to 10^39 opportunities for them to make up such an elaborate plot. Are they really suggesting that it's that unlikely?

One of my favored arguments against the historicity of the miracle accounts in the gospels is drawn directly from my own experiences in middle school.

I went to some lengths to convince other children at school that I was an alien. I was smarter than the vast majority of students at my school, and was able to blind them with science so that a fair number actually came to believe my claims. Not only did I manage to convince a number of students myself, many went on to convince other students, making up feats I had not and could not perform as "evidence."

I can't say for sure that all the students who claimed to believe that I was an alien actually did, but a number staked a considerable amount of social status on their belief in my claims, so I'm fairly confident they were not all faking it.

Anyway, it was that experience that taught me about people's propensity to simply make up evidence to convince others of their beliefs.

My favorite part of this anecdote is that it still gets the point across even if I am lying, and made the whole thing up myself.

I may be late to the party, but I really have to ask. Why is this a featured article? Bayesian defense of the resurrection of Jesus gives me a 404, so I cannot even read it.

Ignoring the fact that any argument that comes up with a number on the order of 10^39 is obviously flawed in some way, even if the flaw isn't itself obvious (I don't have the patience to read through the entire article and frankly doubt I would gain much from it, so that's about as far as my analysis on the article itself goes), any argument from human psychology is screened off by lower-level arguments. To put it directly: even allowing the argument as valid, simple physics says "no". For Jesus to be resurrected, the following had to have occurred:

1. The information in his brain would have had to been preserved despite him having being warm and dead for three days (violating thermodynamics and information theory), or else some incorporeal spirit-substance exists which can preserve information and does not interact with the physical world except through the tiny subset of possible molecular arrangements present in human biology (violating a great number of things).
2. His body would have had to have been healed of all fatal wounds and restored to a viable state (violating conservation of energy), while at the same time not healing the injuries to his hands or side (not a violation per se, but improbably extreme selective targeting). Alternatively, he got a new body while the old one disappeared (also violating conservation of energy).
3. Somehow he unraveled his burial shroud without suffocating and managed to remove the stone in front of his tomb, which for a man of normal size and musculature should be close to impossible (and Jesus wasn't described as particularly buff), which is a violation of simple biology. Or else he teleported out, which violates even more stuff.

So, now we have two options. We can assume approximate independence of the above three statements, in which case I wonder what you'd get if you multiplied their probabilities together, or we can contend that they were all caused by a common factor (Jesus being God), in which case I'd like someone to please calculate Kolmogorov complexity of God.

Either way, you're going to get a Bayes factor of more than 10^39 against the resurrection from scientific considerations alone, and that's assuming there was nothing wrong with the original argument from human psychology. Realistically speaking, there's simply no way you're going to get a Bayes factor of 10^39 out of an argument involving human behavior; we're far too noisy for that.

Ad hominem: I also note that the authors are Christians, which strongly suggests to me that motivated reasoning is occurring, even if I can't pinpoint where exactly the flaw(s) is/are. At the very least, there's some major hypothesis privileging going on; why are you looking at Jesus specifically? For example, I wonder what a Bayes calculation for Islam's account of Muhammad's vision of the angel Gabriel being true would look like?

I'll have to check this out. For those interested, here's Richard Carrier's stab at something similar on behalf of the opposing side (LINK).

This doesn't appear to consider the implications this has for other religions; namely, if the story of the resurrection is true, that means that all (or most) other religions must be wrong. Thus, evidence that other religions are not wrong (and I imagine many have as much going for them as the resurrection, if not far more) is pretty necessarily additional evidence against the resurrection (or at the very least against attaching religious significance to it).

This is still a much weaker counterpoint that the impropriety of multiplying probabilities, unfounded assumptions of honesty, and (not mentioned) the problem of survivorship bias: there were likely hundreds of such accounts during that era, but only one of them happened to evolve into a religion and have its writings and accounts preserved long enough for us to see them today.

The link to the bibliography on Bayesian reasoning is dead for me :-(

ETA: Google cache.

ETA #2: While looking for that link I came across this paper by the above mentioned Richard Carrier: “Bayes’ Theorem for Beginners: Formal Logic and Its Relevance to Historical Method — Adjunct Materials and Tutorial”

The linked article has 76 pages :-|

The likes of Pythagoras got attributed with performing miracles too. Although Mark, the first synoptic gospel to be written, is claimed to be an eyewitness account in Christian circles, it is likely that none of the gospels were. Paul was writing before then, but he never directly met Jesus, he only had a vision of Jesus. Also, Paul does not mention the empty tomb anywhere.

I don't think jesus even existed in the first place.