A Bayesian Argument for the Resurrection of Jesus

by lukeprog1 min read8th Jan 201141 comments


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I think LWers may be intrigued...

Tim McGrew, author of this excellent annotated bibliography on Bayesian reasoning, recently co-authored with his wife Lydia a Bayesian defense of the resurrection of Jesus. I interviewed Lydia for my podcast, here. Atheist Richard Carrier has leveled some objections to their article, but his objections are weak.

Have at it.

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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').

Lydia McGrew responded to you saying:

... the earlier commentator who says that the probability is "approximately 1" that there would be made-up resurrection stories (and apparently thinks that this applies to the gospels) ignores various obvious distinctions. For example, the distinction between stories by people who had nothing to gain and everything to lose for making up such stories and people who had nothing to lose and something to gain by doing so. Also, the distinction between people's elaborating stories when they themselves were in a position to know what really happened and people who were not in a position to know what really happened.

We are talking in the paper about what the disciples themselves claimed. They were in a position to know whether what they were claiming was true or false, and they had a great deal to lose and nothing to gain by simply making up such tales. - link

Thanks for pointing that out. Needless to say I don't agree, but I respect her decision not to get in an endless internet argument about it.

Would you be willing to elaborate on that? I have a strong personal interest in your thoughts on the matter, having previously spent some time on the bizarre world of Christian apologetics, myself.

I would like to hear your disagreements too, even if Lydia McGrew is not interested.

Obviously, outputting numbers like 10^39 is a sign that your argument is flawed. Nonetheless, I have sympathy for McGrew because so many are misunderstanding her argument.

Christian: If they were independent, the chances of the disciples coming up with the same story are tiny. So it is most likely they are all reporting reality.

Non-Christian: I agree that would be the case if they were independent, but it is more likely that they were in communication and conspired than that there is a supernatural/Jesus rose from the dead/etc.

C: If they were in communication, each martyr had the opportunity to sell out the conspiracy when threatened with death. As unlikely as all the disciples independently hallucinating and dying for a lie is, it is even less likely that each martyr independently chose to die for a conspiracy when each martyr knew any of the other disciples could render their martyrdom pointless by selling out the conspiracy (i.e. defecting in the prisoner's dilemma).

It is even less likely that all of them would cooperate in a many-way prisoner's dilemma when each knew the others knew how unlikely it would be for each to cooperate in a many way prisoner's dilemma when each knew...etc.

Therefore, the conservative assumption is that each was independent, which yields 10^39 to one that Jesus rose from the dead at the least (though it is really more likely than that because I am assuming independence, for which my argument is weaker than had they conspired). Consider: each would be consciously dying for a lie (nothing to gain, everything to lose), unlike people who later made up stories to be famous or for whatever reason (everything to gain, nothing to lose) when they were not in position to now what had happened.

So I am using 1 - [P(people make stuff up about Jesus) P(they don't get called on it)], P(they don't get called on it) is tiny for cases in which each disciple is claiming that the other disciples were eyewitnesses, particularly* when they are not independent.

N-C: Aha! So you admit that you got 10^39 from an assumption of independence!


We know that many zealous followers are willing to die for the honor of their leaders. It would not be very surprising to see that happen in early Christianity.

There isn't even a requirement that they all do so - or even most! Those who recanted would be forgotten, their recanting being attributed to pressure rather than belief.

You said pretty much exacty everything I would have said and more.

One question--I only read the first third of so and skimmed the rest. The bits I read seemed to give a false dichotomy for dates of the composition of the gospels. The authors discussed atheistic schools that believed the gospels were all composed post 100 and contrasted these with the pre70 dates of Christian belief. Do they ever discuss the modern scholarly mostly-consensus of 70-90?

Relatedly, do you know of any good arguments for post 70 composition dates, especially for Matthew and Luke, other than fulfilled prophecies of the destruction of Jerusalem? I've always found the arguments that these books were written before 70 because they could not have predicted the destruction of Jerusalem suspiciously question-begging about the possibility of miracles.

I'm afraid I really know very little about dating the Gospels; I just trusted what I saw on Wikipedia.

[-][anonymous]10y -3


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Why would the apostles all die martyrs deaths for someone who didn't live up to his promises? Especially since the gospels show they weren't of the most courageous character either. That is pretty convincing to me, I don't know of a good counter.

Also, if there were so many Christian communities so soon after Jesus' death, then there would be a good community of knowledge to filter false and true accounts of Jesus life.

Finally, why didn't any of the other unorthodox accounts start similar communities? Why are the communities so similar in their beliefs about Jesus, if it is quite likely to have been made up, as you suggest?

Finally, why didn't any of the other unorthodox accounts start similar communities? Why are the communities so similar in their beliefs about Jesus, if it is quite likely to have been made up, as you suggest?

They did. There were plenty of wildly disparate sects of Christianity early on, out of whose beliefs the gospels that were declared noncanonical rose up in the first place. Most of these communities died out over time, although some lasted for centuries, and Gnostics, who existed in several branches and were the most significant competitors for what became "mainstream" Christianity, still exist today. I suggest reading up a bit on Gnostic mythology to see just how disimilar it is to all mainstream branches of Christianity.

As for why the apostles would die martyrs' deaths for someone who didn't live up to his promises, we have no reason to think they did. That is, they weren't killed for their beliefs after being given the option of recanting to have their lives spared. This is a popular meme, but there's no historical basis for ever suspecting it happened in the first place. jhwendy's link at the bottom of the page provides more information on this.

As for the Christian communities being able to filter true and false accounts of his life, we already know that they didn't; witness the proliferation of sects and gospels declared noncanonical. Most of them had probably never known him during his life.

Even if we take as given that the apostles died bravely defending the resurrection, you can't take people dying martyr's death as evidence for their beliefs, only for their level of belief. People have martyred themselves for many CONFLICTING ideologies. Islam and Christianity to pick 2 of the most obvious examples, can't both be correct.

Finally, why didn't any of the other unorthodox accounts start similar communities? Why are the communities so similar in their beliefs about Jesus, if it is quite likely to have been made up, as you suggest?

Paul's letters explain this. The communities were so similar because they were all so strongly influenced by Paul.

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?

Lydia McGrew addresses your post saying:

"The fellow who sneers at our combined Bayes factor on the grounds that we are assuming independence appears to have overlooked the fact that we have an entire section discussing that very issue and offering, as far as I know, a new technical point in the literature concerning the question of whether assuming independence strengthens or weakens a case and relating this to the question of situations of duress." - link

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.

Just from very quickly skimming the paper, what bentam said seems denotatively true but connotatively very incomplete, not totally untrue though.

McGrew argues that, assuming independence, the Bayes Factor would be 10^39, and they do use it throughout the paper. It is a silly number, and they do reach it by assuming independence - which is a ridiculous hypothesis.

bentam implies that, had they not done so, they would have reached a more sensible figure, and that by assuming the generous (to them) hypothesis in the paper, true they have not argued against the least convenient likely position for them, which makes the paper dismissible.

What they actually do is conclude that, the less independent the testimony of the apostles, the more likely the whole story is to be true, by virtue of the evidence going from the likelihood of the supposed apparent conviction of them to the likelihood of the event's truth swamping out that of the evidence going the other way.

Yes, you read what I wrote correctly, and I didn't misspeak. I think that's what she's saying.

So McGrew does her intellectual duty by arguing throughout the paper for what she believes to be the lower bounds of the Bayes Factor, the true least convenient possible world, contrary to as implied by bentam.

She's not arguing dishonestly, so she has to compensate with unreasonable assumptions that lead to conclusions like 10^39 being the lower bound.

John DePoe, Western Michigan University has a paper on this too. He calculates the probability of the resurrection, given 10 fair and independent testimonies ≈ 0.9999.

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.

Operating under the assumption that this actually happened: What was the backstory behind your alien-ness (e.g. where did you claim to be from?) What were the reactions of the parents of your peers, and your teachers?

I claimed to be from the planet Myridia (spelling ambiguous, I never wrote it down.) I believe I said it was something like seven light years away (if not seven, then some single digit number,) and that it was part of a relocation project due to overpopulation.

I don't remember if I ever talked to my parents or teachers about it, but they knew me well enough to figure that it was something I'd do for entertainment, rather than a delusion or cry for help.

A majority of my peers didn't pay much attention, and probably figured it was just a story I came up with, but a considerable number took it quite seriously, and while I can't say they weren't gullible in light of what they actually fell for, some of them were considerably smarter than the average student. I tailored my lies to hold together on a much higher level than most students were likely to address them at, and think it flattered their intelligence to think that they had investigated the claims further than others, and reasoned their way to a conclusion contrary to what the majority believed.

Some of the students were just idiots though.

I can see a few problems with your example:

  • you were all kids (kids are more credulous)
  • there was not much at stake (on the contrary, increased social status for them; kinda cool to be associated with you)
  • the whole gig was short-lived (I hope they still don't believe you are an alien)

Now, compare that with the Hebrew apostles, and consider that, even today, to become a "completed Jew" can cut you off from your entire family. Imagine what it would be like in those days.

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.

Why is this a featured article?

Presumably because today is Easter and therefore the article is relevant to the date.

Bayesian defense of the resurrection of Jesus gives me a 404, so I cannot even read it

The referenced article can be easily located using Google. Here's a current link:

Bayesian defense of the resurrection of Jesus

The referenced article is quite long (75 pages). Luke's podcast interview with Lydia McGrew is quite interesting, IMO, if the article is longer than you wish to read. The podcast is a great example of a civil dialog between an apologist and a skeptic. Ms. McGrew's outlook is somewhat different from many well-known apologists and I think the podcast (which I am listening to now) will be interesting to many LW'ers. Interestingly, about 2/3 through the interview, she puts forward a refutation of the fine tuning argument - it is a refutation that had occurred to me before, but that I had never thought all the way through, so I was surprised to hear it precisely articulated (particularly by a Christian apologist).

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).

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”

Some theists are mocking the Carrier article's mistakes over here.

Hmm, having read that comments thread I now need to worry that Carrier's prior tutorial on Bayes's theorem might have egregious errors. There are a lot of basic probability errors outlined in that thread.

The linked article has 76 pages :-|

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.

I'm glad you mentioned survivorship bias. It allows us to consider the possibility that there were reasons why the story of the resurrection of Christ would be more likely to survive than others.

The story of a great savior dying and/or descending into Hell to save someone they love was very old even at the time. The cult of Persephone was well-known to the Jews; Persephone spending a season each year in Hades bought life for the land and special rewards for followers in the afterlife. Gilgamesh went into the depths to save his dearest friend Enkidu; Gilgamesh is thought to have lived around 2500 BC, and the Epic of Gilgamesh was well-known to the ancient world (one copy was dated to the 7th century BC).

Those are stories Jesus and his contemporaries would already have heard. Plus, they have come through the ages to us today. The story of Jesus going to Hell and coming back followed a well-trodden path, one that made many a religion popular.

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.

But conditional on his existence, the moon is probably made out of cheese.

But conditional on his existence, the moon is probably made out of cheese.

Is there some joke I'm missing? P(Moon made out of cheese|Jesus is a historical figure) is still very very low.

It's just a joke about gullibility, at least that's how I read it.

Oh, I thought it was an attempt to apply some sort of (nonexistent) analog of the principle of explosion...

Actually straightforward explosion works. "The moon is probably made out of cheese" can be taken as a statement in propositional logic.

[-][anonymous]11y 0

There was once a person who wanted to convince others that the moon is made of ice. Maybe it's a parody on that.