Bayesian evaluation for the likelihood of Christ's resurrection (Part 11)

We've just touched on the lack of evidence for doubting the resurrection. This is important, because it allows me to answer all the other skeptical arguments and distinguish my argument from them. A skeptical reader may wonder whether I've ignored any evidence against the resurrection, or how I would answer this or that argument from this or that website. A significant part of my reply would be that there is no evidence against the resurrection.

Let me reiterate and clarify that, because it's important. There is an utter lack of evidence for disbelieving the resurrection: literally every single record we have from the people who were actually connected to the event to any reasonable degree ALL portray the resurrection as something that actually happened.

If you believe in the resurrection, you have the unanimous support of all the people who were actually close to the event and would know for certain. If you disbelieve the resurrection, literally every piece of evidence - every single testimony of every single person who ever testified about the actual event - is against you.

So, I'm not being selective about the evidence. There is nothing to be selective about, because there is literally no evidence for the opposing argument. This is why I'm fundamentally unconcerned about the arguments against the resurrection: because they have no evidence. The only thing I've done in choosing my evidence was to handicap my own argument, by only using a tiny fraction of the total evidence available.

If there were any evidence against the resurrection, I'd be glad to incorporate it into the calculation. I've already said elsewhere that a sufficiently strong evidence against the resurrection can falsify the whole hypothesis for me - if, you know, such things actually existed.

So, does anyone know of a cave in Israel that houses Jesus's mummified corpse? By all means, tell me about it. Is there an ancient manuscript that exposes the disciples' conspiracy to fake the resurrection? Let me know. Is there a record of a Roman interrogation where an apostle confesses to having made up the whole resurrection thing? Is there an epistle where a disgruntled disciple warns the others about staking the faith on a schizophrenic woman and her crazy resurrection story? Is there any record of a psychoactive plant in first century Jerusalem that causes vivid mass hallucinations about the recently dead? Is there a complaint from Jesus's family about how his message has been hijacked by a bunch of lunatics and their crazy resurrection story?

You see, nothing remotely like any of the above actually exists. There is literally zero evidence for disbelieving the resurrection.

This is why every single skeptical attempt at explaining the resurrection relies entirely on ignoring the existing evidence, and making stuff up instead. They have no other options, because they have no evidence on their side. That's why the only thing they can do is to ignore the existing evidence, and make stuff up.

So, when they say that Jesus's resurrection was a myth that grew over time to be accepted as fact, they're ignoring the existing evidence that says that the resurrection was at the very core of Christianity from its inception, and making stuff up instead about how a myth might have eventually gained enough traction to be accepted as dogma.

When they say that Paul might have converted because he already had second thoughts about Judaism before encountering Jesus on the road to Damascus, they are ignoring the existing evidence in Paul's own testimony, and making stuff up instead about what they think went on inside Paul's head.

When they say that the early Christians didn't believe in a real, physical resurrection, they are ignoring the existing evidence that unanimously say that Jesus's body was missing from the tomb, and are instead making stuff up about what they think the early Christians really thought.

When they say that Jesus might not have really died, but only swooned, they're ignoring the existing evidence that clearly presents Jesus's death, and making stuff up instead about the combination of circumstances that might have allowed Jesus to survive a crucifixion.

When they say that the post-resurrection appearances were only visions or hallucinations, they're ignoring the existing evidence that unequivocally states the physical nature of Jesus's new body, and making stuff up instead about the disciples' mental conditions.

When they say that the gospel writers were only interested in the theological and literary dimensions of their story, and showed no concern for the truth, they're ignoring the existing evidence from these writers themselves that directly contradicts them, and making stuff up about the writer's "true" motivations instead.

So, let's not be distracted by such made-up speculations, and instead stick to the existing evidence that we do have. Remember the outline of the argument at hand. We are using Bayesian reasoning. We start with a prior probability for the resurrection, and modify it according to the existing evidence that we actually have. There is no place in this calculation for speculations about what evidence we might have if some made-up stuff happened instead. Such speculations cannot modify the probability, for any possibility for such made-up scenarios are already included in the calculation: the inherently unlikely nature of the resurrection is already included in the prior, and the possibilities for the disciples being wrong are included in the Bayes' factors. Upon carrying out this calculation, using absurdly conservative values, we find that the odds for the resurrection are at 1e32 to 1, at a minimum. Therefore, Jesus almost certainly rose from the dead.

There is more to come in the coming weeks - starting with the next post.

You may next want to read:
Basic Bayesian reasoning: a better way to think (Part 4)
Sherlock Bayes, logical detective: a murder mystery game
Another post, from the table of contents

Bayesian evaluation for the likelihood of Christ's resurrection (Part 10)

Here is another typical attempt to deny Christ's resurrection:
"It may be that some of the disciples were crazy or especially grief-stricken after Jesus's crucifixion. This lead them to see some vivid visions of Jesus, which they related to the other disciples. Some of these other disciples, who had not seen the visions themselves, then spread the story about the 'resurrection' based on the vision of these few crazy people. Then, a few other disciples, who were dissatisfied with Judaism, formed an opportunistic conspiracy to start a new religion based on these budding stories about this 'resurrection', and that's how Christianity started.  
Or, it could have gone another way. A few disciples wanted to start a new religion and formed a conspiracy. After Jesus's death, they suggested to some of the other, more gullible and mentally unstable people that Jesus rose from the dead. With a little faking of evidence, social pressure, and the power of suggestion, they eventually got enough of the other disciples to say that they saw the resurrected Jesus themselves. From there, the resurrection became part of their faith narrative, and that's how Christianity might have started. 
There are dozens of other possibilities like these - it doesn't have to be that everyone was lying or crazy. We just need the right combination of lies, mistakes, and insanity at the right times and situations for Christianity to start. Surely, it is more likely that one of the many possibilities represented here lead to the belief in the resurrection rather than for Jesus to have really come back from the dead."
This is merely an attempt to muddy the waters by complicating the issue.

First, note how weak this argument is, even if we were to grant it everything that it asked for. Remember, the odds for the resurrection are currently at 1e32, so the odds against it are therefore at 1e-32. Now, we'll allow for each independent objection to count as having the full weight of these odds. Never mind that many of these objections contradict one another and therefore reduce the probabilities of the other objections (increasing the probability for 'insanity' decreases the probability for 'conspiracy', because a conspiracy is less likely to succeed with insane people in it). We'll just ignore that. Never mind also that these complex speculations are naturally less likely because of their complexity. We'll also ignore that as well. So, if we can think of a hundred such objections, each of which carries the full weight of the 1e-32 odds for 'no resurrection', the final odds for the resurrection would drop all the way down to... 1e30.

In short, if you're serious about this approach, go ahead and write out a billion independent objections of the kind demonstrated above. That would drop the odds for the resurrection to 1e23, and it might then merit a footnote as something that someone might want to look into sometime.

But more importantly, this kind of objection is simply, fundamentally wrong: it would not fly in any other investigation into a personal testimony, because it completely ignores the rules about how we evaluate evidence in a Bayesian framework.

Imagine, for instance, that your friend claims to have been struck by lightning. You've taken stock of this claim and have decided to assign it a Bayes' factor of 1e8. But then you say, "well, you may be just a little crazy. And you might have had a nightmare about a thunderstorm last night. Then you might have gone to a hypnotist and who had you recall your dream, which you're now confusing with reality. Or maybe it was the hypnotist who planted the suggestion in your mind first and that caused your nightmare. Really, it might have been any of these things - and isn't it more likely that at least one of these possibilities is true, rather than for you to have been actually struck by lightning?"

Should you or your friend then discount the previously assigned Bayes' factor in light of these new possibilities? Absolutely not. The thing to note here is that the Bayes' factor ALREADY includes all of the ways that this claim may be wrong. It is the numerical estimation of the weight of evidence for a human testimony, and as such already inherently includes the possibility that the evidence may be misleading.

Having established its value, it is simply incorrect to further modify it with no evidence, based on enumerating possibilities that were already included in its evaluation. Your friend's proper reply to your wild speculation would be to say, "what makes you think that I had visited a hypnotist or had a nightmare? Of course, anyone might be wrong about anything in any number of ways - but don't you already know how much you trust me? How does a list of ways that I might be wrong, with no evidence behind any of it, make you trust me less?"

Again, this goes back to the "barrage of objections" tactic I mentioned earlier, and why it fails against the resurrection argument presented here. The trap is to get you to think of the many possible objections against the argument, then confuse you into thinking "at least one of them must work!" It requires you to forget that the argument here is fundamentally immune to that line of attack. Once again, my argument is not a deductive argument. It is an order-of-magnitude probability estimation using Bayesian reasoning. It starts with a prior probability, and then it modifies that probability based on the evidence. So, is there any evidence that your friend had a nightmare about a thunderstorm? Then it is proper to include that evidence to re-calculate the probability of the lightning strike. Is there any evidence that a crazy group of disciples reported on the resurrection, which then got hijacked by a conspiratorial group of disciples? Then it would be proper to include that evidence to re-calculate the probability of Christ's resurrection. However, in the absence of such evidence, the mere existence of that possibility should not change our calculations. Such possibilities are already included in the initial calculation.

Let me give an even simpler example. Suppose you flip a coin, then cover it up so that you don't know the outcome. Not having investigated the coin all that carefully, you assume that the probability of it turning up 'heads' is 0.5. Now, someone comes up to you and says, "but consider all the ways that it may turn out to be tails. It might have hit the tabletop, flipped three times after the bounce, landed on its edge, then fallen over to show tails. Or it may have flipped fifteen times before the first bounce then landed flat with the tails side up. In fact, if the coin's leading edge strikes the table at 15 degrees with an angular velocity of 12 rev/s and a downward linear velocity of 2 m/s, it's guaranteed to end up tails. And this is only a small sample of the innumerable ways for you to get tails. Given all these different ways, shouldn't you decrease your 'heads' probability?"

The answer, of course, is that you should not. You should only consider the evidence that you DO have in modifying your probability. You must leave alone any evidence that you MIGHT have. So, in the absence of any evidence, the probability for 'heads' is still 0.5, and the innumerable ways that the coin might turn out to be 'tails' does nothing to change it. Now, it may be that you recorded the first part of the coin flip in slow motion, and it turns out that the coin did indeed strike the table at an angle of 15 degrees for its leading edge, with an angular velocity of 12 rev/s and a downward linear velocity of 2 m/s. That would be evidence. That would cause the probabilities to change. But the mere possibility of this happening, in the absence of the actual evidence, does not change the probability.

Here is the evidence that we DO have: numerous witnesses gave their earnest, personal testimonies, saying that they personally saw the risen Christ. We know how to numerically evaluate such evidence. Earlier in this argument, we have already numerically taken into account the many ways that they may have been wrong, whether through honest mistakes, deception, or insanity. We have no evidence that anything like the speculations of the skeptics have taken place, and the mere possibilities for these speculations cannot change the probabilities. The odds of the resurrection, even with the most conservative estimates, remains 1e32, at a minimum.

We will continue with other parts of the argument next week.

You may next want to read:
Miracles: their definition, properties, and purpose
Sherlock Bayes, logical detective: a murder mystery game
Another post, from the table of contents

Bayesian evaluation for the likelihood of Christ's resurrection (Part 9)

After hearing many objections in succession as we just have, it's easy to lose sight of the big picture. For instance, one may fall into the trap of thinking that if even one of these objections has even the slightest chance of being true, the argument would fall apart. But is that really the case? If the disciples had even the slightest chance of being crazy or mistaken or deceptive about the resurrection, would that cause the whole chain of reasoning to break and the case for the resurrection to collapse?

This is where it's useful to remember the big picture. You see, a standard deductive argument does work like that - A and B together lead to C, which lead to D, which then leads to the conclusion. For such an argument, all of its premises must be entirely true and each step of its reasoning must be completely correct. Anything else invalidates the whole argument. That is why a barrage of objections can sometimes succeed against such an argument, or at least cast doubt on its soundness.

But my argument for the resurrection is not a deductive argument. It is an order-of-magnitude probability estimation argument using Bayesian reasoning. The objections against it can take two forms: you must either claim that I'm misusing the mathematical apparatus (that is, Bayes' rule), or disagree with my estimated values for the probabilities.

If you think that I've made a mistake in applying Bayes' rule, then by all means point it out. Otherwise, the objections against it all come down to wrangling over the probability values. The point here is that in such wrangling need not produce absolute certainty. The argument does not depend on it. I do not need to claim, for example, that there is absolutely no chance that the disciples were lying. Having demonstrated that the Bayes' factor for a typical, relatively unconditioned human testimony is around 1e8, I only need to demonstrate that the disciples are not more likely to be liars than such a "typical" person. In fact, anything which suggests that the disciples' honesty exceeded that of the "typical" person actually strengthens the argument beyond its original form, by increasing the Bayes' factor. This is what has actually happened upon the examination of every single objection thus far.

Furthermore, even if one of the objections were to "succeed", it would not be a fatal blow to the argument; we would merely have to re-calculate the final odds. So, for instance, let's say that the objection about the disciples being mistaken somehow "succeeds", and it results in the Bayes' factors from their testimonies dropping from 1e8 to 1e4. In fact, let's say that these objections are so wildly successful that we must take the square root of every single Bayes' factor we used. Such an instance would not cause the whole argument to be simply invalid. Instead, we would just have to recalculate the final odds with the new numbers. We'd find that the final odds dropped from their original value of 1e32 to 1e5 - corresponding to around a 99.999% chance FOR the resurrection still having occurred.

So, let's be clear about the effect of these repeated objections. Our argument is not a deductive argument. If it were, any objection might cause the whole argument to be invalidated if we can't demonstrate with absolute certainty that the objection is false. It is easy to think this way when you hear many objections in succession - that one of them must eventually get through a chink in the armor and deliver the fatal blow. But it simply does not apply to our case.

Rather, our argument is an order-of-magnitude probability estimation using Bayesian reasoning. From the beginning, it is strong enough to survive multiple successful objections against it. We are then fielding objections against this argument. If an objection succeeds, that would decrease the power of the argument - but if it fails it must correspondingly increase the power, by demonstrating that the resurrection witnesses were more honest, correct, and sane than what we had initially assumed. And this latter case is what has happened in every objection thus far.

So, we've started from an incredibly strong original argument, and each of the repeated objections have only strengthened it further. We will continue to look at more opportunities for strengthening next week.

You may next want to read:
A real discussion on the problem of evil and omnipotence.
Isn't the universe too big to have humans as its purpose?
Another post, from the table of contents

Bayesian evaluation for the likelihood of Christ's resurrection (Part 8)

Another class of objections would just argue that the witnesses to the resurrection were crazy:

"Obviously anyone who claims that they saw someone coming back from the dead is crazy. How can we take their stories about these outlandish miracles seriously? Clearly there was something mentally wrong with these people, and we ought to dismiss their 'testimonies' as the ramblings of the insane or the schizophrenic."

By now, it ought to be obvious that I'm going to handle this objection like all the others. Did the witnesses to the resurrection act like they were crazy? Did they exhibit the typical behaviors of the insane or the schizophrenic? If they did, we should rightly lower the Bayes' factor for their testimonies from the relatively unconditioned value of 1e8. But if they did not, then by the same logic we must increase the Bayes' factor.

This investigation is straightforward enough: read the New Testament, and look for symptoms of mental illness in areas that are not directly related to supernatural claims (one must be careful about circular reasoning). So, does the New Testament read like the work of a schizophrenic? Does it seem to describe people who were afflicted by mental illness? Would you say, for instance, that Peter's sermon at Pentecost exhibits problems with attention or memory, or that Paul's letter to the Romans demonstrate disorganized thinking?

In fact, apart from the supernatural components, I have not heard of anyone citing any part of the disciple's work in the New Testament as being characteristic of mental illness. If there is such a passage, I'd love to know about it. Can anyone point to a verse and say, "here is where Paul shows clear signs of psychosis", or "this is where Peter displays the classic symptoms of schizophrenia"? It says a great deal about the "insanity" accusation that the only evidence they can find for it are the very parts that make up the question at hand, the very parts they object to. In short, the objection effectively only amounts to saying "I disagree with these people on these points, so they must be crazy!"

On the other hand, there are plenty of reasons to think that the witnesses to the resurrection were of sound mind. Remember, they were the organizers and leaders in the early Christian church - a movement that spanned their known world. Furthermore, recall that they were successful beyond any naturally possible expectations: Christianity has lasted thousands of years until the present day, multiplied wildly, and now spans the whole globe. Can anyone give any example of an organization run by insane people that was even a millionth as successful?

In particular, the ideas behind this organization - that is, the theology of the early Church - are readily available to us as the text of the New Testament. They are the most read, discussed, studied, and applied texts to have ever been written. If you're reading this blog you're also free to go and read the New Testament. Does it seem like the work of the insane? What work by any mentally ill persons has ever reached a fraction of its stature?

So the conclusion is clear enough. Once again, upon actually considering the facts surrounding the resurrection witnesses, we find that they do not correspond at all to the scenario in the objection. The disciples display no sign of insanity, instead demonstrating many characteristics of sound and acute minds. So, according to the very logic embedded in the objection itself, this must again increase the Bayes' factor of their testimonies.

We will continue with more next week.

You may next want to read:
Miracles: their definition, properties, and purpose
Why are there so few Christians among scientists? (part 2)
Another post, from the table of contents

Bayesian evaluation for the likelihood of Christ's resurrection (Part 7)

Yet another class of objections may argue for 1e8 being too large, on the basis of people being intentionally deceptive rather than being mistaken. It may go like this:

"1e8 is a ridiculously large Bayes' factor for people's testimonies. People lie all the time. Do you really think that only 1 out of 1e8 things that people say are lies? There are conspiracies, con artists, and fame seekers everywhere, at all times. What makes you think that the disciples reporting on the resurrection were not just one of these people?"

The objection here, and its answer, is much the same as before. Yes, people lie, or are otherwise unreliable, in some circumstances. These circumstances rightly require us to adjust the Bayes' factor downwards. But the comparison of such circumstances with with what the disciples actually faced will only reveal their vast differences. If you think that people are likely to lie under certain circumstances, you must then therefore think that the disciples were highly likely to be truthful about the resurrection, due to the absence of these circumstances.

So, taking lottery winners again as an example: if someone claims to have won the lottery, their claim should be given about a 1e8 Bayes' factor. But what if they then go on to say that they've left their winning ticket with a Nigerian prince, and that they would share their winnings with you if you would only give them $5000 to cover their travel expenses to retrieve the ticket? Well, now the Bayes' factor drops precipitously, down towards zero.

However, what if the supposed lottery winner instead gives lavish gifts to their friends and family, buys a new house, then hires a financial adviser to discuss the tax implications of their sudden windfall? Then the Bayes' factor would dramatically increase, towards values like 1e120.

So then, what are the circumstances under which people are likely to lie? And in contrast, what are the circumstances that the disciples faced?

Well, people often lie for material gain, as in the above example of a con artist. The disciples, however, did not accrue wealth by claiming that Jesus had risen from the dead; in fact the very nature of their claim made this outcome highly unlikely, with the emphasis on serving the poor and a general disdain for worldly gain. If money was their goal, this was certainly the wrong way to go about it.

People may also lie under social, psychological, or physical pressure, as in the cases of false confessions obtained under harsh interrogation or torture. The disciples, however, resisted such pressure, and held on to their testimony under immense opposition of all kinds. The imminent possibility of persecution is a constant theme throughout the entire New Testament. In fact, many of the early Christian leaders underwent torture and martyrdom, including all three of the named witnesses I used in my calculation (James, Peter, Paul). We know how effective such treatment can be in eliciting false confessions even from their modern victims. We must therefore consider anyone who resisted the far harsher ancient versions of these treatments to be exceptionally trustworthy.

One may argue that at least the negative social pressure from society at large may be made up for by the approval from the close-knit Christian community. But this simply does not apply. Again, among the three named witnesses I used in my calculation, only one (Peter) was originally one of Jesus's disciples. James and the rest of Jesus's family are considered to have been in a somewhat disharmonious relationship with Jesus before the resurrection, and Paul was a complete outsider - an early persecutor of the church, whose personal and social identity was very much set in opposition to Christianity. So in a majority of these cases, the social pressure would have gone the other way: they would have ample reasons to reject the resurrection. Their testimonies in spite of this, therefore, must be counted as being much more reliable than the average.

Incidentally, if you thought that I forgot to adjust my calculations for the fact that the testimonies are not independent, this is why - the three named witnesses in my argument ARE largely independent; they come from very different backgrounds and met the risen Christ under different circumstances. Especially in Paul's case, if anything you'd expect his testimony to be anti-correlated with Peter's. For the other witnesses where dependency is expected, I explicitly called it out and severely discounted the Bayes' factor values in the calculation.

Now, back to the subject of lying: people may also lie for fame - they claim to have achieved something remarkable or to be someone special. But as we have just seen, the fame that came with proclaiming the resurrection would have been exactly the wrong kind of fame; the witnesses would have been shunned both by the Roman and Jewish society at large, and in many cases by their immediate social circle. Furthermore, it is the nature of fame to be fleeting; few would continue to lie for fame, in the face of intense opposition, for decades at a time, long after the shock of the initial claim wore off, to the point of death. Indeed, if the witnesses were fame-seekers of this type they would have done quite well by recanting the resurrection at the last minute and becoming a kind of whistle-blower for this deception that Christians pulled over the world. And yet, the witnesses did no such thing; they all died as martyrs.

People also sometimes lie for a cause. If they believe that some agenda is good and important, that may cause them to be deceptive "for the greater good", to advance that agenda. But this is impossible given the theology of the early church. Jesus was the greatest good; his resurrection was the most important event in the whole world. There was nothing greater which would be worth lying about the resurrection.

In all this, the actions of the witnesses were in perfect accord with their genuine belief in the resurrection. They had no reason to lie and every reason to tell the truth. We, also, have no reason to believe they were liars and every reason to believe that they were truthful.

So, it is true that men often lie. But this is a shallow observation. Upon considering the actual, specific circumstances surrounding the resurrection testimonies, we find that they are diametrically opposed to the circumstances conducive to lying. Therefore, the observation that "men often lie" only serves to enhance the trustworthiness of the witnesses to the resurrection, by pointing out how different these witnesses are from typical liars.

We ought to have reduced the Bayes' factor for the resurrection testimonies down from 1e8 had we found the surrounding circumstances conducive to lying. But since the opposite has happened, we must therefore increase the Bayes' factor. 1e8 is a drastic underestimate of its true value.

We will continue with more possible objections next week.

You may next want to read:
Key principles in interpreting the Bible
A common mistake in Bayesian reasoning
Another post, from the table of contents