Bayes' Theorm Part 2: The New Testament as History

In my last post, I introduced Bayes’ Theorem and utilized it the assessment of the plausibility of an ESP claim. In this post, I will use it to examine how historians could assess the resurrection of Jesus if they were to use the New Testament as they would any other text found from that era. However, in this post, I am not going to detail the constituent historical evidences. That will have to wait for future posts.

Christian apologists often state that historians should treat the New Testament merely as any other document that they may find from that era. Then test the books according to the standards of historical research to see if they are, in fact, reliable. The one caveat added is that one cannot presume that miracles are impossible. That is what I will attempt here. This post will not presume that the canonization of the Scripture is indicative of divine preservation and approval. The assumption of divine preservation seems to be outside the normal considerations of a historian.

There are three main hypotheses I will consider. The first is that Jesus was resurrected from the dead on the third day. His resurrected body had properties previously unseen in history. In short, this is an event that requires a supernatural cause. The second hypothesis is that the reports of these events are either legends or an author mistakenly reported a legend as history. In either case no resurrection occurred. The third hypothesis is that the resurrection is historical, the authors are passing a record of true events, and those events can be explained by natural causes.

The assessment of initial probabilities needs to be understood in terms of background assumptions. Keep in mind that one can initially assess the plausibility of a hypothesis, compute a new plausibility based upon evidence, and the resulting assessment may be considered a "prior" for a new assessment based upon other evidence. In other words the a priori values are based upon experience and evidence. If someone thinks my prior assessments are unjustified, feel free to show how I should make my initial assessment.

My initial assessment of the plausibility of a real resurrection in the absence of evidence would be very low. As in my previous post, I am initially skeptical of claims requiring a supernatural cause. I do not think they are impossible. In my lifetime I cannot think of any event that could potentially require a supernatural cause. I have seen magic tricks that I can’t explain, but the magicians didn’t claim to use supernatural powers. It certainly doesn’t seem unreasonable for a historian to think (in the absence of evidence) the probability a reported event requires supernatural cause is one in a million 10-6.

If one were to receive historical books from about 2000 years ago, what is the likelihood that the books were passing off a legend as history? I suppose that my initial probability would be low. I expect most people to honestly pass on what they know. However, there is a great deal of precedent for having an expectation of fraud in a religious work. There was a Christian forger who attempted to pass off a third letter to the Corinthians and was caught in the act according to the church father Tertullian. In the New Testament, the writer of 2 Thessalonians 2:2 is warning of a false letter. Either Paul has knowledge of fraud or 2 Thessalonians itself is fraudulent. In either case, fraud is known to occur in religious writing. False teaching seemed to be rampant according to Paul. For examples see Galatians 1:6-9, 2 Corinthians 11:4, and 1 Timothy 4:1-3.

Further, the Gospel of Thomas, Gospel of Peter, and Acts of Peter are examples that Christians presume are pious fraud. The fact that the NIV Bible notes that Mark 16:9-20 is not in the earliest and most reliable manuscripts (and other verses believed to be interpolation) is also indicative that some early Christians may have felt justified in passing on pious fraud.

There are other examples of works of fantastic claims from that era. Apollonius of Tyana reportedly was half god and half man, healed the sick, raised the dead, and at the end of his life ascended to heaven. There were ceremonies commemorating the ascent of Romulus (the founder of Rome) into heaven after he was murdered by the senate and rose from the dead.

Even noted historians reported unbelievable events. Josephus recorded in the Jewish Wars that a cow gave birth to lamb; a bronze gate (that was so large it required 20 men to move) unbolted itself and opened itself at midnight. Herodotus recorded many obvious legends as well such as the temple of Delphi magically defending itself and a mass resurrection of cooked fish. Richard Carrier gives much more context in Chapter 5 of the book "The Empty Tomb." In light of this data, it seems reasonable that a historian would have an a priori expectation of fraud at least as high a 1 in 10.

My a priori value for the natural/default hypothesis is the higher than the other two. However, the probability of the data (a resurrection) is so implausible on this hypothesis, that I will ignore it in my calculations, (just as I ignored it in the second calculation in the ESP post.)

The historical evidence for the resurrection comes primarily from the four Gospels and the letters of Paul, particularly 1 Corinthians. In my previous post, I went to the trouble to calculate the probabilities of each data on each hypothesis. In the case of two hypothesis, it is only necessary to compare the relative explanatory strengths of the hypothesis. For this initial argument, assume that the Resurrection hypothesis has twice the explanatory power of the Legendary hypothesis. So if the probability of observing the historical evidence on the Legendary hypothesis is Z the probability of observing the evidence on the resurrection hypothesis is 2.0× Z. (As I stated previously, detailing the evidence will have to be done later.)

These assessments are summarized in the table below. From the values in the table, one can utilize Bayes' Theorem to assess the plausibility based upon the evidence.

Hypothesis P(Hypothesis)
a priori
HResurrection 10-6 2.0× Z
HLegend or Deception 0.1 Z
HDefault 1.0 - 0.1 - 10-6 negligible

Putting these values into Bayes' Theorem gives:
P(HR|E) =         P(E|HR) P(HR)        
         P(E|HR)P(HR)+ P(E|HL)P(HL)+P(E|HD)P(HD)

P(HR|E) =         2× Z× 10-6       
           2× Z× 10-6 + Z × 0.1 + 0.0
P(HR|E) ≈ 0.00002

Thus it seems very plausible to think that the Gospel writers were passing off a legend (either knowingly or unknowingly). Note that even if the resurrection hypothesis does a better job of explaining all the observed evidence, belief in the resurrection may still not be warranted. This is because we have observed both deceit and legendary development in similar settings. In order to avoid this conclusion, one would need to have data that is extremely implausible on the legendary hypothesis.

One example of evidence offered is given by the rhetorical question "Would the disciples have died for a lie?" A problem with this rejoinder is that one would have to show that the reports of martyrdom could not be part of the legendary development. The New Testament does not record the deaths of eyewitnesses other than James (Acts 12:2), and it is not clear what charges he died for, or if recanting could have spared him. Books that do record the apostles deaths (such as the Acts of Peter), seem to have legendary characteristics, even according most Christians. Belief in reports of martyrdom is susceptible to the same "deception" hypothesis that had the effect on the assessment of ESP.

This assessment can again be characterized by the parable of the boy who cried wolf. Even if the events are historical, the fact that so many have made fantastic claims makes rejection of all reported supernatural claims reasonable. This problem seems inherent to establishing very unusual claims on the basis of testimony, particularly hearsay.


Jon Curry said...

If someone thinks my prior assessments are unjustified, feel free to show how I should make my initial assessment.

I have a major problem with your initial assessment. Your numbers are radically biased in favor of the Christian.

For the record I expressed to Bill before he posted this that I disagreed with the values he used, but he prefers to give the Christian every possible break so that he cannot be accused of being unfair.

First off, the initial probability for a person having ESP in your prior post was one in a billion. Why would the initial probability of a resurrection be higher than that? One in a million seems high. I will use one in a billion.

Second, the initial probability for legend or deception should be much higher. Even the Christian would grant that when you are considering a text that makes miraculous claims usually you are dealing with legend or deception. Whether it's Benny Hinn, Joseph Smith, Judge Rutherford, St. Genevieve, stigmata, etc, most Christians (Protestants at least) regard them as fraudulent. So the presumption must be that Scripture is legend or deception as well. I would put the initial probability of fraud or deception somewhere closer to .99, as opposed to what you have (0.1).

Third, why should we assume that the miraculous explanation provides greater explanatory scope? Does the miraculous explanation explain the parallels to Horus, Inanna, or Osirus? Does it explain the early confusion about where Christ was born or when he was born? Does it explain why Paul isn't aware of an earthly ministry for Christ, or why the stories of his life become more and more impressive as subsequent texts are written? These are all clear markers of human invention, not divine origin. Legend explains all of these factors while an actual resurrection does not.

I am just flabbergasted that you could conclude that there is a one in 50,000 chance that a resurrection ocurred. Using my values we reach a far more reasonable number. 1 in 990,000,000.

John W. Loftus said...

Jon, you just offered what I consider to be the whole reason I don't place much stock in Bayes' theorem. Although in Bill's defense, it does mathematically specify and lay out one's assumptions. As Bill has said: I would agree that the assigning of specific numbers (probabilities) to indicate degrees of belief is subjective, and I wouldn’t try to give the results airs of numerical accuracy. But I see Bayes' Theorem mainly as a way in which fair-minded thinkers can discipline themselves.

Bill Curry said...

If the argument about the resurrection were “Is it 70% likely or 30% likely?” then the results would be very sensitive to the numbers we would assign. But keep in mind, that the Christian position is the probability of the resurrection is very close to one. Skeptics think the probability is very close to zero. Either the evidence should push us strongly in one direction or the other. Jon has mentioned some of the evidence that supports the legendary hypothesis, and I will also examine evidence used in support of the resurrection. The point this post is that the Christians appear to bear a very large evidential burden.

The Christian position is that we reject Christ because of rebellion in our hearts, not because we are using the tools of rationality provided to us by God. If following reason effectively causes individual to be condemned, that is a challenge to Christian theology.

Prup (aka Jim Benton) said...

The trouble with your arguments is that they give too much credence to the Christian position. The contradictions between the Synoptics and John show there is -- at best -- honest error in the Scriptures. The deliberate writing of a book purporting to come from a past figure (the Timothys and Titus, supposedly by Paul but obviously much later) demonstrates either 'pious fraud' or, better, the attitude in traditionalist societies that denied the value of innovation and demanded that one own's ideas be attributed to a respected past figure (as Plato claimed his own arguments were Socrates').

And that some stories in the Bible are legend is demonstrable by the simple 'if this REALLY happened, somebody else would have noticed' test. (Herod's 'slaughter of the innocents,' the drowning of the majority of Pharaoh's army, the simultaneous death of all the firstborn children of the Egyptians -- is it possible that there would be no hint of these anywhere else but in the Bible if they actually happened. We may not have documentation for those times the equivalent of what we have today, but that somehow this type of slaughter didn't get a footnote somewhere, or get mentioned in any surviving letter or tablet is simply absurd.)

Bill Curry said...


In a sense, I agree with you. Since I have recently de-converted, I still may have a pro-Christian tilt to my evaluations of the evidence. However, keep in mind that my goal in these posts is to evaluate a subset of the evidence and leave a foundation for further analysis. I know there is a lot I am leaving out (for now, I hope to get to more). I want to show how the claims of Christians can be evaluate using the best inferential method available and illustrate a systematic way to evaluate a large body of evidence. (I am little surprise that people haven’t disagreed more strongly with my methodology here.) My evaluations are will likely change even after examine the claims more deeply and as more evidence is brought to my attention.

I have used your 'if this REALLY happened, somebody else would have noticed' test in my response to Jason Engwer here. It is implausible to think the earth shattering events recorded in Matthew 27 would have only been recorded (and survived) in only Matthews writing. The evidence you list can and should be rolled into my evaluation for the cumulative case. However, notice the trend here, even when I am biasing my evaluations in favor of Christianity, it is clear that the evidence is moving me away from belief in Christianity’s core tenants.

Thanks for the comments.