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.