Betting on horses and the resurrection of Jesus (II)

Versione italiana

Thomas Bayes (1701–1761)

In the last article I used a horse racing / mathematical problem to introduce Bayes' theorem in its odds-based form, ie the one using the ratio of the probability p that an event 'A' occurrs and of the probability 1-p that it does not occur: O (A) = p / (1-p).

At the end of that same article, I also promised a connection between this formulation of Bayes' theorem and the resurrection of Jesus. Obviously the key to this promise is found in the article immediately before, "On the validity of the testimony of the apostles about the resurrection of Jesus", in which I explained why the testimony of the apostles of Jesus about his resurrection is not an evidence strong enough to accept as true the hypothesis that a human being has risen from the dead. Now, with the help of Bayes' theorem, we can calculate how unlikely this hypothesis is.

Bayes' formula

First a small summary. Let O (H) be the odds of the hypothesis 'H' regardless of the occurrence of event 'E', P (E | H) the probability of the event 'E' when the hypothesis 'H' is true, P (E | ¬ H) the probability of the event 'E' when the hypothesis H' is false, and O (H | E) the odds of the hypothesis 'H' when event 'E' is taken into account; then Bayes' theorem is expressed in the following form:

O (H | E) = O (H) * P (E | H) / P (E | ¬ H),

that is the odds of hypothesis 'H' when observing event 'E' are equal to the odds of hypothesis 'H' regardless of the observation of 'E' multiplied by the likelihood ratio, the ratio between the probability to observe the event 'E' when the hypothesis 'H' is true and the probability of the event 'E' when the hypothesis 'H' is false. Through this ratio it is possible to update the odds of a hypothesis following the observation of an event.

The subject of the inquire

Our hypothesis 'H' is "Jesus was truly risen", meaning that Jesus was a human being and that his body returned to life. We have no direct observation of this resurrection, but we observed the event 'E' "the apostles of Jesus were witnesses of the resurrection".

The question we ask ourselves is what is the value of O (H | E), what are the odds that the hypothesis "Jesus is truly risen" is true, taking into account the event 'E' "the apostles of Jesus were witnesses of the resurrection". Applying Bayes' theorem, we find that this quantity depends on three factors:

1. the odds that the hypothesis 'H' is true, regardless of the testimony of the apostles, O (H);
2. the probability that the apostles would have been witnesses of the resurrection if Jesus was really risen, P (E | H);
3. the probability that the apostles would have been witnesses of the resurrection if Jesus was not really risen, P (E | ¬ H).

How many people have lived on Earth?

What is the probability that Jesus rose from the dead, regardless of the testimony of the apostles? Given that this testimony is the only evidence of such an event, it is not unreasonable to think that the resurrection of Jesus has in general the same probability of occurrence of the resurrection of every other human being.

Betting on horses and the resurrection of Jesus (I)

Versione in italiano

A friend of yours, a real fanatic of horse races, has convinced you to follow him at the racecourse on a racing day. While you are waiting for the beginning of the races, you decide that, after all, a small betting would be fine. So you read the program of the first race, and the name of a horse comes to your attention: Soldatino!

You ask your friend if Soldatino is a good horse, but the answer is negative: in 105 races in which it participated, it "showed" (i.e., it arrived within the first three places) in just 7, that is, for each time it showed it did not for 14 times! Well, not exactly the favourite of the race...

Seeing your disappointment, your friend tries to get you a bit on the moral: "During the night it rained a lot, so the ground is very heavy." Noting your quizzical expression, your friend tells you that in 70% of the races in which Soldatino showed, the ground was heavy, and in those races in which it came in fourth or worse, the ground was heavy in 10% of cases.

On the validity of the testimony of the apostles about the resurrection of Jesus

Some Christian apologists (William Lane Craig, Is There Historical Evidence for the Resurrection of Christ?; Mike Licona, The Case for the Resurrection of Jesus) argue that the resurrection of Jesus must have been a real event because otherwise it would be impossible to explain the availability of the apostles to be martyred for witness: if Peter had not been convinced that Jesus was truly dead and truly risen, he would not had let himself be killed in his name, but he would have confessed the deception and got saved.

On this topic, some preliminary considerations should be discussed: for example, we are not sure that Peter was indeed martyred, nor we know with certainty that the deny the resurrection of Jesus would have saved his life, nor can we rule out that he had no particular reason to prefer death the unveiling of lies (think of Ron Hubbard and Scientology). But for this discussion, we will assume that Peter would deny Jesus without further consequences, but he chose to die to bear witness to his resurrection.

It should also be noted that the argument presented is valid only if the apostles (Peter) knew that Jesus had died and had risen again: it is important to emphasize that their mere belief in the resurrection is not sufficient evidence to demonstrate its actual historicity, as it is possible that they were wrong. In other words, with respect to the relationship between the resurrection and the apostles, there are three possible scenarios: the apostles knew that Jesus had risen, the apostles believed that Jesus had risen (for example, through a re-reading of the biblical allegories to understand the reasons for the death of their master, an event incompatible with their faith), or the apostles knew that Jesus had not been resurrected (and lied about his resurrection). Of these three scenarios, the only favourable to the apologists is the first one, in which the apostles are witness of the resurrection (as described in the Gospels, for example) and not merely convinced of its occurrence.

Well, the apologetic defence of the resurrection is just disowned by the existence of the Christian martyrs! Of all the Christian martyrs, in fact, the vast majority were killed for their faith, because they were convinced of the resurrection without being witnessed; just a minority of them (Peter, besides the "other" apostle and the women, if they were actually martyred) died because they were convinced by the facts.

Of course, it is possible that Peter was an eyewitness of the facts and died to bear witness of the resurrection, while the other (tens of) thousands of dead for their faith have taken this step without being witnesses of that event; this does not affect the possible truth of the resurrection. But what this reasoning proves is that the argument of the martyrdom of the apostles is not evidence for the truth of the resurrection as, if anything, of the fact that the apostles were convinced that it had taken place without being really been witnesses.

The picture is The martyrdom of Saint Peter, by Michelangelo Merisi da Caravaggio, through Wikimedia Commons.