I came across the following articles which I believe make for an interesting juxtaposition:
The first is by Stephen Law and suggests that there’s good reason to at least remain skeptical about the existence of Jesus. I’m less interested in this thesis than in a thought experiment that Law introduces in the course of his argument. If you skip down to the subheading “The Ted and Sarah Case”, Law relates a hypothetical scenario in which Ted and Sarah, two close friends who are generally reliable, not given to practical jokes, etc. tell you that a man named Bert “flew around their sitting room by flapping his arms, died, came back to life again, and finished by temporarily transforming their sofa into a donkey.” Law concludes that he is not justified in believing that his friends have witnessed a miracle. Although his friends’ testimony provides some evidence, it is by no means sufficient. Law then makes explicit the analogy between the Ted and Sarah case and the gospels:
“Of course, we should acknowledge there are differences between the historical evidence for the miracles of Jesus and the evidence provided by Ted and Sarah that miracles were performed in their sitting room. For example, we have only two individuals testifying to Bert’s miracles, whereas we have all four Gospels, plus Paul, testifying to the miracles of Jesus. However, even if we learn that Ted and Sarah were joined by three other witnesses whose testimony is then added to their own, surely that would still not raise the credibility of their collective testimony by very much.”
Law also adds “the fact that it remains blankly mysterious why such reports would be made if they were not true does not provide us with very much additional reason to suppose that they are true.” He then derives a variation of the principle “extraordinary claims require extraordinary evidence.” I am on record as having expressed dissatisfaction with the way this principle is formulated. Law, for the purposes of this essay at least, is content to leave it vague.
That brings us to the second essay. This one is by Daniel Bonevac and is an argument for the rationality of belief in miracles. Following in the tradition of others, such as Swinburne, Bonevac takes a Bayesian approach to miracles. He argues that miracle claims are credible in Bayesian terms if certain conditions are met. Specifically, the number of witnesses matters. Take the following set-up. Let’s assume that the probability of a resurrection is 1 in 10 billion. Let’s further assume that the probability that someone would report a miracle if it occurred is .99. Finally, let’s suppose that the probability that someone would report a miracle claim if it did not occur is .1. If we only have one witness, on Bayes’ theorem, the odds that a resurrection occurred are one in a billion. The skeptic appears to be justified. But Bonevac contends that it doesn’t take many more witnesses to drastically increase the odds. Given the numbers, it only takes 10 witnesses to bring the probability up to .5 and twelve to make it highly likely (.9888). Using slightly less conservative probability estimates (.999 and .01 in place of .99 and .1) he argues that it only takes 5 witnesses (the gospels and Paul, we might say) to bring the probability of the resurrection up to .5 and six witnesses to make it a near certainty. The application to Law’s hypothetical scenario are clear. It’s also much less clear that ‘extraordinary claims require extraordinary evidence.’ According to Bayes’ theorem, Bonevac argues that ordinary evidence will suffice.
Now there are some issues one could raise against Bonevac’s methodology. For example, one might quibble with the priors he assigns. As Law says, the fact that we don’t know why people report a miracle when none has occurred doesn’t necessarily raise our credence in the claim as Bonevac seems to assume. Also, one might raise the problem of dwindling probabilities. Later in the essay, Bonevac suggests that a series of miracles might be more credible than one miracle in isolation. Of course, a series of miracles raising our credence in subsequent miracles only works if we already know earlier miracles occurred. In other words, if we already know that Jesus did in fact turn water into wine, feed the five thousand, and raise Lazarus from the dead, then his own resurrection becomes more probable. But it would be question begging to assume all of that. In the absence of iron-clad evidence for these earlier miracles, the series of miracles reported may serve to decrease our credence in these reports. For example, if the probability of miracle #1 is .5, the probability of miracle #1 and #2 is .25. Furthermore, the probability of miracles 1,2 and 3 is (roughly) .13. This is the problem of dwindling probabilities. I think this is partly what Law is trying to articulate when he says that the admixture of ‘extraordinary claims’ into the gospel narratives decreases our overall credence in those accounts. Finally, one might also question the extent to which the gospels are independent and to what extent, if any, the gospels are eyewitness accounts. Nonetheless, Bonevac’s calculations are enough to warrant caution in accepting the intuition behind Law’s thought experiment and the principle he derives from it. Again, we need a clearer understanding of the maxim ‘extraordinary claims require extraordinary evidence.’