I agree that we should not assign too much significance to the general rarity of supernatural events - as you argued on page 182 (quoting McGrew), the probability of a generally rare event could go up significantly in light of new evidence. That’s why in my probability calculation above, 1) I did not include an independent factor for the general rarity of supernatural events and 2) I also added that the probability assessment for statements 2 and 3 (that God would want to reveal himself to humanity through Jesus) should be considered not in isolation, but also in light of the historical evidence surrounding the Resurrection that we have, just as we did in the case of the naturalistic hypotheses. (In addition, I note that in this case we have the benefit of two independent pieces of evidence - the empty tomb and the post-mortem appearances. They can be used to support each other.)
This is also reflected in the case I suggested to Faizal, namely that the normally low probability of a large asteroid hitting Earth shouldn’t prevent us from regarding it as a likely hypothesis for the mass extinction of the dinosaurs in light of independent evidence supporting it and also the failure of other hypotheses to explain the same phenomena. That being said, I think it’s obvious that, say, if we had large asteroid impacts every 1000 years instead of every 100 million years, it would be much easier to prove that it explains the mass extinction of the dinosaurs. So the general rarity of the event can play a role, even if it shouldn’t be overstated compared to specific considerations of the case.
However, while you and McGrew correctly argue that the probability of the supernatural should go up in light of the evidence for the Resurrection, I think that you must also concede that the skeptic can also argue that the probability of mass hallucinations, people dying for beliefs they know are wrong, etc. can also increase in light of this same evidence. This symmetry is seen by considering the two hypothetical cases:
- If we assumed for the sake of argument that mass hallucinations happened in this case, for example, then skeptics can use that assumption to argue that other claimed supernatural phenomena (e.g. that Jesus turned water into wine) are also less likely to have happened, because apparently mass hallucinations happen more frequently than what we previously thought (and psychologists have to get to work explaining this).
- If on the other hand for the sake of argument we assumed that Jesus was resurrected supernaturally in this case, then Christians could argue that other claimed supernatural phenomena (e.g. Jesus’ other miracles, the miracles of the Twelve, modern-day claims of miracles) are more likely to have genuinely happened as well, because apparently supernatural events happen more frequently than what we previously thought.
Thus, to be fair, we have to allow both types of hypothesis (i.e. natural and supernatural) to “benefit” from the relevant evidence under consideration. Now, whether the probability of both types should increase equally is unclear to me. In my above calculation I have assumed that they increase proportionally. But perhaps one could argue on other grounds (e.g. explanatory scope, coherence, etc.) that it should benefit the supernatural resurrection hypothesis more.
I agree, and that’s why I think it should be part of the calculus, along with many arguments for the existence of God that have been offered by other philosophers.
Yes, I see that now on page 185. I just am not convinced that an argument purely by exclusion of other hypotheses is legitimate. I think the renormalization approach preserves the benefit of your systematic logical structure while treating hypotheses equally. I believe this should be done also for claims of resurrections and miracles in other religions. However, the exclusion approach could be persuasive as a quick approximation tool for people who are already OK with the idea of supernatural occurrences, such as perhaps the Catholic Church when it is evaluating whether a miracle happened after praying for intercession from a saint.