(Continued from the previous post)
So, all that gives us that Bayes' factor of 1e54. Now, as I've said I'm okay with its large magnitude, under the specification that this is for a certain model evaluated under some well-justified degree of independence. Given its large value, Jesus would have clearly risen from the dead under these conditions. I also think it's clear that nearly no amount of partial-dependence hypotheses, like ordinary social pressures, can nullify this value. So I do think that this large Bayes' factor is useful in these broad cases.
But as you've pointed out, we now need to worry about low-probability hypotheses that would wipe out that Bayes' factor by asserting a near-total dependence of the evidence. That is to say, we need to consider hypotheses which are specifically constructed to allow for ignoring the evidence, like conspiracy theories. I had initially planned to simply dismiss things like conspiracy theories at the end, but this conversation with you has convinced me that I need to address them.
So here's my plan. I'll group the spectrum of prior possibilities for the "no resurrection" hypothesis into the following regimes, in the order of decreasing probabilities involved:
1. Largely independent testimonies
2. Partially dependent testimonies
3. Near-total dependency in testimonies (conspiracy theories, other theories specifically designed to allow for ignoring the evidence)
4. Epistemological obliteration (brain in a vat, multiverse, all just a dream, you can never know anything, possibilities you can't even think of, etc.)
I do plan on just dismissing that last one at the end. Possibilities 1 and 2 are taken care of with the enormous Bayes' factor of 1e54. So now, we must start considering possibility 3.
I think I can argue convincingly against hypotheses like conspiracy theories in the upcoming posts of my series. In particular, the part of the series on resurrection stories from non-Christian sources are not just a "Christianity is better than these others" compilation. It's a way to double check the Bayes' factor, and to provide protection against hypotheses like a conspiracy theory. If, in fact, a conspiracy (or alien interference, or malicious spirits, or whatever) can produce results like Christianity, then over the course of world history you can expect for it to have done so once before, or at least come somewhat close. But empirically, no such results exist. None even come remotely close. Christianity is a distinct outlier.
You said, in attempting to estimate a Bayes' factor from historical data, that "For the kinds of skeptical reasons I stated above, it would be hard to get this much above 10^11 by itself since then we run out of the ability to check how many potential parallels there are." But you can check not only how many parallels there are, but how close they come. Assuming independence, you can even put precise numbers on the Bayes' factor involved by measuring the degree to which Christianity is an outlier. Even without independence you can definitively say that that the Bayes' factor was at a minimum around 10^11, and likely a good deal larger.
That's the great thing about arguing from empirical, historical records. You can bypass all the calculations about the probability of conspiracies or exactly what kind of dependence the testimonies might have had, or whether it was some other kind of hypothesis that generated this dependence. All of that automatically gets incorporated into the historical data at their actually correct historical values, and all we have to do is to read off the final result.
Anyway, that's my plan for the future of the series. I'll look at the historical comparisons, then use it to argue that the Bayes' factor of 1e54 is about correct assuming mostly independence. Furthermore, the historical comparisons allow us to say that Jesus is very likely to have risen even after all the other hypothesis, such as a conspiracy, are taken into account. That would probably be a good time to re-iterate that the 1e54 was for a specific model, that the final probability value would be not so extreme in reality, but still plenty high.
If you looked at how I write for my blog, I generally make a final compilation post at the end of a long, multi-part series, where I clean things up and maintain it as the final link. There, I'll probably rearrange the material so that the issues you brought up are resolved from the beginning. I do want that final post to be good, and clear of sloppiness and error.
So if you would share your thoughts on the future of the series, I would be grateful.
(To be continued in the next post)