More on independence after a recent conversation

Two days ago (5/20/24) I had a very interesting conversation about minimal facts with theist (but not at this time Christian) Youtuber and philosophy student Matthew Adelstein. Toward the end of our conversation he brought up the issue of independence, multiplying Bayes factors, and the very large cumulative Bayes factor in Tim's and my 2009 paper on the resurrection. Matthew was critical of this very large cumulative factor on the grounds a) that it's just too large for any empirical matter (I just disagree) and b) that if some non-resurrection explanation would explain some of the individual testimonies, it would probably explain more of them, so that there should be diminishing returns, and the individual Bayes factors should not be multiplied.

In our conversation, I felt that this very interesting and complex topic was arising too close to the end of our time together to receive a good enough discussion, so I indicated serious awareness of it and tried to make a somewhat different but related point about maximal data, which was the topic of our overall conversation. But I'm concerned that that looked dismissive, so I've decided to follow up here.

Here I'd like to restate that point that I was trying to make in the video and also discuss some more of the issues surrounding independence in the argument for the resurrection.

In the discussion context, I was urging the importance of the maximal data approach and mentioned that in Tim's and my original resurrection article, the Bayes factor that we used was explicitly based on the claim that the detailed, polymodal resurrection stories in the Gospels give us the content of what the original (alleged) witnesses claimed. Matt immediately stated that he thinks that Bayes factor is wildly over-optimistic anyway and gave as one of his reasons the problem of independence. The cumulative Bayes factor was calculated by multiplying individual disciple testimony factors together.

The point that I wanted to make in response in the video was this: Even the individual Bayes factors of 10^3 depended upon the polymodal and detailed nature of the claims. For any one ostensible witness, the question arises whether this is the kind of thing that he could be simply mistaken about, whether it was the kind of thing that, if he really experienced it, would reasonably lead him to think that Jesus was risen bodily (as opposed to unreasonably over-interpreting his experience), and whether it was the kind of thing that could have some other plausible non-resurrection explanation. The answers to these questions depend crucially upon the content of the testimony. If we don't have detailed testimony but just something like "He was seen by the disciples," that makes it much harder to argue for even a single strong Bayes factor in favor of the resurrection. And if many liberal scholars are right that the disciples didn't experience anything detailed and physical-like, as reported in the Gospels, in a group, then a "mistaken" option of some kind becomes much more plausible. (I note here that Matthew himself, earlier in our discussion, really pressed on the idea that the Gospels have signs of "development" and "apologetic additions," so he should be in a good position to realize how important it is to have a good answer to these claims that the most interesting parts of the Gospel narratives are just made up!)

So even before we get to the concern about independence and multiplying Bayes factors, the issues between minimalists and maximalists become relevant. In raising Tim's and my Blackwell article, I wasn't trying to inaugurate a debate about the actual cumulative Bayes factor we gave there; rather, I was trying to point out that even that long ago we were advocating a maximalist approach in the sense that we recognized the extreme epistemic importance of the detailed and extensive nature of the disciples' testimony, which can be found only in the Gospels (and Acts) if it is to be found anywhere.

Next, I want to point out that the detailed Gospel accounts are also related to the issue of independence and group appearances in a way that is positive for the resurrection case. In a series of technical articles, I've picked up on a suggestion that Tim made in the Blackwell article and run with it; this suggestion concerns a way of correcting for dependence among individual items of evidence. A slightly non-technical way to describe it is to say that we need to ask whether the individual items of evidence are more dependent upon one another given the affirmation of the hypothesis in question (in this case, the resurrection) or more dependent upon one another given its negation, and finally what the ratio is between dependence given the affirmation and given the negation of H. I argued here (in the journal Ergo) that independence given the negation sheds important light on the value of diverse evidence, long recognized in the philosophy of science. In two other articles (not currently available online for free) I discussed the use of the correction factor to correct for dependence in cumulative case arguments. (It appears that I now have permission to post the accepted manuscript version of both of these to a personal website. If I do that I'll post links here. Otherwise, if you are an academic, you probably have institutional electronic access to the journals in question. The Ergo article is available by open access.)

“Accounting for Dependence: Relative Consilience as a Correction Factor in Cumulative Case Arguments,” Australasian Journal of Philosophy. 95:3 (2017), 560-572, DOI 10.1080/00048402.2016.1219753.

“Bayes Factors All the Way: Toward a New View of Coherence and Truth,” Theoria (2016) 82:329-350. DOI 10.1111/theo.12102.

Matthew was emphasizing the plausibility of dependence on the negation of R: If something-or-other had the explanatory power to explain one disciple's testimony to a group experience, given that R was false, then that same something-or-other would plausibly explain some other disciple's testimony, given ~R. 

But that's not even close to being the only question. Consider the possibility of dependence on R given the following aspects of the testimony: 

--Jesus appeared to them in various groupings.

--Jesus didn't just appear visually in some paranormal-like way; rather, he was tangible and audible as well, to multiple people at a time, on more than one occasion.

--On multiple occasions, he gave long speeches and/or had detailed conversations with multiple people at once.

--On more than one occasion, he was able to eat and on one occasion even suggested to them that they give him something to eat in order to show that he was not a ghost.

--It seemed to them, in groups, that Jesus was physically present in the room, present in 3D, solid, standing before them with his feet on the ground, not floating in the sky or appearing from heaven.

Now, suppose that Jesus really rose bodily from the dead--R. (I am not counting as R merely his exaltation to heaven.) In that case, if one of his friends claims the above things, including that that person himself was present at such a group experience (T1), then the probability that another such friend will say the same (T2), given (R & T1), is greater than given R alone. T1 gives us information about when and how Jesus appeared to a group or groups, leading us to have greater reason to expect multiple testimonies indicating the same type of thing. An analogy would be this: Let H be, "Lydia McGrew lives in Kalamazoo, Michigan." Let T1 be some specific person's statement, "I saw Lydia McGrew at____church in Michigan on ____date, at the morning service." Let T2 be a similar testimony from some other person who goes to that church. P(T2|H & T1) > P(T2|H). There is helpful dependence among the testimonies given the truth of the proposition that I live in Kalamazoo, since the statement that I was really present on a particular occasion in a particular place in Kalamazoo, attested by one witness, gives us reason to believe that I was genuinely, physically encountered on that occasion by more than one person and hence that someone else will also be able to confirm this.

What all this means is that there is arguably dependence on R among the attestations by multiple disciples, not just on ~R. (And as I've pointed out in some recent videos, Acts 1 very carefully lists the eleven by name and reports that Peter urged the election of a replacement, who ended up being Matthias, so that there would be at least twelve people to attest to Jesus' resurrection.)

Moreover, the importance of the highly detailed stories in the Gospels to a cumulative Bayes factor is also relevant to dependence on the negation. Here's why: Above I mentioned that dependence on the negation involves some kind of subhypothesis of ~H, a something-or-other that would explain one testimony for H (though H is false) and would simultaneously explain multiple testimonies to H (though H is false). Something we emphasized in our Blackwell article is that the probability of a subhypothesis of ~H given ~H is an important issue when it comes to how helpful that subhypothesis is in explaining away evidence for H. (Actually I think I coined the term "subhypothesis" later than that article and used it in the Ergo article, which I wrote individually, but the concept is there, and the point about the probability given ~H was originally Tim's.) The specific subhypothesis of ~R that would act as the "something-or-other" mentioned above becomes more and more bizarre and improbable given ~H itself when it has to explain the detailed stories in the Gospels. This is extremely important. 

One skeptic (Arif Ahmed) has written a technical article about dependence given the negation of a miracle story with reference to an event like a magic show, someone appearing to walk across a swimming pool in front of a large audience.

But in the case of the Gospel stories, the disciples are all present together in a place where they are able to get close to Jesus. He invites them to touch him. He talks to them at length. Etc. This is far more difficult to account for than some kind of illusion, put across to an audience sitting at a performance, using modern technological resources for creating illusions. It's all very well to say that if something-or-other could explain why one person would describe such a group experience, even though Jesus wasn't bodily risen, it's somewhat plausible that multiple people who were allegedly present at the same event would say the same. But when we consider these details, what would such a something-or-other be? It's precisely here that group hallucination theories become so improbable. Even if you think that there are real group hallucinations in some sense (like a bunch of people simultaneously thinking they see some shape at a distance, which they identify with a saint), these kinds of detailed, polymodal, lengthy group hallucinations are the kind that we really can say we don't have any instances of. 

This supports the point I was making in the conversation--namely, the great importance of a maximal data approach. The minimalists like to brush off the hallucination possibility; what they don't seem to realize is that really wildly improbable hallucination theories aren't in fact needed to explain the facts found in a minimal facts case. For suppose that all that we had, instead, were summary statements like those found in I Corinthians 15--he appeared to the twelve, he appeared to this person, he appeared to that person. No criticism of the Apostle Paul. He's just giving a summary. He couldn't have known that in the 20th and 21st centuries people would be trying to lean on his summary instead of more detailed accounts! If we have no idea what their experiences were like, we are fairly free to develop some not-R subhypothesis that would explain such bare claims, even from multiple people. This, indeed, is what Bart Ehrman himself does. He says that he doesn't grant group experiences anyway, but that if they did have group experiences, they were merely seeing at a distance, like alleged Marian apparitions. Norman Perrin suggests that they had some feeling of theological enlightenment while they were together (that Jesus was "risen into their lives") and that this (he may also have in mind some kind of garden-variety mental imagery) was called "seeing" Jesus. 

Or suppose that we had to make our argument for Jesus' bodily resurrection while relying on "the appearance experiences" as understood by Dale Allison. Allison thinks that Jesus spoke only briefly and that the highly physical-like experiences, like his asking for food to eat and offering to let Thomas touch his scars, simply didn't happen. (Notice here the similarity to Matthew's own concerns about "apologetic development" in the accounts, shared by so many critical scholars.) In that case it's much  easier to find a subhypothesis of ~R that explains even multiple testimonies to that sort of experience. Indeed, that's Allison's whole point. In his opinion, the experiences were vision-like rather than physical-like. So some sort of exaltation followed by visions rather than a bodily resurrection (R) would make a better explanation of the fact that multiple people testified to...vision-like experiences. 

One more point: As I've argued in an older post, there is variation present in the maximal data resurrection evidence that we didn't really access in the Blackwell article. Remember that variation in testimony is helpful in avoiding dependence on the negation of H. This includes variation in the backgrounds of the people involved, their peer groups and influences on them, the geographical settings of the events, and the groupings involved. While the post refers specifically to conspiracy theories, the same point is relevant to "mistake" theories and dependence on the negation of H.

This has been a rather technical post, but I didn't want it to seem that I was brushing off Matthew's question about dependence on the negation, and I've decided to put this into a blog post, as that is a more permanent form (more so than Facebook) for such lengthy comments.