In addition to the items summarized in the last post, we have now seen that there is little reason to regard Paul's conversion as itself making significant contribution to a cumulative Bayes factor, even when taking the relevant salient facts of the McGrews at face value - where they are consistent and actually salient. We have therefore reduced the McGrews' final Bayes factor from 1044 to 1041. Admittedly, this change is very slight. As previously discussed, the most important features of CCRJ are as follows: the independence assumptions and the effect of the disciples, particularly in conjunction. These ideas alone contribute a multiplicative factor 1039 to the McGrews' final likelihood ratio. Before discussing the details surrounding the disciples, their independence should be treated first.
The McGrews do not argue that their conditional independence assumptions are plausible. On the contrary: "the invocation of independence assumptions at several points is contestable; in fact, we believe that the case of the calculation for D the independence assumption almost certainly breaks down." So why do they invoke it? Because "this fact does not necessarily lessen the strength of the argument. Everything depends on the balance of considerations regarding the direction and extend of the breakdown of independence under R and ~R" (p.40). This approach is quite sensible: start out with an admitted simplification, critique it, and argue that the critiques generally favor the proponent of the argument.1 I think that the only other even approximately accurate response available on the web - at least that I know of - fails to adequately address this.
Allow me to motivate the discussion by being self-referential. If one grants a significant number, say n, of events Ei where i is a positive integer less than or equal to n, and one can assume that the Ei are conditionally independent under a hypothesis H and its negation ~H, then even a very small individual factor
is a big deal. With only 13 witnesses, even assigning a Bayes factor of 10 to each individual - even this seems uncharitable - still gives you a cumulative factor of
where the notation is exchanged as needed. This is a big number, even if its nowhere near that proposed by the McGrews.2
As we noticed, the McGrews will not be surprised if we directly challenge independence. Instead, we have to focus on pages 40-46 of the CCRJ. In order to do this, we have to start discussing and disputing facts about the disciples. This is because of the straightforward fact I noted in the other post in the context of evidential variety: the invocation of independence across a significant number of events `filters out' hypotheses which do not convincingly allow these events to be correlated. Less abstractly, the fact that the disciples not only witnessed as they did individually but did so in agreement must be plausibly explained by some element in ~R, if we grant that agreement.3 `Bad' hypotheses, for our purposes, are those which are intrinsically implausible and those which are only plausible with respect to one or a few disciples. Even if a hallucination happened to plausibly explain the witness of one disciple, it does not without lots of dubious conjecture help to explain the correlation of the witnesses.
The key facts about the disciples4 are as follows:
1. They were not expecting the Crucifixion or Resurrection in advance.
2. They were willing to die - or at least take great risk - in order to spread Jesus' message. (pp.17, 20-24, 30-37.)
3. There was little to no material or social advantage in preaching this message.
4. They attested to a physical resurrection. They claimed to have seen him and spoken with him for some lengthy period of time, e.g. 40 days. (pp.17-8)
5. They did not present a self-flattering account of the Resurrection. For example, they claimed to not readily understand, to be fearful, to have doubts, and to be chided and corrected by Jesus. (pp.17-8)
A hefty confidence in these is required to stick to the McGrews' analysis. For example, the importance of consensus amongst the disciples, and that there were no omitted complaints from purported witnesses, is of central importance (p.32). While I agree with the McGrews that it is very difficult to seriously attribute most or all of the disciples' testimony to cynicism or fabrication, my confidence in the uniformity of their testimony with respect to these key facts is much less. There is little reason, had there been substantive dissent, to expect that it would have made it into the gospels. Still, my purposes at this time are not to dispute these items. However, such discussion will be an important part of a general analysis like that presented in part 2.
Now, I agree with the McGrews that `external' theories, e.g. the `stolen body hypothesis', do very little to explain the facts in question (p.32). The point is to account for these facts in a convincing manner, and their origin is not at all explained by people stealing Jesus' body to corroborate the claims of early Christians. What we are looking for are `internal theories', i.e., those which convincingly explain the actions and statements of the disciples. It is here that I think the McGrews grossly underestimate the strength of potential naturalistic alternatives.
Before moving on, I should say something about the significance of these facts, especially (5). The idea is that were the disciples to be manufacturing stories or exaggerating in order to advance their cause, we might reasonably expect them to not be so hard on themselves. I do not think, especially in the context of Christianity, that this is a significant consideration. I think we are all familiar with examples of false humility, or we understand at the very least that confessions of guilt and personal inadequacy are very often encouraged in Christian communities, even admired. Perhaps my personal experience is overshadowing the general picture, but I understood early as a child that confession of guilt in church and begging for redemption was admired and expected of me. That the disciples do not flatter themselves is insignificant in the context of Jesus' teachings, quite apart from the Resurrection, "for all have sinned and fallen short of the glory of God." There are similar considerations for (1). Evidently, and I think everyone involved agrees, Jews did not expect that the prophesied Messiah would be anything like Jesus. That the disciples understood, empathized, or even shared in part this lack of expectation is not overly surprising. What matters is how we would expect the disciples to "normally behave" after Jesus' death.
To address naturalistic alternatives to the Resurrection which explain (1)-(5), the McGrews rework in probabilistic terms the good ol' "nobody would die for a lie" claim. This argument has its merits, as far as it goes, but it does not go as far as the McGrews think.
It is sometimes urged that kamikaze pilots, suicide bombers, and Nazis were willing to give their lives for what they believed was true. The objection may be put more broadly. Virtually every religion has its zealous adherents who have been willing to die for what they believe; why, then, should the willingness of the apostles to die as martyrs be of special epistemic interest? The answer is that this description blurs the distinction between the willingness to die for an ideology and the willingness to die in attestation of an empirical fact. (p.32) [citations omitted.]
It is clear that neither kamikazes, Nazis, nor suicide bombers died to affirm the reality of something that they had seen with their eyes and their hands had handled. Thus, their deaths and the falsehood of some of their beliefs tell us nothing about the probability that a man will die to make an affirmation like that of the apostles when it is in fact false. The educational resources of an entire nation, applied over the course of a decade or more to minds at their most impressionable stage, may be sufficient to induce in the young the general belief that their country or their religion is worth dying for. But what would induce grown men to break with the religious community in which they had been raised and confess with their blood that they had seen with their own eyes and handled with their own hands their dead rabbi raised again to life? (p.33) [Emphasis in original.]The McGrews partially answer their own question or are really asking it to themselves. The disciples had already broken with their religious background to follow Jesus - with the possible exception of James. They were already committed to the heretical philosophy of Jesus. They were not merely dying to attest the Resurrection; they were dying for the belief that the Messiah had arrived, that only His followers would find salvation, and that the end was near. The distinction which the McGrews make is valid, but it is extremely narrow in this context.5 To divorce the Resurrection from the other claims, moral and otherwise, of Christianity is misleading.
The previous considerations apply to the "disciples witnessed but did not really believe" section of alternatives. Now we can look at the "disciples witnessed and really believed" section of alternatives. Here is where we find claims about delusion and hallucination:
Suppose, on the other hand, that the witnesses did have good reasons for their belief in the resurrection but were nevertheless mistaken. How is this supposed to come about? The hallucination theory has at least this advantage over both external naturalistic explanations and the appeal to enthusiasm: the supposition that the disciples suffered from sufficiently vivid and persistent hallucinations provides the resources to explain why they firmly believed they had seen Jesus risen. But this gain in explanatory power comes at a prohibitive cost in prior probability... (p.33) [Citations omitted]Instead of looking at how the McGrews corroborate this last statement, try imagining for yourself why this should be. Is it really at all likely that these committed disciples should individually experience vivid hallucinations or powerful delusions on the event of their Messiah's death, and that these delusions, if that is what they were, should have the staying power that they did? How common are events like this at all? If we want to substantially reduce the Bayes factor proposed by the McGrews in a way that should be at all convincing to both skeptics and believers, we need to look elsewhere for alternatives. As the McGrews note, "the problem with the hallucination theory is that it has a vanishingly small probability conditional on ~R. The sort of complex, repeated, integrated hallucination that would be required to maintain even one disciple's testimony and willingness to die for it would represent a serious mental illness" (p.35). There are qualifications to the McGrews' argument that I would add, in particular that extreme distress can very plausibly result in a resilient, complex delusion, and need not require the positing of serious mental illness, but I will not dwell on these details. The fact remains that there is little reason to think such a thing happened, or would likely happen, and ultimately result in the texts as we find them.
Assuming plausibly that p(D|R) is quite high - say 1 for purposes of simplification - our attention focuses entirely on p(D|~R). We want to know whether or not p(D|~R)=10-39 is at all realistic. Although I agree with the McGrews that hallucination, delusion, and cynical fabrication are very unlikely, we still need to know whether their disjunction is well below 10-39. Unlikely as I think these are, I think that they are at least slightly more credible than that. However, if we are to propose a substantial increase in p(D|~R), we are going to have to look elsewhere. Namely, we want to look for alternative hypotheses H such that p(H|~R) and p(D|H) are significant. In the case that H is `fully explanatory' of ~R, the former quantity is p(H)/p(~R). Assuming that our prior confidence in ~R is high, this approximates the absolute probability p(H). The moral of the story? If you are proposing alternatives to the Resurrection which are designed to completely explain it, you have to be careful to avoid ad hoc thinking: you have to argue that all concerned should find that alternative explanation plausible for reasons other than that the Resurrection has low prior plausibility.
Failing to find any explanatory hypothesis of significant probability, the McGrews assign p(`a disciple'|~R)=0.001, which with independence gives a Bayes factor of 1039.
In order to discuss significant alternatives, question their defense of independence, and propose an alternative Bayes factor, we need to compare the independence case to the more general likelihood formula, which they provide in a footnote (p.26). This work will be formal, abstract, and address the most important part of their argument, so I give this work its own post.
1. To avoid confusion, the vernacular sense of `independent witnesses' is completely opposite to that of the probabilistic sense of `independent witnesses'. What we expect witnesses to do, if none influence the other and the circumstances are clear, is to produce correlating accounts. That is, what one witness says usually strongly affects what we expect other witnesses to say, which is the very opposite of conditional independence.
2. We'll see that the disciples should contribute heavily to the Bayes factor if one is willing to grant near-certainty to all of the important premises entertained by the McGrews. I do not think that skeptics should want (or need) to conclude something other than the following: if the gospel accounts are accurate as regards the relevant, secular evidence for R, then they strongly evidence R. I accept what probability tells me I must, if I assent to the following:
In other words, is there anything in the reports coming out of the first-century church that is more like what you should expect if Jesus was raised than if Jesus was not raised. If the answer to that question is yes, then the evidence confirms the resurrection, but it might still be rejected by reasonable people on the grounds that a Resurrection would commit you to the existence of God, or other features of Christianity that you consider to be improbable. Fine, but you can at least say, in response to the evidence, that the evidence directly bearing on the resurrection of Jesus is easier to explain if the Resurrection occurred than if it didn't. In other words, we can isolate one particular piece of evidence from the total evidence we have that bears on the issue and ask whether this piece of evidence supports the Christian claim that Jesus was resurrected or not.Again, I think that the most important part of rejecting confirmation of R as derived from the Bayes factor is in rigorously defending a very small prior odds and presenting at least a very minimal case for skepticism as regards characterizations of the text like those employed by the McGrews. Both of these feats are easily done, I think, but I leave them to my betters for now.
3. There's much more to be said about this, but that discussion falls well outside of the salient facts as characterized by the McGrews.
4. Recall that there are 13, counting the original disciples minus Judas, Mathias, and James the Just (called `Brother of Jesus'). The details about James are sufficiently different that I would in future analyses recommend separating him from the rest of the disciples. In particular, he is argued to not have been a believer before Jesus died (p.22), and quite plausibly was not present to witness the events attested by the others (p.34).
5. I add also that we have many cases where people are willing to die for false witness. Does anybody here watch House? Have there ever been false confessions to murders? I'll leave this tangent to others.