Wednesday, July 27, 2011

Tim and Lydia McGrew on the Resurrection, part 1 (introduction)

When I was beginning to do serious reading on Bayesian philosophy a few months ago, the first thing I wanted to do was this: find examples in action, then figure out what I needed to understand them. In my experience, this is a good way to start studying abstruse topics like philosophy and mathematics. As a beginning, you cannot expect to read a chapter of a technical text and be able to recall the theorems and important argumentative techniques. You certainly cannot expect to `re-derive' the chapter you just read. Instead, you absorb the techniques through practice. Like puns, nerds love a good continuity, so I sought applications relevant to my previous interests. What better topic for me could there have been than those same arguments about gods which had served me so well as a springboard into philosophy? Naturally, the first topic that came to mind was one which had always bothered me: Hume's argument against the possibility of confirming a miracle.1 By obvious tangents, I soon discovered Tim and Lydia McGrews' The Argument from Miracles: A Cumulative Case for the Resurrection of Jesus of Nazareth (CCRJ).

I have been writing down my thoughts about this for a while, but I had only been doing so for auto-didactic purposes related to Hume's argument. Since I've only found one (inadequate) rebuttal, I feel that I should share my thoughts.

Here I'll pull a Vonnegut: I will say that I disagree with the conclusions of the paper, and then I will try to realize that in an interesting way. I'm not here to surprise the readers. But I do not want these posts to be thought of as a `debunking'. If you come away from these posts feeling that reading the McGrews' CCRJ has been rendered unimportant by my awesomely insightful analysis, then I have failed you miserably. If you come away feeling that the McGrews are lazy, unscrupulous apologists, then I have failed you super miserably.2 They sought to start an analytical conversation and send the topic our way. Stop, read the paper carefully, and please, please try to understand it before breaking the internet. I heartily recommend it as an application of Bayesian principles, and I have learned much from it.

My response will have limitations. First, I'm new to this stuff and they are not. Second, I am not an expert on Biblical criticism and historical method. Third, and partly as a function of the first two, my discussion will necessarily be incomplete. As I hope you will see, I am going to try to build on what the McGrews started. I will attempt to suggest a better formula to analyze so that those with more expertise than myself might converse in a common framework. Since the CCRJ is the best relevant article that I have managed to find, I will use it to open a more general discussion. As I have yet to find any other Bayesian analysis on the same level, I think this the best place to start and I plan on referencing it heavily in the future. If there are other, better presentations, I would appreciate a reference.

As I interpolate it, the core of the CCRJ is as follows3:

1. There are salient, secular facts surrounding the Resurrection (R, which Christians and skeptics can reasonably accept.
2. These facts (F) constitute powerful evidence for the Resurrection.

These are the two items which I wish to discuss. As against these, I propose two counter-statements:

1. The set F proposed in the CCRJ may also be reasonably disputed, and this observation severely constrains the evidential strength of any argument from them.
2. The McGrews grossly overestimate the strength of F as evidence for the Resurrection.

The first Big Issue is the most obvious one: what exactly is this textual record we have, and how should we deal with it? That will be the topic of my next post.

Outline and summary:

1. Part 1: You just read it, I hope.
2. Part 2: I prove that even minor disputes about textual assumptions would undermine the McGrews' Bayes factor as an estimate of a genuinely cumulative Bayes factor. I propose a general analysis to avoid this trap, and one which allows experts to continue the discussion.
3. Part 3: I introduce the McGrews' argument, discuss how one can question it and why, and what one should expect in the details.
4. Part 4: I argue that Paul's conversion does not significantly contribute to the argument.
5. Part 5: I introduce the disciples, discuss their importance, and the effects of independence assumptions. I introduce their arguments and begin presenting my own.
6. Part 6: I present an alternative hypothesis to explain the disciples.
7. Part 7: I discuss the testimony of the women and arrive at a final replacement Bayes factor.
8. Part 8: I make some concluding notes and comments.

1. Yes, pace Keith Parsons, I think that Hume argues that in some circumstances it is impossible to confirm a miracle. No, I'm going to leave that topic for a different series of posts. No, I don't think that his unconfirmability argument is valid, for reasons discussed by Earman in Hume's Abject Failure. I think I have a way of updating the argument, with restrictions, such that it covers the Resurrection, but I leave that for later. For this topic and generally, one can start by reading the (and recently updated) SEP article on miracles, which was itself written by Tim McGrew. In particular, I would like to cite part of the conclusion of that article:
For the evidence for a miracle claim, being public and empirical, is never strictly demonstrative, either as to the fact of the event or as to the supernatural cause of the event. It remains possible, though the facts in the case may in principle render it wildly improbable, that the testifier is either a deceiver or himself deceived; and so long as those possibilities exist, there will be logical space for other forms of evidence to bear on the conclusion. Arguments about miracles therefore take their place as one piece—a fascinating piece—in a larger and more important puzzle.
2. Partly, I feel a need to say this because `apologist' is very often used as a curse word. So if I call the McGrews or others `apologists', I want to renounce the bad connotations. I am often guilty of using the term pejoratively, so I think it important to give this disclaimer. In other contexts, I have used (and will use) it pejoratively without apology. I think this is legitimate, but generalization as mixed with emotive judgment should be done cautiously.

3. The McGrews are clear about what they are doing and how. They are not here arguing for theism or Christianity. Rather, they are focusing on the Resurrection. They are also not focusing on rebutting Hume's argument or determining what the prior odds on the Resurrection should be. They are arguing for a very large cumulative Bayes factor in its favor. Nor are they claiming that their case is cumulative in the broadest sense; they are restricting the discussion to the relevant textual evidence and its characterization. There are also issues which are inessential to this discussion, such as the proper definition of `miracle', which they do not concern themselves with here (CCRJ, pp.2-4).

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