Monday, June 23, 2008

The Documentary Hypothesis, Torah Min Hashamayim, and Bayes' Theorem - The Implications

Now for the qualitative implications of Bayes' Theorem to TMS / DH debate. Bayes' Theorem starts with an initial probability (or a probability estimate) prior to any information. It then shifts this initial probability as new information comes out that is either more consistent or less consistent with each of the two theories. There are at least five implications for the TMH/ DH debate.

First of all, Bayes' Theorem requires an initial probability estimate. In the example above, we could make the assumption that 50% of the jars were Type Y jars. But there's no good way to make any estimate in the TMH / DH debate. Some people might start with the initial premise that it is highly likely that there is a God and that He would want to give a set of instructions to people. They would start with the premise that the probability that TMS is true is very high. Others would think it is highly likely that there is no God and, if there were, He already gave sufficient guidance through natural law and reason, and so there is no need for Him to do so by some divine revelation. These people would the premise that the probability that TMS is true is very small.

One implication of this is consistent with what we see on both sides of this debate. As proponents of one theory present what they think is a pretty compelling argument, the other side responds with a bored yawn. "That may be fascinating, but I just don't see that that gets you very far." But the proponents disagree and think the argument is brilliant and airtight and proves their theory is correct. Neither side understands how the other can either miss the power of their airtight argument or make such a silly argument. The explanation for this breakdown in communications may lie in Bayes' theorem.

The argument might in fact be quite good. But the opponents are starting with a very low estimate of the prior odds. Consequently, this very good argument does not shift the odds that much. Or alternatively, the argument might not be that good. The proponents think it is great because their estimate of their theory being correct is very hight. But their odds started off high in the first place. In either case, Bayes' theorem explains the frequently observed result of debates in this area: a frustrating sense that the other guy just does not get it.

The second implication of Bayes theorem is that it points us to what sort of arguments should be convincing. A convincing argument is one where the following condition holds: the probability of the new fact being true given that one theory is true is greater than the probability of the fact being true given that the other theory is true. The focus has to be on relative probabilities here, not absolute probabilities.

Here's a real example of this problem. I once mentioned to an Orthodox friend that many other ancient cultures had flood stories similar to the Biblical flood, and the Gilgamesh story is remarkably similar to Noah's flood story. To me, this seemed like a good argument supporting the claim that the Biblical flood story was derived from these other stories. My friend argued that this cuts the other way: this independent corroboration supports the historicity of the flood story.

It took me a while to unpack this exchange, but Bayes' theorem provided the key. My argument, more fully expressed, was that if you assume the DH is true, then it is not surprising (that is, there is a high probability) that there are actual ancient sources for the various Biblical stories and that there is some chance that we can actually find some of these. And we did. That argument is right, as far as it goes. My friend's point was that if you assume TMH is true, then it is not surprising (that is, there is a high probability) that there is independent corroboration of these historical stories. And that is right also, as far as it goes. But both of us were looking at only half of the problem.

The way to advance this argument is to look to relative probabilities, not absolute probabilities. That is, we each need to find facts that are more consistent with our theory and less consistent with the other theory. For example, as many have argued — including most recently James Kugel in How to Read the Bible — some of the literary aspects of the Gilgamesh story are virtually identical to the Noah story. This is pretty likely if one was copied from the other, but it is pretty unlikely if these are two independent literary witnesses to the same historical event thousands of years earlier. I don't mean to start a debate on the flood here (plenty of time for that later), but my point here is simply that Bayes' theorem points us to this type of argument.

Of course, these arguments are qualitative, not quantitative. We cannot estimate the actual probabilities of any of these things with any precision. Even a general estimate of likeliness is made all the more complicated by the fact that we just don't have any idea of the sort of book that God would write if He were to write a book. We just don't have a good data set there.

Third, there is no magic bullet or killer argument. Each argument is of the form "This is more likely to have occurred if Theory X is correct than if Theory X is not correct." And each argument like that just shifts the odds, either a lot or a little. The only argument-ending argument would be one where the odds of a particular thing happening is zero if Theory X is correct. (Suppose that Type Y jars also had one purple marble, but Type H jars did not. If you drew a purple marble, you would know for sure that you had a Type Y jar, regardless of anything else.)

Fourth, the only way to have a comprehensive understanding of this debate is to consider all the arguments together. You cannot just look at one draw of a marble. You need to look at all draws — all the yellow marbles and all the green marbles. And here, this is complicated. There are lots of different arguments covering lots of different areas. It is virtually impossible to master them all.

Fifth, ideas and terms like "burden of proof" and "presumption" have no place in this debate. These are legal terms that reflect policy decisions. They involve who needs to come forward with evidence, what we will believe (as a matter of policy) in the absence of evidence, and what happens if the weight or convincing force of the evidence is exactly equal. But there should be plenty of evidence and argument on both sides. And in the extremely unlikely event that the weight of the evidence is exactly equal, one should just get more evidence and argument.

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