The TMH / DH Project - Discourse on the Method

Here's the way I tentatively plan to proceed. Please comment if you have any suggestions or criticisms.

The first thing to do is to decide on the methodology. I think I covered the ground for that that in my Bayes' theorem posts on the basics, the implications, and three more implications. For any particular fact or issue or anomaly in the text, we do three things:

- (1) assume that TMH is true and see how well TMH explains the issue.
- (2) assume that DH is true and see how well DH explains the issue.
- (3) compare (1) and (2).

A good and helpful argument is one where (1) is greater than (2), or (2) is greater than (1). These are the arguments that move the ball forward.

Second, we need to identify the specific versions of both theories. That is, we need a working definition of both TMH and DH.

For TMH, my initial thought it to use the claim that the Torah was written by God, physically written by Moses (with the possible exception of the last few lines of Deuteronomy), is instructions for living, and contains important insights (some explicit, so esoteric and hidden) about all sorts of important things.

For DH, my initial thought is to use Richard Elliot Friedman's book "The Torah With Sources Revealed." This book is scholarly, is recent, is widely available, classifies each verse into one of the sources, and notes its reasons much of the time in footnotes. Of course, other scholars will disagree with Friedman about the particular classifications of particular verses, but I'm not sure that these differences matter for our purposes of comparing the DH with TMH. If the overall theory holds, the fact that some particular verse might actually be P and not J is irrelevant. And if the theory does not hold overall, these debates are beside the point.

Friedman ends his introduction with the following: "Here, rather, is the evidence, for anyone to see, evaluate, acknowledge, or refute." (P. 31.) The book was written with exactly this purpose in mind.

Third, I need to figure out what specifically to look at. The Torah is a big book, with odd features, TMH is a simple theory with complex and extensive commentary, and the DH is itself a complex theory. We can't just point at the text as a whole or a stray verse here or there.

For the DH, Friedman makes a 7 arguments in the introduction to The Torah With Sources Revealed. Each source is largely internally consistent and different from the other sources in the following areas: (1) linguistic patterns (from different historical periods of Hebrew), (2) terminology, (3) content, (4) continuity of the texts, (5) connection with other parts of the Bible, (6) relationships to each other and to history, (7) and convergence of all these. That is, if we look at any particular J story, it will have lots of characteristics of J. And if we look at any particular characteristic of J, we will find it a lot in the J stories but not very much if at all elsewhere.

For TMH, we will look at the various kiruv-type books and arguments out there. These would include Aish HaTorah's Discovery program (my first introduction to some of these issues), the Kuzari argument, etc. At the same time, we will examine any traditional alternatives to DH. I think Rabbi David Weiss Halivni and Rabbi Yitzchak Etshalom are the leading writers here. Any additional recommendation for books and sources would be welcome.

To examine all this critically, I think, takes three separate phases of examining the text.

In Phase 1, we will look at each particular story that DH claims comes from a separate source. If DH is correct, each will show lots of signs of that source, relatively few signs of other sources, and will be continuous with earlier and later parts of that source. If this is part of a joined story, we will see how well the unjoined part of the story stands. And at the same time, we will examine traditional TMH commentary on and explanations for anything anomalous. Little Foxling has started essentially this, although I think he is not going to continue with it. The purpose here is mainly to examine how well each story fits into a particular DH source.

In Phase 2, we will look at each particular characteristic of each source and see how it holds across the Torah as a whole. We will also see if the usage is related to content. And we will see what traditional TMH commentary has to say. (For example, Friedman argues that the phrase "gathered to his people" as a euphemism for death occurs 11 times and all 11 are in P. We will look at these 11 times as well as other words mentioning death and see what all this tells us.) The purpose here is mainly to see how well each characteristic of each source explains the sources as a whole.

In Phase 3, we will look at the TMH arguments. These obviously do not break along the DH lines. Instead, they will each cover a particular issue or fact, and each one needs to be critically examined.

These phases do not have to proceed in order but can be examined simultaneously.

That is my current thinking on the best way to proceed. Any comments, criticisms, or alternative or additional approaches would be appreciated.

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

Following up on my earlier post, there are at least three more implications about the use of Bayes' Theorem, after the 5 listed there.

6. An additional comment about prior probabilities and "assuming away the problem." There is nothing wrong with prior probabilities; we use them all the time. Here's a simple example.

Suppose your good friend was supposed to meet you at 7:00 to see a movie that starts at 7:20. It's 7:15 and he has not shown up. You assume he is late, but then ha-Satan shows up and makes a series of clever argument (isn't that just like him): Your friend is not late, but he really hates you. He is ending your friendship and deliberately making you wait solely to inconvenience you.

This is certainly possible, but your prior probability estimate of that would be quite low. After all, he is your good friend. But now ha-Satan starts piling on the evidence. Your friend has a cellphone; he would certainly call if he were running late. Hmmm. Good point. Your friend has always been very reliable, and thus the statistical odds of him running 15 minutes late when you only have 20 minutes to spare are very small. Hmmm. Good point. Your friend really wanted to see the movie, and in fact you two spoke about it in the late afternoon and specifically discussed both the time and place. He is not likely to have forgotten or gone to another theater. Hmmm. Good point. And so it goes.

Each of these facts is easily explained by the friend-hates-you theory, but not so easily explained by the friend-is-just-late theory. Using Bayes' Theorem, these facts are shifting the probability towards the friend-hates-you theory. But if your estimated prior probability of this theory is microscopically small (say, 1 in a billion --- I'll plug in numbers here just to illustrate), then you might estimate the odds now at 1 in 1 million. You now conclude that it is 1000 times more likely that your friend really hates you, but you still place the odds at something so microscopically small that it is still essentially zero.

That's the way some TMH / DH debates go. (More often on the pro-DH side, but not always.) One person keeps making good points, and the other person keeps offering weak responses but is just not budging. The proponent gets agitated, the opponent seems unfazed, and each side thinks the other is crazy. I think what is happening in those debates is the opponent simply assigns such a high prior probability to his theory, that the net effect of the proponent's arguments is simply to move the probability of that theory from almost zero to a slightly larger almost zero.

7. There's another unresolved issue: what should the prior probability be? There's no good way to answer that question since it depends to one's subjective beliefs before any evidence. For whatever reason, some of us tend to think that the
idea that God wrote the Torah is obviously true and others of us tend to think that the idea that people wrote the Torah is obviously true.

I think each person must decide this issue for his or her self. It might be useful as a heuristic device simply to assume the prior probability is 50%. That is, assume that each theory is equally likely and then go look at the evidence. The advantage of this approach is that avoids biasing the outcome based on initial probabilities. The disadvantage is that no one really estimates this at 50%. All of our prior intuitions is that TMS is either likely or not likely, but not exactly equal to the not-TMH. But this might all be academic. Pick a probability for the sake of the discussion, and one can always revise it later.

8. The evidence can persuade even a harsh skeptic. Go back to the jar examples, and take two really ambiguous jars with the following percentage of yellow, green, blue, and red marbles:

Type 1: 40%, 25%, 20%, 15%
Type 2: 30%, 20%, 15%, 35%

If you draw (say) a yellow marble out, it is just not going to shift the odds that much, regardless of your prior probabilities. Type 1 jars have 40% yellow marbles and Type 2 jars have 30%. So a yellow marble just does not give you much information.

But suppose you randomly draw 1000 marbles (with replacement, for you math geeks out there). And you find that your random sample gives the following probabilities

Sample: 39%, 26%, 21%, 14%

The probability of drawing this from a Type 1 jar is quite high, and the probability of drawing this from a Type 2 jar is quite low. (Someone can crunch the numbers if they can find a standard normal chart with that many standard deviations.) So even if your prior odds were that there was only a 1 in a million chance that you had a Type 1 jar, the evidence here is so compelling that it would be a virtual certainty that you did in fact have a Type 1 jar.

The implication of this is that regardless of whether one initially thinks TMH is highly likely or the DH is highly likely, enough evidence consistent with the other theory and inconsistent with your should persuade you. And this is true even if the evidence is somewhat ambiguous, so long as it fits better with the other theory.

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

There are two competing theories for the origins of the Torah: (1) Moses wrote it under God's guidance or dictation (often called "Torah from Heaven" or "Torah Min Hashamayim" or simply "TMH") and (2) multiple authors well after Moses' time wrote separate parts, and these were later compiled and edited into one document (the "Documentary Hypothesis" or "DH"). There are many arguments on all sides of this issue. (For what its worth, I think the DH is correct, and I will be examining the arguments for and against this in future posts. It is hard to beat the job that Little Foxling has done on his blog, although I will be approaching the problem from a slightly different perspective.)

But now I would like to focus on a logically prior issue: as we gather and consider evidence and arguments for and against each theory, how do we go about deciding which theory is correct? There's a lot of muddled thinking on this issue, and people recklessly throw around terms like "presumptions" and "burden of proof" here.

I think the answer lies in Bayes' Theorem, a well-known idea from probability theory. This theory tells us, in a rigorous way, how new information changes the relative probability of two separate and competing theories. And there are many implications of this theorem for the TMH / DH debate. For example, this theory explains why different people might reasonably reach different conclusions, even though they are looking at the same evidence and arguments.

The math is not that hard, although for these purposes the broader implications of Bayes' theorem are what's really important, not the technical mathematical ideas. After all, none of the TMS/DH claims can be given precise probability values. So if math isn't your "thing", don't worry. Skim the math, read the text, and you'll be fine.

Here's the basic problem Bayes' theorem addresses. Suppose you start with an initial estimate of the probability that a particular theory is true. Then you get new information that makes that theory more likely or less likely to be true. How does that effect your overall probability estimate?

The simplest example (and one used in just about every probability book) involves jars of colored marbles. So here goes. Suppose you have 100 (opaque and identical) jars filled with marbles. There are 50 "Type Y" jars (for "yellow") that have 90 yellow marbles and 10 green marbles. And there are 50 "Type "H" jars that have half-and-half: 50 green marbles and 50 yellow marbles.

Suppose you pick a jar at random. What is the probability you have a Type Y jar? That one shouldn't be too hard: 50%. (If you missed that one, you'll have to stay and clean the erasers.)

Now, here's the good part. You randomly pick one marble from your mystery jar (without looking inside), and it is a yellow marble. Great. 90% of the marbles in Type Y jars are yellow, but only 50% of the marbles in Type H jars are yellow. This new information --- your yellow marble --- is more consistent with a Type Y jar than a Type H jar. It is still possible you have an H jar, but it now seems more likely that you have a Y jar. How much did this new information shift your initial 50% chance of having a Y jar?

OK. Here comes the math. (Feel free to skim this part.) Here's Bayes' Theorem, with the explanation to follow.

P(A|B) = P(B|A) * P(A) / P(B)

P(something) means the probability of that something occurring.

A is the "prior event." In our example, it is "picking a Type Y jar" It is "prior" in the sense of not taking into account the later information.

B is the "posterior event." In our example, it is drawing out one yellow marble.

The vertical line | means "given that".

So this theorem in English says

The probability of prior even A given posterior event B is: the probability of B given A, times the probability of A, divided by the probability of B.

Lets see how this works out with our example.

P(A) is the prior or initial probability of getting a Type Y jar. That's 50% (That one is easy.)

P(B|A) is the probability of drawing out the yellow marble given that we picked a Type Y jar. That's easy too. There are 100 marbles in a Type Y jar, 90 of which are yellow. So it is 90%. Note that P(B|A) is the reverse of what we want to find, P(A|B). And that's where the power of Bayes' theorem comes in. We cannot easily figure out the latter, but we usually can figure out the former. Bayes' theorem tells us how to use the information we have to figure out what we don't have.

P(B) is the overall probability of drawing a yellow marble. Well, there are 10,000 marbles total (100 jars with 100 marbles each). Of those, 4,500 are yellow in Type Y jars (50 jars x 90 per jar), and 2,500 are yellow in Type H jars (50 jars x 50 per jar). So 7,000 of 10,000 marbles are yellow, and so P(B) = 70%.

Now, plugging all this in gives P(A|B) = (.9 * .5) / .7, which equals about 64.29%. Cool. We stated with a 50% chance of a Type Y jar, drew out one yellow marble, and now have a 64% chance of a Type Y jar.

Suppose we replaced the marble, shook the jar, drew a second marble, and it was yellow. The probability of 2 yellow marbles in a Type Y jar is 90% of 90% or 81%. But the probability of 2 yellow marbles in a Type H jar is 50% of 50%, or 25%. If we plug all this in, we get the probability of a Type Y jar given 2 yellow marbles is just over 76%. (I leave the math to the interested reader.)

So as we keep drawing marbles, the odds would continue to shift up or down, depending on whether we drew a yellow or green marble. As we draw lots of marbles, if our sample starts approaching 90% yellow, we become very likely to have picked a Type Y jar. And if our sample starts approaching 50% yellow, we become very likely to have picked a Type H jar.

Let me make one more quantitative observation. Suppose we start with a very unlikely initial probability estimate. To revise our example, suppose there are only 5 Type Y jars and 95 Type H jars. The initial odds are very small (only 5%) that we picked a Type Y jar. But if we keep drawing yellow marbles, those odds will go up dramatically and eventually get close to 100%.

I'll end this post here, and start the qualitative implications in the next post. Please comment in the next post only.

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