Tuesday, February 20, 2007

More on Daniel

I thought I would follow-up on a couple of things related to my previous post, On Daniel, but to do so, I want to back up a little bit and consider very briefly the subject of miracles. David Hume, an 18th century philosopher, wrote about the subject of miracles and one of his arguments is relevant here. He argues that in order for us to accept someone's testimony about the occurrence of a miracle (a highly improbable event), all other possible explanations for that testimony (including human fallibility and deceit) would need to be even less probable. That is, even if a miracle did occur, it would be nearly impossible to have sufficient reasons to believe that it occurred.

This argument, and others that Hume presented, are not uncontroversial, not least because they appear in some cases to beg the question. My goal here is not to dive into that mess, but simply to introduce the idea that when we are confronted with testimony of a miraculous or supernatural event, we ought to have very good reasons for finding that testimony reliable before drawing any conclusions from the occurrence of the event itself. If the testimony to an improbable event is questionable, we ought not rely on that testimony to draw important conclusions.

Now, as I mentioned in my introduction to Daniel, the prophecies recorded in Daniel are often used as evidence for the inspiration of the Bible and the truth that it therefore contains. Relating this back to the point of the previous paragraph, the prophecies are said to be supernatural in origin, and we have a conclusion being drawn (or at least supported) by the supposed reality of those supernatural events. This motivates the question, then, whether we really have good reasons for finding the testimony sufficiently reliable to justify the conclusion that the prophecies were inspired.

An important point to keep in mind is that we are not talking about absolute proof one way or the other. It is not the case that we can prove with 100% confidence either that the Daniel was written about 630 BCE and contained actual prophecies, nor is it the case that we can prove with 100% confidence that Daniel was written about 165 BCE and contained only successful retrodictions (and failed prophecies). Rather, we are looking for a conclusion best supported by the evidence available to us, and the degree of certainty that we can reach will restrict the certainty with which we can make further conclusions. If we could be 99% confident (whatever that means) that Daniel was written in 165 BCE, then despite the 1% chance that Daniel is authentic, we would be unjustified in relying on its authenticity to draw further conclusions. According to Hume's argument, we would need to be nearly 100% certain that Daniel is authentic before accepting its miraculous accounts as true. Rather than quibbling about how close to 100% we need to get, let us use a very generous threshhold of 51% certainty, that is, barely more likely than not.

But how do we establish, or calculate, the degree of certainty afforded by the evidence? One way is to use Bayesian inference, which involves assigning probabilities to various alternative hypotheses with or without each piece of evidence. In some situations the probabilities involved can be determined with a fair degree of precision; in other situations, assignment of probabilities is more problematic. I will not try to assign probabilities related to the hypotheses and evidence concerning the authenticity of Daniel. Instead, I will only point out that, qualitatively, a piece of evidence E makes a hypothesis H0 more certain if the probability of E given H0 is higher than the probability of E over all possible hypotheses Hi.

(The probability of a hypothesis being true, independent of any evidence, is called its prior probability. Hume's argument can be understood in terms of Bayesian inference by assigning low prior probabilities to miraculous explanations, and higher prior probabilities to non-miraculous explanations.)

Suppose, for example, that we observe a sequence of coin flips, but we do not know if the coin is fair or if it is two-headed. So long as the result of each successive coin-flip is heads, the evidence grows stronger and stronger that the coin is two-headed, since the probability of (say) ten heads in a row is far higher under the hypothesis that the coin is two-headed compared to the hypothesis that the coin is fair. We can never be absolutely certain that the coin is not fair so long as the flips continue to result in heads. However, as soon as tails is observed, the evidence for a two-headed coin drops to zero since the probability of a tails occurring under the two-headed hypothesis is zero. In other words (and in line with our intuition), since the probability of a long string of heads is high for a two-headed coin and low for a fair coin, the observation of a long string of heads is evidence for a two-headed coin.

Now (without bothering to assign precise probabilities) we can look at how the various pieces of evidence contribute to the conclusion that Daniel was written about 165 BCE. Let's call that hypothesis H165 and the competing hypothesis H630. (And we will pretend that these are the only two hypotheses.)

Consider the point concerning Daniel's description of Darius the Mede. Under H165, the author of Daniel was mistaken about the identity of the king who conquered Babylon. You can immediately see how it might be difficult to assign actual probabilities. What is the probability that an unknown author would make a mistake about events that occurred almost 400 years previously? It would depend on the background and resources available to that person. The value would certainly be greater than zero and less than one but it seems folly to attempt to assign a value with any precision. On the other hand, we may still be able to make a meaningful comparison with the probabilities associated with other hypotheses.

Under H630 there are (at least) three sub-hypothesis alternatives. First, Daniel may have simply been mistaken in what he wrote about Darius the Mede. He was incorrect about the identity and nationality of this ruler. Since (under this hypothesis) Daniel is supposed to have been intimately acquainted with the rulers of Babylon, the probability of his making this kind of mistake must be very nearly zero. Second, perhaps it really was an otherwise-unknown Darius the Mede that conquered Babylon and all of the other sources that indicate otherwise are incorrect. An evaluation of this possibility requires information about the nature and volume of contrary sources. The third possibility is a mixture of the first two with an additional twist: that there really was a Darius the Mede involved in conquering and ruling Babylon that somehow was never mentioned in the other records available to us, and that either Daniel was mistaken about the scope of his role or that we have misinterpreted the text as it describes that role.

In both of the last two cases we are faced with the possibility that there was an actual person of some importance who was Darius the Mede. No mention of this person has been found in contemporaneous Babylonian records or in other comparably ancient accounts. Are we justified in assigning a very low probability to any hypothesis that requires the existence of such an important yet unknown person?

If we stated that based on the lack of evidence of such a person that he (probably) did not exist, a critic might accuse us of an "argument from silence". "Absence of evidence is not evidence of absence." Is this criticism valid?

There are certainly cases where an argument from silence is fallacious. Just as certainly, there are cases where it is not. If I stated that there was an elephant in my living room, and when you looked, you could not see one, you would hardly give me any credit for saying "Absence of evidence is not evidence of absence" and continuing to believe that there was an elephant in my living room. On the other hand, if I stated there was an invisible, incorporeal elephant in my living room, then the lack of visual and tactile evidence would not be evidence against my claim. (Of course, it is hardly evidence for my claim either.) How can lack of evidence be conclusive in one case and not the other?

We can frame our answer to this question by going back to Bayesian inference. The probability we would assign to the piece of evidence "no elephant is visible in my living room" given the hypothesis that there is an elephant in my living room is very low compared to the hypothesis that there is no elephant, so the lack of evidence strongly confirms the no-elephant hypothesis and disconfirms the elephant hypothesis. However, the "no elephant is visible in my living room" evidence is equally probably under the invisible-elephant and no-invisible-elephant hypotheses, so that this evidence fails to provide suppport for either. To put it another way, we do not expect visual evidence for an invisible entity, so the lack of such evidence is not meaningful.

In a similar fashion we can address the second and third sub-hypotheses concerning Darius the Mede and the lack of evidence for his existence. If we have reason to expect that we would have found such evidence had he actually existed, then the lack of such evidence is meaningful. Not conclusive, but meaningful. Since we do have evidence for the identities of both the Babylonian kings as well as their actual conqueror (Cyrus the Persian), and since this evidence has no temporal gaps where another king might fit in, the lack of evidence for the existence of Darius the Mede as ruler of the empire that conquered Babylon is meaningful. Further, since we also have evidence regarding names of other officials of the empire, including the name and nationality of the governor of Babylon under Cyrus, the lack of evidence for someone named Darius the Mede in such a capacity is meaningful. So, these sub-hypotheses are not certainly false, but they are probably false.

To take another example, consider the facts that the earliest manuscripts of Daniel (from the Dead Sea Scrolls) come from late in the second century. Is this evidence of late authorship? This, in a sense, is another argument from lack of evidence. The late manuscript dates (compared to 630 BCE) would only be strong evidence for later authorship if we had reason to expect to find earlier manuscripts. In this case, the oldest manuscripts we have of any Old Testament book (so far as I know) are less than one hundred years older than Daniel manuscripts, so this is a case case where the lack of evidence is not particularly meaningful. On the other hand, like the coin-flipping example above, a single contradictory result would have been a tremendous blow to the case for late authorship. Also, beyond there being no earlier manuscripts for Daniel, there are no references to Daniel from earlier sources, while such references do exist for other books, and that does have some evidentiary value.

(I should note that the Dead Sea Scrolls contain fragments from all of the Old Testament books except Esther and Nehemiah. If it were the case that all of the other books were represented in manuscript fragments from the earliest part of the second century BCE, the later dates of the Daniel fragments would be more significant. However, I have not found any indication that this is the case.)

As a final example, consider my treatment of Josephus' account of Daniel being shown to Alexander the Great. Under H630 this could be true and if so it is not particularly improbable that Josephus would have reported it. Under H165, this event could only be a legend (or perhaps an outright lie) that was incorrectly reported as fact by Josephus. Assuming H165, is this improbable? No. Josephus was not himself witness to the events; they occurred nearly 400 years before he reported them. The story could have developed as a legend. Josephus had a fairly obvious apologetic purpose in writing his history; he has a recognizable bias that attempts to present the Jews and their religion in a positive light to the Romans. Further, he represents other demonstrably incorrect statements as facts. So under both H630 and H165, it is not improbable that Josephus would have included the account of Daniel being shown to Alexander the Great, which means that these statements cannot be taken as strong evidence in favor of H630. This is not an outright rejection of Josephus. We might even conclude that, as an individual piece of evidence, Jospephus' account provides more evidentiary value to H630 than to H165. But it cannot provide significantly stronger support to H630 than to H165, and it is not our only piece of evidence. The weight of the larger ensemble of evidence, most scholars conclude, is for H165.

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