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January 22, 2007
Working with Probabilities not the Possibilities
What follows is a short reflection on methodology. A post I read over the weekend prompted this reflection but I want to generalize it to some extent. Philosophers and mathematicians have written books on this subject, so please treat this note as my own personal snap shot of the issue.
I worry that the "possible" too easily gets confused with the "probable." Many of us fall into this confusion. I am guiltier of it than I'd like to admit. Claiming that something is "possible" particularly when it aligns with one's own ideas avoids an important question. Is the merely possible probable? When we are working with highly lacunose evidence, as we always are when studying the ancient world (and most other things), claiming that something is possible, or even "eminently possible," says no more than "I agree" with whatever proposition is under consideration. But the merely possible often has the appearance of some kind of argument in favor of that position. Assertions of the possible also appear in camouflage. This occurs when the writer or speaker presents his or her position without reference to other positions and without any comment on the probability that they are correct. Of course saying that something is possible translates in to saying that its probability is not zero but it says nothing beyond that.
But evaluating a probability of the truth of any hypothesis is difficult. It involves "weighting" the evidence or, if we lack expertise, looking to someone we trust to do it for us. In considerations where real statistical analysis in impossible, it also involves a large subjective element that we must none-the-less be prepared to defend on the evidence. Often conflicting hypotheses have nearly equal probabilities. When there are only two or three of them, we may have to "pay our money and take our chances" or make sure that any conclusions we draw beyond these conflicting hypotheses can accommodate them all. Either way, it is incumbent upon us to state clearly how and why we judge the probabilities of any hypothesis and the probabilistic consequences of building on it.
When there are many conflicting hypotheses each one having a relatively low probability of being correct or when the probability of the most compelling hypothesis is still extremely low, we are faced with a somewhat different problem. I feel that the various competing hypotheses regarding the origins of Israelite culture in Palestine fall into this category. (Not everyone will agree with me.) That doesn't mean that there wasn't a fact or facts of the matter. It only means that we can have little confidence in our understanding whatever that may have been. Again, if we choose one hypothesis to the exclusion of the others we must be very clear why we are doing so and be properly tentative about our conclusions. My own inclination is to side with the hypothesis that provides the riches mix of predictions as to what scholars may discover in the future. But when one uses this approach in one's analytical scheme one must be prepared to take up some other hypothesis when and if disconfirming evidence discovered.
For those of us seeking certainty, what I am suggesting here may seem a methodology of despair and frustration. But for those who are more interested in gleaning whatever understanding the evidence has to offer I think it the only route open.
There is a very high probability that this post is correct. 
Posted by Duane Smith at January 22, 2007 1:43 PM | Read more on Odds and Ends |
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