Biblical Criticism & History Forum - earlywritings.com

to Peter,

The equation is always applicable.

For other problems, certainly, but not for this one.

Think about what happens when you already have N known interpolations. For example, 6 known interpolations. All of them regarding things like son of Abraham, son of Jesse, whatever interpolation that supposedly shows a belief in a HJ. Doesn't affect your estimate of the 7th, a comment of the same type, which similarly supposedly shows a belief in a HJ?

Well, that's unreasonable. Interpolations are not done by scribes by coin flip.

First, you would have to demonstrate you have these N interpolations. Second, if you achieve that, then my ratings of probabilities would need to be changed drastically to very low values. But don't put the plow before the oxen. First things come first.
You need to "prove" a lot of interpolations before you can doubt that my point 7 is not an interpolation.

Cordially, Bernard

Bernard Muller wrote:to Peter,

The equation is always applicable.

For other problems, certainly, but not for this one.

Wrong.

Bernard Muller wrote:First, you would have to demonstrate you have these N interpolations.

Wrong.

Bernard Muller wrote:if you achieve that, then my ratings of probabilities would need to be changed drastically to very low values.

Then the subsequent ones "need to be changed drastically to very low values" (e.g., after the sixth, say, per the example, and less drastically before that), since the probabilities need to be rated based on the condition that we're considering the event space where all the previous ones had failed. For example, after the first one, we're not talking about that 90% of the probability space where things do work the way that you expect them to work -- we're talking about the 10% of the probability space where things didn't work out how you expected them. We're thinking about what's likely, assuming that the unlikely (in general) has already obtained -- specifically, the unlikely thing that the first had failed. That's because you want to compute the intersection, to find out the probability that "all the arguments had failed."

For all of them to fail, the first must fail, the second must fail too (so we want to know with what probability the second fails, when we "know" the first has - i.e. a conditional probability of the second event given the first event), etc. Please review something, anything to get a better understanding here.

Technically, it should be said that "the background information that each interpolation has a chance of 20%" is just not enough information. We want conditional probabilities, after considering the event chosen to be considered first (which has nothing to condition on). After that point, it actually doesn't matter much at all what their unconditional probabilities are. What matters are the conditional probabilities. Having that number is both sufficient and necessary to continue with the calculation.

Here's another way to visualize the second image above:



Where A, B, C, D are the events of the first, second, third, and fourth interpolation, respectively.

(The numbers, obviously, are invented here... but the general idea is a lot stronger than the alternative in the first image...)