Our Mormon protagonist, still shaken by his discovery about the book of Abraham, now discovers another fact:

(A) Although Joseph Smith claimed to translate the Book of Mormon from ancient golden plates, there are many passages that evidently borrow from the King James Bible in particular.

Our protagonist considers this for a while and then thinks, (B) “God is just more tolerant of this sort of thing than I realized…”

On my earlier post, Michael Bolin commented:

While this is technically correct, it is worth noting that something akin to the evidence changing sides does happen, due to the practical difficulty with assigning probabilities. Namely, realizing that some fact is true, which in itself lowers the probability of the original hypothesis, may cause one to assign different values to the probability of a bunch of other facts given the hypothesis, such that the net effect after taking those other facts into account is to make the hypothesis more likely than it would have been if one had taken those other facts into account without the original observation.

I responded at the time:

It’s not clear to me what you are saying in practice, and seems to me that such a thing cannot happen without a violation of the laws of probability (this does not necessarily mean it cannot be reasonable, if the meaning is that you realize that your prior probability distribution was simply mistaken in the first place).

This is in fact what is happening when our protagonist concludes that God is more tolerant than he supposed. Fact (A) is evidence against the truth of Mormonism. But when this fact is considered together with the original fact about the book of Abraham, our protagonist concludes that “God is tolerant about false claims about the origin of his revealed texts” is more probable given the truth of Mormonism than he originally supposed. This is a change in his prior probability distribution, and it weakens the evidence against Mormonism found in the two claims about the Book of Abraham and about the Book of Mormon.

If someone in fact adjusted his probability of the truth of Mormonism based on the fact about the Book of Abraham, then discovered (A) and adjusted his probability of (B) by changing his prior, then the probability of Mormonism being true might indeed become somewhat higher than it was simply after the discovery about the book of Abraham.

However, several things should be noted concerning this:

(1) In practice, people have a very hard time admitting that there is any evidence at all against their position. Now if someone believes that the Book of Abraham was in fact translated from an ancient Egyptian manuscript, he would probably realize (if he thought about it), that if this turns out to be false, it would be evidence against Mormonism. Consequently, if he thinks that Mormonism is true, he likely sets a prior where it is nearly impossible for Smith’s claim about the book of Abraham to be false. In other words, he more or less thinks that if the Book of Abraham was not translated from the Egyptian manuscript, Mormonism would be false. But when he realizes that the Book of Abraham was not translated from the manuscript, he does not conclude that Mormonism is false, but rather tries to make the evidence change sides. So in effect he already adjusts his prior, and in fact in an inappropriate way, because even if his original prior was excessively against the possibility of the fact about the Book of Abraham, that fact is objectively evidence against Mormonism, not in favor of it. And when he discovers fact (A), this too is evidence against Mormonism, and he should adjust his probability in this direction, and not in the opposite direction.

(2) If someone actually adjusted his probabilities in the appropriate way after the discovery of the first fact about the Book of Abraham, the discovery of (A) and the conclusion (B) could somewhat increase the probability of the truth of Mormonism over what he supposed it was after the original discovery about the Book of Abraham. However, according to the new prior, both the fact about the Book of Abraham and the fact (A) would still constitute evidence against the truth of Mormonism, and thus the probability of Mormonism would remain less than it would be with the new prior but without the facts concerning the origin of the texts.

(3) Similarly, there is little reason to suppose that the final probability of Mormonism would be greater than the original probability before the change in the prior. Rather, you would have something like this:

1. Original probability of Mormonism: 95%.
2. Probability after adjusting for discovery about the book of Abraham: 25%.
3. Probability after adjusting for fact (A): 10%
4. Probability after adjusting the prior with conclusion (B): 75%.

Of course these are randomly invented numbers, and in practice a real person does not adjust this much, and his original probability is likely even higher than 95%. Nonetheless it is an illustration of what is likely to happen in terms of the evidence. Even after adjusting the prior, the facts about the origins of the texts simply remain evidence against Mormonism, not evidence for it, and consequently the final probability remains less than the original probability.

The evidence still does not change sides.