Suppose someone holds the following position:
(1) Mormonism is the true religion.
Then he discovers this fact:
(2) Joseph Smith claimed to have translated the Book of Abraham from an Egyptian manuscript, but in reality the Egyptian manuscript was about something completely different.
Now this doesn’t look good. In fact, it looks exactly as though the Book of Abraham is a complete fraud, which seems to imply that position (1) is false. In other words, (2) is strong evidence against (1).
So our protagonist modifies his position like this:
3) Mormonism is the true religion, and Smith interpreted the Egyptian manuscript by divine inspiration, revealing its spiritual sense.
Now he notices something. After the discovery of fact (2), position (3) becomes more probable than it originally was, since part of position (3) is now verified to be definitely true, namely the fact that the book of Abraham is a not a literal translation of the Egyptian manuscript. Thus, the original disturbing fact which seemed to be evidence against his position, is now evidence in favor of his new position! And the new position includes position (1), so there is no need to change a thing!
This reasoning is technically valid, of course, but our protagonist is overlooking a few things.
First of all, (1) is in itself more probable than (3), since (3) requires the truth of (1) and something else in addition.
Second, after the discovery of (2), (1) becomes less probable, likely significantly less probable, than it was before. This fact remains unchanged by the rest of the process.
Third, (3) does indeed become more probable than it originally was, after the discovery of (2). However, (3) was less probable than (1) in the first place, and even after it becomes more probable, it remains less probable than (1) originally was, and it also remains less probable than (1) became after the discovery of (2). This is necessary because (3) is nothing but a particular way that (1) could be true. So by adopting the new position, our protagonist has not benefited by (2) in the way that he believes. Rather, he ends up holding a position that is even less probable than claiming that Mormonism is true, admitting that the Book of Abraham is not a valid translation of the Egyptian manuscript, admitting that this makes his original position regarding Mormonism less probable, and making no other changes.
In other words, the evidence does not change sides.
11 thoughts on “The Evidence Does Not Change Sides”
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.
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). Do you think your scenario could happen in the situation under discussion (Mormonism etc.)? If so, how would you flesh that out with a concrete example?
If it couldn’t happen in the case under discussion, what would be an example of a case in which it could happen, and what would the details of the concrete example be? And if it could not apply to the original situation discussed, why not?
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