The thread descending from this comment exemplifies a pit that is easy to fall into when reading an informal moral drawn from a precise mathematical result: mistaking the former for the latter, and arguing about the former instead of going to the latter. The whole nugatory discussion would be avoided had people gone back to the original mathematics, which is not deep, and is given in one of the Sequence posts the OP linked to.
This mathematics, which is simple and straightforward, but not a complete triviality, says precisely what is meant by the informal phrase, “Conservation of Expected Evidence”, and provides an immediate answer to questions such as “but making an observation will change your belief, so you can expect your belief to change!”, or “but what about a lottery ticket, you expect that to lose, don’t you?”
There’s no point in basing an argument on secondary sources when the primary source is right there.
The thread descending from this comment exemplifies a pit that is easy to fall into when reading an informal moral drawn from a precise mathematical result: mistaking the former for the latter, and arguing about the former instead of going to the latter. The whole nugatory discussion would be avoided had people gone back to the original mathematics, which is not deep, and is given in one of the Sequence posts the OP linked to.
This mathematics, which is simple and straightforward, but not a complete triviality, says precisely what is meant by the informal phrase, “Conservation of Expected Evidence”, and provides an immediate answer to questions such as “but making an observation will change your belief, so you can expect your belief to change!”, or “but what about a lottery ticket, you expect that to lose, don’t you?”
There’s no point in basing an argument on secondary sources when the primary source is right there.
I think the problem is that people tend to derive incorrect, or at least misleading, informal beliefs from the correct math.