army1987 comments on What Bayesianism taught me - Less Wrong
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I don't think it is. If Zeus really had eaten the homework, I wouldn't expect it to be reported in those terms. Some stories are evidence against their own truth -- if the truth were as the story says, that story would not have been told, or not in that way. (Fictionally, there's a Father Brown story hinging on that.)
And even if it theoretically pointed in the right direction, it is so weak as to be worthless. To say, "ah, but P(A|B)>P(A)!" is not to any practical point. It is like saying that a white wall is evidence for all crows being black. A white wall is also evidence, in that sense, for all crows being magenta, for the moon being made of green cheese, for every sparrow falling being observed by God, and for no sparrow falling being observed by God. Calling this "evidence" is like picking up from the sidewalk, not even pennies, but bottle tops.
What I was just about to say. See also Yvain on self-defeating arguments.
Okay, but...
How so?
Every white wall is a non-sparrow not observed by God, hence evidence for God observing every sparrow's fall. It is also a, um, no, you're right, the second one doesn't work.
How do we know that the wall is not observed by God?
Ah, quite so. God sees all, sparrows and walls alike. Both of those examples are broken.
An omnipotence-omniscience paradox: "God, look away!" - "I can't!"
“There's something a human could do that God couldn't do, namely committing suicide.”
-- someone long ago, IIRC (Google is turning up lots of irrelevant stuff)
And since we usually desire the one thing we cannot have ...
That one's easily solvable, isn't it? God could look away if he wanted to, but chose not to.
If sparrows do not exist, then "every sparrow falling is observed by God" and "no sparrow falling is observed by God" are both true. (And of course, every white wall is a tiny bit of evidence for "sparrows do not exist", although not very good evidence since there are so many other things in the universe that also need to be checked for sparrow-ness.)