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linkhyrule5 comments on Harry Potter and the Methods of Rationality discussion thread, part 21, chapters 91 & 92 - Less Wrong Discussion
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Excuse 1) The world will end if Lily is nice to her sister (with no source cited).
Excuse 2) A centaur told Lily not to give Petunia the potion (with no explanation of why not).
These are two completely separate assertions.
Furthermore,
Petunia states that Lily came up with a number of other, equally ridiculous excuses, which means those two shouldn't be assigned any special importance in the list.
From what we know of centaurs, they are rare and typically hostile to humans, which makes it highly improbable that Lily had any sort of meaningful conversation with one.
All prophecies we know of are highly cryptic, and there is no reason to believe that centaurs can decode them well enough to identify two specific, highly obscure humans.
Lily already has far better motives not to give Petunia the potion, namely 1) they dislike each other and Lily doesn't want to grant her sister's wish and/or 2) the potion is very dangerous to take and she doesn't want to endanger her sister's life. Prophecies of doom are a much less probable explanation than either.
If Lily heard what she thought was a prophecy of doom, she would be very stupid not to share it with anyone, say Dumbledore. Lily was not stupid, but there is no evidence that she told anyone about such a prophecy.
Conservation of detail. The two excuses mentioned can be assigned greater significance on a meta level.
And an apocalyptic prophecy is much like Pascal's Mugger: the centaur may not be in prophecy mode, so fear-of-embarrassment might keep you from telling Dumbledore, but you'd still rather not take the risk.
"I talked to a centaur and he told me x" is hardly embarrassing. She wouldn't even have to claim to believe it, just say "what do you think of this claim based on your superior experience?" And it's obvious Dumbledore would want to know.
Isn't it?
"Hey, most powerful wizard in the world. I know you're very busy, but a centaur told me that if I give my sister a beauty potion the world will literally end."