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DanArmak comments on Harry Potter and the Methods of Rationality discussion thread, part 5 - Less Wrong
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It's still about consequences, just not causal consequences. It might be that saving the murderer has an acausal consequence of leading to more murders in the past. This should of course be taken into account, and is harder to guarantee.
If you buy the acausal "reality is not turing-computable" view of the HPMOR universe, then none of our usual reasoning methods work all that well. I'm surprised Harry hasn't been making a bigger deal of this fact.