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by Sam Eisenstat 1218 days ago | link | parent

Condition 4 in your theorem coincides with Lewis’ account of counterfactuals. Pearl cites Lewis, but he also criticizes him on the ground that the ordering on worlds is too arbitrary. In the language of this post, he is saying that condition 2 arises naturally from the structure of the problem and that condition 4 is derives from the deeper structure corresponding to condition 2.

I also noticed that the function \(f\) and the partial order \(\succ\) can be read as “time of first divergence from the real world” and “first diverges before”, respectively. This makes the theorem a lot more intuitive.



by Alex Appel 135 days ago | link

Yeah, when I went back and patched up the framework of this post to be less logical-omniscence-y, I was able to get \(2\to 3\to 4\to 1\), but 2 is a bit too strong to be proved from 1, because my framing of 2 is just about probability disagreements in general, while 1 requires \(W\) to assign probability 1 to \(\phi\).

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