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Eliezer_Yudkowsky comments on Stuff That Makes Stuff Happen - Less Wrong
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Yes. An argument similar to this should still be in the other-edited version of my unfinished TDT paper, involving a calculator on Venus and a calculator on Mars, the point being that if you're not logically omniscient then you need to factor out logical uncertainty for the Markov property to hold over your causal graphs, because physically speaking, all common causes should've been screened off by observing the calculators' initial physical states on Earth. Of course, it doesn't follow that we have to factor out logical uncertainty as a causal node that works like every other causal node, but we've got to factor it out somehow.
My point is more general than this. Namely, that a calculator on Earth and a calculator made by aliens in the Andromeda galaxy would correspond despite humans and the Andromedeans never having had any contact.
Is there some reason not to treat logical stuff as normal causal nodes? Does that cause us actual trouble, or is it just a bit confusing sometimes?
In causal models, we can have A -> B, E -> A, E -> ~B. Logical uncertainty does not seem offhand to have the same structure as causal uncertainty.
You seem to be confusing the causal arrow with the logical arrow. As endoself points out here proofs logically imply their theorems, but a theorem causes its proof.