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Eliezer_Yudkowsky comments on Stuff That Makes Stuff Happen - Less Wrong
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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.