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selylindi comments on Decision Theories: A Semi-Formal Analysis, Part I - Less Wrong
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This branch of math is outside my training. I'm stumbling over the self-fulfilling prophecies section.
How can these two statements
both be true?
Because in the second example, it's been deduced that (output X)=a. It's like how you can prove anything from a false premise.
I think it might help to say that explicitly.
Good call. Is my edit better?
Yes, though I would say "because you can prove anything from a false premise".
Subtle distinction: it's not unconditionally taking a false axiom and deriving a spurious conclusion, it's proving a conditional by proving the antecedent is false.
I'll see if I can improve the wording.
These articles seem beyond my skillset also, but this may help you:
In math, the sentence "if A then B", is equivalent to "(not A) or B"
So, "if A then B" is considered true if "A" is false, regardless of what B is.