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Vladimir_Nesov comments on Stupid Questions Open Thread - Less Wrong Discussion
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No. There's also no proof that it's possible to prove that P!=NP, and for the Friendliness problem it's much, much less clear what the problem even means. You aren't entitled to that particular proof, it's not expected to be available until it's not needed anymore. (Many difficult problems get solved or almost solved without a proof of them being solvable appearing in the interim.)
Why is it plausible that Friendliness is provable? Or is it more a matter that the problem is so important that it's worth trying regardless?
There is no clearly defined or motivated problem of "proving Friendliness". We need to understand what goals are, what humane goals are, what process can be used to access their formal definition, and what kinds of things can be done with them how to what end. We need to understand these things well, which (on psychological level) triggers association with mathematical proofs, and will probably actually involve some mathematics suitable to the task. Whether the answers take the form of something describable as "provable Friendliness" seems to me an unclear/unmotivated consideration. Unpacking that label might make it possible to provide a more useful response to the question.