Vaniver comments on Don't You Care If It Works? - Part 1 - Less Wrong
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I would not expect it to be possible to derive the observations without additional postulates; I think that it's possible to do it with any of some partially known set of possible postulates, and the hunt is on for the most palatable postulate. At the time that the QM sequence was written, Eliezer was aware of multiple proposed solutions, none of which he found fully satisfying.
For example, consider this new argument whose additional postulate is a specific version of 'locality.' I don't know whether or not Eliezer finds that one satisfying (note that MrMind has a whole list of limitations associated with that argument!).