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MugaSofer comments on Privileging the Hypothesis - Less Wrong
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The "Truman Show Hypothesis" may violate the Copernican Principle, but it cannot be experimentally disproved.
I am not using this to argue for Many-Worlds; merely that we should care if Many-Worlds is true.
EDIT: A similar analogy would be that the ship turns into pure utilitronium, rather than vanishing. This might be a better analogy for the MWI for you.