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Carinthium comments on Study shows existence of psychic powers. - Less Wrong
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To rip off Steven Kaas for a moment, I wonder if rather than saying "Study shows existence of psychic powers" it might be better to say "Nonexistence of psychic powers shows a study was wrong".
What sort of hypothetical evidence would convince you that psychic powers existed?
http://xkcd.com/298/
I'm not sure I can actually come up with any, because I know how frail human minds can be. My prior that I'm insane is higher than my prior that magic exists, and I can't think of any evidence for the second that isn't at least as strong evidence for the first.
(Here, I am assuming that by psychic powers we're talking about magic, rather than unarticulated intuition, which I believe can exist; I also expect I would adapt to being insane pretty quickly, and would react as if it were reality, but would expect it more likely that I'm gibbering in a mental institution than that I've been transported to Narnia.)