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Qiaochu_Yuan comments on Causal Universes - Less Wrong
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Point.
If I lived in such a universe, then it seems like I could potentially entertain uncountably many disjoint hypotheses about something, all of which I could potentially write down and potentially distinguish from one another. But I wouldn't be able to assign more than countably many of them nonzero probability (because otherwise they couldn't add to 1) as long as I stuck to real numbers. So it seems like I would have to revisit that particular hypothesis in Cox's theorem...