Eugine_Nier comments on Causal Universes - Less Wrong

60 Post author: Eliezer_Yudkowsky 29 November 2012 04:08AM

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Comment author: Eugine_Nier 29 November 2012 05:56:35AM 3 points [-]

If you ever plan on talking about your hypothesis, you need to be able to describe it in a language with a finite alphabet (such as English or a programming language). There are only countably many things you can say in a language with a finite alphabet, so there are only countably many hypotheses you can even talk about (unambiguously).

Only if you live in a universe where you're limited to writing finitely many symbols in finite space and time.

Comment author: Qiaochu_Yuan 29 November 2012 06:25:26AM 3 points [-]

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...

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