# jsteinhardt comments on Non-trivial probability distributions for priors and Occam's razor - Less Wrong

2 11 January 2011 03:59AM

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Comment author: 13 January 2011 04:58:27AM 1 point [-]

You don't need finite, only countable. Assuming that our conception of the universe is approximately correct, we are only capable of generating a countable set of hypotheses.

Comment author: 13 January 2011 12:42:20PM 0 points [-]

Huh? There are only countably many statements in any string-based language, so this includes decidedly non-Occamian scenarios like every statement being true, or every statement being true with the same probability.

Comment author: 14 January 2011 06:34:26AM 0 points [-]

I'm confused. What is the countable set of hypotheses you are considering? My claim is merely that if you have hypotheses H1, H2, ..., then p(Hi) > 1/n for at most n-1 values of i. This can be thought of as a weak form of Occam's razor.

In what sense is "every statement being true" a choice of a countable set of hypotheses?

I think maybe the issue is that we are using hypothesis in a different sense. In my case a hypothesis is a complete model of the world, so it is not possible for multiple hypotheses to be true. You can marginalize out / observe a bunch of variables to talk about a subset of the world, but your hypotheses should still be mutually exclusive.