Surely, this is dealt with by considering the amount of information in the hypothesis? If we consider each hypothesis that can be represented with 1,000 bits of information, there will only be a maximum of 2^1,000 such hypotheses, and if we consider each hypothesis that can be represented with n bits of information, there will only be a maximum of 2^n - and that is before we even start eliminating hypotheses that are inconsistent with what we already know. If we favor hypotheses with less information content, then we end up with a small number of hypotheses that can be taken reasonably seriously, and the remainder being unlikely - and progressively more unlikely as n increases, so that when n is sufficiently large, we can, practically, dismiss any hypotheses.
I agree with most of that, but why favor less information content? Though I may not fully understand the math, this recent post by cousin it seems to be saying that priors should not always depend on Kolmogorov complexity.
And, even if we do decide to favor less information content, how much emphasis should we place on it?
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