I believe this argument. One way of thinking about it, that may seem less counter-intuitive, is to imagine that the RH is one of a large group of math proposition each of which (for arguments sake) we give a subjective probability of 50% of being true.
Then if one of the propositions X is selected at random, and we know that X implies 10^500 times more observers. In this situation, we are more in a situation akin to the old fashioned SIA situation; we expect that roughly half the propositions will be true, so standard proability is all we need to state SIA.
But now suppose we find out that X is the RH, and that we don’t get any extra information about the likely truth of the RH. By Bayseian rules, if we wish to shift our proability away from standard SIA (towards, for example, making the large universe less likely), then there must be some mathematical proposition that, if we used it instead of the RH would shift the probability the other way (towards making the large universe more likely). Since all we know about these propositions is that they all have a subjective proability of 50% of being true, making them interchangeable, this cannot be the case.
Take home message: SIA for uncertainty over empirical facts works only iff SIA for uncertainty over logical facts does as well.
I believe this argument. One way of thinking about it, that may seem less counter-intuitive, is to imagine that the RH is one of a large group of math proposition each of which (for arguments sake) we give a subjective probability of 50% of being true.
Then if one of the propositions X is selected at random, and we know that X implies 10^500 times more observers. In this situation, we are more in a situation akin to the old fashioned SIA situation; we expect that roughly half the propositions will be true, so standard proability is all we need to state SIA.
But now suppose we find out that X is the RH, and that we don’t get any extra information about the likely truth of the RH. By Bayseian rules, if we wish to shift our proability away from standard SIA (towards, for example, making the large universe less likely), then there must be some mathematical proposition that, if we used it instead of the RH would shift the probability the other way (towards making the large universe more likely). Since all we know about these propositions is that they all have a subjective proability of 50% of being true, making them interchangeable, this cannot be the case.
Take home message: SIA for uncertainty over empirical facts works only iff SIA for uncertainty over logical facts does as well.