There is a 1:1 mapping between “the set of reals in [0,1]” and “the set of all reals”. So take your uniform distribution on [0,1] and put it through such a mapping… and the result is non-uniform. Which pretty much kills the idea of “uniform ⇔ each element has the same probability as each other”.
There is no such thing as a continuous distribution on a set alone, it has to be on a metric space. Even if you make a metric space out of the set of all possible universes, that doesn’t give you a universal prior, because you have to choose what metric it should be uniform with respect to.
(Can you have a uniform “continuous” distribution without a continuum? The rationals in [0,1]?)
There is a 1:1 mapping between “the set of reals in [0,1]” and “the set of all reals”. So take your uniform distribution on [0,1] and put it through such a mapping… and the result is non-uniform. Which pretty much kills the idea of “uniform ⇔ each element has the same probability as each other”.
There is no such thing as a continuous distribution on a set alone, it has to be on a metric space. Even if you make a metric space out of the set of all possible universes, that doesn’t give you a universal prior, because you have to choose what metric it should be uniform with respect to.
(Can you have a uniform “continuous” distribution without a continuum? The rationals in [0,1]?)