I always thought it was based on definitions. For example, the hypothetical value you gave for the fine structure constant is definable, but not computable.
I don’t see any reason it would have to be computable unless it was actually being computed, which would mean that it’s emergent behavior and not actually part of the laws of physics.
I also don’t see much of a problem with uncountable priors, so long as you have some sort of probability density. For example, you could have an indeterministic universe that lasts forever. Once you get everything except the random numbers, that still leaves you with uncountable universes, but you could still use and update priors with little difficulty.
I always thought it was based on definitions. For example, the hypothetical value you gave for the fine structure constant is definable, but not computable.
I don’t see any reason it would have to be computable unless it was actually being computed, which would mean that it’s emergent behavior and not actually part of the laws of physics.
I also don’t see much of a problem with uncountable priors, so long as you have some sort of probability density. For example, you could have an indeterministic universe that lasts forever. Once you get everything except the random numbers, that still leaves you with uncountable universes, but you could still use and update priors with little difficulty.