This is an imaginary conversation between me and a Bayesian. His answers are in parenthesis. Do you find this line of argument convincing?
---- Consider all possible worlds consistent with your memories and current experiences. In other words, all possible worlds that contain at least one observer with memories and current experiences exactly identical to yours. Are there more than one such world? (yes) Is every one of these worlds isomorphic to some mathematical structure? (How do you define "mathematical structure"?) A set class. (then yes) What criteria would you use to decide which of these possible worlds is actual, given that they are all consistent with your memories and current experiences? (more observations, experiments) Ok, but after every new observation or experiment, there will still be more than one possible world that is consistent with the new emperical result, right? (yes) So then what? (apply Bayes's rule) Where does the prior come from? (???) Do you assign a non-zero prior to the class of all sets being the actual world? (yes) Pragmatically, how does that differ from assigning a prior of 1 for the class of all sets? (What do you mean by "pragmatically"?) I mean are there any circumstances in which you'd act differently if you assigned a prior of 1 instead? (no) So why not just assume that the actual world is the class of all sets? (My principles of reasoning do not allow me to do so.) If you go back and look at how those principles of reasoning were derived or justified, it was on the basis of simplicity and avoiding absurd actions ("absurd" being defined by intuition or common sense). The assumption that the actual world is the class of all sets is equally justified on the basis of avoiding absurd actions and is simpler than having a prior over possible worlds, so why not? (...)