After writing this I realize that there is a much simpler prior on finite sets S of consistent statements: simply have a prior over all sets of statements, and keep only the consistent ones. If your language is chosen such that it contains X if and only if it also contains ¬X, then this is equivalent to choosing a truth value for each basic statement, and a uniform prior over these valuations would work fine.
The key here is that you are using finite S. What do you do if S is infinite? More concretely, is your schema convergent if you grow your finite S by adding more and more statements? I believe we touch on such worries in the writeup.
After writing this I realize that there is a much simpler prior on finite sets S of consistent statements: simply have a prior over all sets of statements, and keep only the consistent ones. If your language is chosen such that it contains X if and only if it also contains ¬X, then this is equivalent to choosing a truth value for each basic statement, and a uniform prior over these valuations would work fine.
The key here is that you are using finite S. What do you do if S is infinite? More concretely, is your schema convergent if you grow your finite S by adding more and more statements? I believe we touch on such worries in the writeup.