Does probablistic reasoning change how we answer these questions?
Edwin Jaynes discusses “lattice” theories of probability where propositions are not universally comparable in appendix A of Probability Theory: The Logic of Science. Following Jaynes’s account, probability theory would correspond to a uniformly dense lattice, whereas a lattice with very sparse structure and a few dense regions would correspond to compartmentalized beliefs.
Edwin Jaynes discusses “lattice” theories of probability where propositions are not universally comparable in appendix A of Probability Theory: The Logic of Science. Following Jaynes’s account, probability theory would correspond to a uniformly dense lattice, whereas a lattice with very sparse structure and a few dense regions would correspond to compartmentalized beliefs.