I ran across an argument a while back, on Ben Wallis’ blog, against omniscience, which he called “Grim’s Cantorian Argument Against Omniscience“. This argument has been addressed variously, usually with an appeal to a strong doctrine of divine simplicity. However, recently Alexander Pruss posted a provocative thought on his blog about divine beliefs, and I recommend people check that out. Given that the argument on offer against omniscience is really an argument against the possibility of having a set of all true propositions, I find Pruss’ response that God might simply believe in one “Maximally Specific True Proposition”, from which all other propositional truths are derivative/derivable interesting because it suggests a way in which we can characterize logically possible worlds.
Generally, Logically possible worlds have been defined as maximally consistent sets of propositions which together provide an exhaustive description of some world. However, in light of the argument against there ever being any set of all true propositions, perhaps it is appropriate to simply talk about logically possible worlds as maximally specific propositions.