There’s some interesting research using “exotic” logical systems where unrestricted comprehension can be done consistently (this thesis includes a survey as well as some interesting remarks about how this relates to computability). This can only happen at the expense of things typically taken for granted in logic, of course. Still, it might be a better solution for reasoning about self-reference than the classical set theory system.
There’s some interesting research using “exotic” logical systems where unrestricted comprehension can be done consistently (this thesis includes a survey as well as some interesting remarks about how this relates to computability). This can only happen at the expense of things typically taken for granted in logic, of course. Still, it might be a better solution for reasoning about self-reference than the classical set theory system.