Circumscribing with sets

摘要

Sets can play an important role in circumscription's ability to deal in a general way with certain aspects of commonsense reasoning. A result of Kueker indicates that sentences that intuitively one would want circumscription to prove are nonetheless not so provable in a formal setting devoid of sets. Furthermore, when sets are introduced, first-order circumscription handles these cases very easily, obviating the need for second-order circumscription. The “Aussonderungs” axiom of ZF set theory plays an intuitive role in this shift back to a first-order language