Epistemic entrenchment and arithmetical hierarchy

摘要

If the underlying theory is sufficiently rich (e.g. like first-order arithmetic), then no epistemic entrenchment preorder of sentences is recursively enumerable. Consequently, the set of all defeasible proofs (determined by such a fixed preorder) is not recursively enumerable and hence, a fortiori, nonrecursive. On the other hand there is a satisfactorily rich epistemic entrenchment preorder < such that < itself, the corresponding set of defeasible proofs, and the corresponding relation of defeasible provability are limiting recursive and, consequently, this type of defeasible provability is closely related to provability in experimental logics in the sense of Jeroslow. Relation to the work by Pollock is also discussed.