On Priest on Nonmonotonic and Inductive Logic
Thought: A Journal of Philosophy
Graham Priest defends the use of a nonmonotonic logic, LPm, in his analysis of reasoning in the face of true contradictions, such as those arising from the paradoxes of self-reference. In the course of defending this choice of logic in the face of the criticism that this logic is not truth preserving, Priest argued (2012) that requirement is too much to ask: since LPm is a nonmonotonic logic, it necessarily fails to preserve truth. In this paper, I show that this assumption is incorrect, and I
... xplain why nonmonotonic logics can nonetheless be truth preserving. Finally, I diagnose Priest's error, to explain when nonmonotonic logics do indeed fail to preserve truth. # # # Non-classical logics are not classical. Sometimes this fact seems like a feature: paraconsistent logics like Priest's LP reject disjunctive syllogism and ex contradictione quodlibet and so, they give us new and fruitful ways to deal with semantic paradoxes unavailable to proponents of classical logic. However, sometimes this fact seems like a bug: there are times we want to endorse those particular rules of proof, not reject them. Priest's favoured way out of this tension is to adopt a nonmonotonic logic, LPm. According LPm, inference steps such as disjunctive syllogism-from p ∨ q and ¬p to q-may be valid, while becoming invalid in the presence of extra premises: in particular, premises which are inconsistent.