The inapplicability of (selected) paraconsistent logics

Abstract

In some cases one is provided with inconsistent information and has to reason about various consistent scenarios contained within that information. Our goal is to argue that filtered paraconsistent logics are not the right tool to handle such cases and that the problems generalise to a large class of paraconsistent logics. A wide class of paraconsistent (inconsistency-tolerant) logics is obtained by filtration: adding conditions to the classical consequence operation (for instance, is a weak Rescher–Manor consequence of just in case follows classically from at least one maximally consistent subset of ). We start by surveying the most promising candidates and comparing their strengths. Then we discuss the mainstream views on how non-classical logics should be chosen for an application and argue that none of these allows us to choose any of the filtered logics for action-guiding reasoning with inconsistent information, because such reasoning has to start with the selection of possible scenarios – and such a process does not correspond to any of the mathematical models offered by filtered paraconsistent logics. Finally, we criticise the recent attempt to defend explorative hypothetical reasoning by means of weak Rescher–Manor consequence operation in Meheus, Straßer, and Verdée (2014).