paraconsistency the property of a logic in which one cannot derive all statements from a contradiction. What is objectionable about contradictions, from the standpoint of classical logic, is not just that they are false but that they imply any statement whatsoever: one who accepts a contradiction is thereby committed to accepting everything. In paraconsistent logics, however, such as relevance logics, contradictions are isolated inferentially and thus rendered relatively harmless. The interest in such logics stems from the fact that people sometimes continue to work in inconsistent theories even after the inconsistency has been exposed, and do so without inferring everything. Whether this phenomenon can be explained satisfactorily by the classical logician or shows instead that the underlying logic of, e.g., science and mathematics is some non-classical paraconsistent logic, is disputed. See also CON- SISTENCY , RELEVANCE LOGI. G.F.S.