Dialetheism and the Laws of Logic

Abstract

AbstractGraham Priest accepts the traditional definition of validity as truth-preservation, but conceptual headaches arise when we try to dialetheically make sense of truth-preservation. Does truth-preservation mean that true premises always lead to true conclusions, or that they never lead to false ones? Problems appear either way. Alan Weir points out that we normally expect valid inferences to preserve falsity in the direction going from conclusions to premises as well as preserving truth in the direction going from premises to conclusions, but it is deeply unclear that dialetheism can satisfy this requirement. Contraposition and Modus Tollens might be invalid if dialetheism is true. When we put this together with more obvious losses such as Disjunctive Syllogism and Reductio Ad Absurdum, it begins to appear that the dialetheist cannot make sense of massive chunks of ordinary reasoning. Thus, “classical recapture,” whereby it is shown that it would still be rational to use the full resources of classical logic to reason about every domain if dialetheism was true, is crucial to making dialetheism plausible. Unfortunately, such recapture is far more difficult than it might appear. An initially promising attempt embodied in Priest’s “Principle R” is shown to fail.KeywordsValidityContrapositionWeirPriestDialetheismReductioTruth-Preservation