Laws of Non-Contradiction, Laws of the Excluded Middle and Logics

“Laws of Non-Contradiction, Laws of the Excluded Middle and Logics,” pages 73–85, G. Priest, JC Beall, B. Armour-Garb, The Law of Non-Contradiction; New Philosophical Essays, Oxford University Press, 2004.

There is widespread agreement that the law of non-contradiction is an important logical principle. There is less agreement on exactly what the law amounts to. This unclarity is brought to light by the emergence of paraconsistent logics in which contradictions are tolerated (in the sense that not everything need follow from a contradiction, and that there are “worlds” in which contradictions are true) but in which the statement ~(A & ~A) (it is not the case that A and not-A) is still provable. This paper attempts to clarify the connection between different readings of the law of non-contradiction, the duality between the law of non-contradiction and the law of the excluded middle, and connections with logical consequence in general.