David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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There is widespread acknowledgement that the law of non-contradiction is an important logical principle. However, there is less-than-universal 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: From the point of view of proofs, not everything need follow from a contradiction — from the point of view of models, there are “worlds” in which contradictions are true. In this sense, the law of non-contradiction is violated in these logics. However, in many paraconsistent logics, statement (it is not the case that ¢ and ¡£¢ ¤ ¢¦¥ not- ¢ ) is still provable. In this sense, the law of non-contradiction is upheld. This paper attempts to clarify the different readings of the law of non-contradiction, in particular taking cues from the tradition of relevant logics. A further guiding principle will be the natural duality between the law of non-contradiction and rejection on the one hand and the law of the excluded middle and acceptance on the other.
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