Negation and Contradiction

The problems of the meaning and function of negation are disentangled from ontological issues with which they have been long entangled. TIle question of the function of negation is the crucial issue separating relevant and paraconsistent logics from classical theories. The function is illuminated by considering the inferential role of contradictions, contradiction being parasitic on negation. Three basic modellings emerge: a cancellation model, which leads towards connexivism, an explosion model, appropriate to classical and intuitionistic theories, and a constraint model, which includes relevant theories. Thes three modellings have been seriously confused in the modern literature: untangling them helps motivate the main themes advanced concerning t radi tional negation and natural negation. Firstly, the dominant traditional view, except around scholastic t irres when the explosion view was in ascendency, has been the cancellation view, so that the mainstream negation of muchof traditional logic is distincti v ly nonclassical. Secondly, the primary negation determinable of natural negation is ·relevant negation. In order to picture relevant negation the traditional idea of negation as otherthanness is progressivel) refined, to nonexclus ive restricted otherthanness. Several pictures result, a reversal picture' a debate model, a record cabinet (or files of the universe) model which help explain relevant negation. Two appendices are attached, one on negation in Hegel and the ~hrxist tradition, the other on Wittgens ein's treatment of negation and contradiction.