A Dictionary of Philosophy, Third Edition
. The view that there are important logical theories that do not allow (as classical logic does) that a contradiction has every proposition among its logical consequences. A system containing contradictory propositions is inconsistent, but if it does not contain every proposition, it avoids being trivial.
It is claimed that various scientific and mathematical theories are in fact of this nature, and so can be logically analysed by paraconsistent logics, and also defended as they stand, in that we need not assume that the inconsistencies in them are merely aberrations that must be removed before they can be properly studied. See also DIALETHEISM.
G.Priest, R.Routley and J.Norman (eds), Paraconsistent Logic: Essays on the Inconsistent, Philosophia Verlag, Munich, 1989.
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