Consistency and Contradiction

Philosophy and Theology 2 (4):327-361 (1988)
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Beginning with an examination of Lukasiewicz’s remarks on the logical status of the law of contradiction, I examine several systems of modal logic in which the law is said to fail. This raises the issue of hypercontradiction and bivalence in the semantics of modal systems, and these are examined in the context of constructing senses for ‘truth’ and ‘meaning’ within systems where the law no Ionger holds. FoIlowing an examination of the work of several later logicians and similar efforts on their part, I conclude that the notion of ‘truth’ is not part or any system of format logic or metalogic.



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