Negation, duality and opacity

Peter Simons


Abstract I argue, along lines first explored by Wittgenstein in the Tractatus and elaborated by Peter Geach, (1) that the logical notion of negation may be illuminated by exploiting the notion of a toggle; (2) that the toggle nature of negation may best be appreciated by studying the logical notion of duality; (3) that apparent obstacles to the application of duality due to semantic opacity in intentional contexts may be overcome, and (4) that the result illuminates the connection between duality and the semantics for relevant logics.

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