The principle of duality in lo gic and philosophy
Keywords:
duality principle, classical logic, modal logic, intuitionistic logic, dual-intuitionistic logic, modal translationAbstract
The paper examines the specificity of the implementation of the duality principle in some important logical systems. We give an exact definition of the logical duality based on the notions of truth and falsity, which play a central role in the understanding of the subjectmatter of logic. We construct the consequence systems for the classical, modal, intuitionistic and dual-intuitionistic logic, and demonstrate that both classical and modal logics are self-dual, whereas intuitionistic logic needs a special dual-intuitionistic logic for its dualization. We propose a function of a modal translation for the dual-intuitionistic propositions which consists in prefixing the possibility operator to every proposition of the dualintuitionistic logic. We also sketch some prospects of an applicability of the duality principles to analysis of philosophical problems, the problem of the subject-matter of philosophy among them.
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