Paradoxes: A Natural Deduction Approach

The chapter introduces the Prawitz-Tennant analysis of paradoxes, according to which paradoxes are derivations of a contradiction which cannot be brought into normal form, due to “loops” arising in the process of reduction. After presenting Prawitz’ original formulation of Russell’s paradox, we introduce a simplified presentation of it, and then discuss the relevance of the difference between intuitionistic and classical logic and of structural properties of derivability for the Prawitz-Tennant analysis.