Natural deduction and Curry's paradox
Following Fitch, the author presents a natural deduction version of Curry's paradox, a well-known set-theoretic paradox that does not involve negation. She then discusses various restrictions proposed independently by Fitch and Prawitz to prevent the derivation of the paradox. These restrictions are ``global'' in nature, having to do with the general logical structure of the derivation, rather than with its set-theoretic aspects. The restrictions themselves also have some unattractive features. Finally she draws attention to an observation by Neil Tennant that a certain characteristic of Prawitz's derailment of Curry's paradox also applies to other derivations of some other paradoxes (including Russell's, the Liar, and Grelling's). However, the author points out that Tennant's approach seems to be restricted to intuitionistic logic and may not extend to classical and other systems.
scientific article; zbMATH DE number 5145081
scientific article