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Variations on a Theme of Curry

After an introduction to set the stage (§1), we consider some variations on the reasoning behind Curry’s Paradox arising against the background of classical propositional logic (§2) and of BCI logic and one of its extensions (§3), in the latter case treating the “paradoxicality” as a matter of nonconservative extension rather than outright inconsistency. A question about the relation of this extension and a differently described (though possibly identical) logic intermediate between BCI and BCK is raised in a final section (§4), which closes with a handful of questions left unanswered by our discussion.