Faithfulness for naive validity

Synthese 196 (11):4759-4774 (2019)
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Abstract

Nontransitive responses to the validity Curry paradox face a dilemma that was recently formulated by Barrio, Rosenblatt and Tajer. It seems that, in the nontransitive logic ST enriched with a validity predicate, either you cannot prove that all derivable metarules preserve validity, or you can prove that instances of Cut that are not admissible in the logic preserve validity. I respond on behalf of the nontransitive approach. The paper argues, first, that we should reject the detachment principle for naive validity. Secondly, I show how to add a validity predicate to ST while avoiding the dilemma.

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Ulf Hlobil
Concordia University

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