Faithfulness for Naive Validity

Synthese (forthcoming)
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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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First archival date: 2018-02-08
Latest version: 2 (2018-02-08)
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References found in this work BETA
Two Flavors of Curry's Paradox.Beall, Jc & Murzi, Julien
Tolerant, Classical, Strict.Cobreros, Pablo; Egré, Paul; Ripley, David & van Rooij, Robert
Reaching Transparent Truth.Cobreros, Pablo; Égré, Paul; Ripley, David & van Rooij, Robert

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2018-02-07

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