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

Ulf Hlobil
Concordia University
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.
Keywords naive validity  v-Curry paradox  nontransitive logic  substructural approaches to paradox  Curry's paradox
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DOI 10.1007/s11229-018-1687-x
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References found in this work BETA

Paradoxes and Failures of Cut.David Ripley - 2013 - Australasian Journal of Philosophy 91 (1):139 - 164.
Tolerant, Classical, Strict.Pablo Cobreros, Paul Egré, David Ripley & Robert van Rooij - 2012 - Journal of Philosophical Logic 41 (2):347-385.
Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.

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Citations of this work BETA

The Cut‐Free Approach and the Admissibility‐Curry.Ulf Hlobil - 2018 - Thought: A Journal of Philosophy 7 (1):40-48.
Expressing Validity: Towards a Self-Sufficient Inferentialism.Ulf Hlobil - 2020 - In Martin Blicha & Igor Sedlár (eds.), The Logica Yearbook 2019. London: College Publications. pp. 67-82.

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