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Synthese

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Faithfulness for naive validity

  • Ulf Hlobil
Article
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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.

Keywords

Naive validity Nontransitive logic V-Curry paradox Substructural approaches to paradox 

Notes

Acknowledgements

I am very grateful for invaluable conversations with and/or comments from Jaroslav Peregrin, Robert Brandom, Daniel Kaplan, Shawn Standefer, Ori Beck, David Ripley, Katharina Nieswandt, Stephen Mackereth, Shuhei Shimamura and two anonymous referees.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of PhilosophyConcordia UniversityMontrealCanada
  2. 2.Affiliated faculty at: University of Hradec KrálovéHradec KraloveCzechia

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