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Curry’s Paradox, Generalized Modus Ponens Axiom and Depth Relevance

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Abstract

“Weak relevant model structures” (wr-ms) are defined on “weak relevant matrices” by generalizing Brady’s model structure \({\mathcal{M}_{\rm CL}}\) built upon Meyer’s Crystal matrix CL. It is shown how to falsify in any wr-ms the Generalized Modus Ponens axiom and similar schemes used to derive Curry’s Paradox. In the last section of the paper we discuss how to extend this method of falsification to more general schemes that could also be used in deriving Curry’s Paradox.

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Authors and Affiliations

  1. Dpto. de Psicología, Sociología y Filosofía, Universidad de León, Campus de Vegazana, s/n, León, Spain

    Gemma Robles

  2. Universidad de Salamanca, Campus Unamuno, Edificio FES, 37007, Salamanca, Spain

    José M. Méndez

Authors
  1. Gemma Robles
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  2. José M. Méndez
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Correspondence to Gemma Robles.

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Robles, G., Méndez, J.M. Curry’s Paradox, Generalized Modus Ponens Axiom and Depth Relevance. Stud Logica 102, 185–217 (2014). https://doi.org/10.1007/s11225-013-9471-x

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  • DOI: https://doi.org/10.1007/s11225-013-9471-x

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