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

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Studia Logica 102 (1):185-217 (2014)
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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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10.1007/s11225-013-9471-x

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Author Profiles

Gemma Robles
Universidad de León
José M. Méndez
Universidad de Salamanca

Citations of this work

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Variable-Sharing as Relevance.Shawn Standefer - 2025 - In Andrew Tedder, Shawn Standefer & Igor Sedlar, New Directions in Relevant Logic. Springer.
Blocking the Routes to Triviality with Depth Relevance.Gemma Robles & José M. Méndez - 2014 - Journal of Logic, Language and Information 23 (4):493-526.

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References found in this work

Entailment and relevance.Nuel D. Belnap - 1960 - Journal of Symbolic Logic 25 (2):144-146.
Relevant implication and the case for a weaker logic.Ross T. Brady - 1996 - Journal of Philosophical Logic 25 (2):151 - 183.
Depth relevance of some paraconsistent logics.Ross T. Brady - 1984 - Studia Logica 43 (1-2):63 - 73.
Routes to triviality.Susan Rogerson & Greg Restall - 2004 - Journal of Philosophical Logic 33 (4):421-436.

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