Journal of Philosophical Logic 44 (4):453-471 (2015)

Authors
Heinrich Wansing
Ruhr-Universität Bochum
Graham Priest
CUNY Graduate Center
Abstract
Curry’s paradox is well known. The original version employed a conditional connective, and is not forthcoming if the conditional does not satisfy contraction. A newer version uses a validity predicate, instead of a conditional, and is not forthcoming if validity does not satisfy structural contraction. But there is a variation of the paradox which uses “external validity”. And since external validity contracts, one might expect the appropriate version of the Curry paradox to be inescapable. In this paper we show that this is not the case. We consider two ways of formalising the notion of external validity, and show that in both of these the paradox is not forthcoming without the appropriate forms of contraction
Keywords Curry paradox  Internal validity  External validity  Internal consequence relations  External consequence relations  Contraction  Higher-level sequent calculi
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DOI 10.1007/s10992-014-9336-4
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References found in this work BETA

Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.
Fusion and Confusion.Graham Priest - 2015 - Topoi 34 (1):55-61.
There is No Paradox of Logical Validity.Roy T. Cook - 2014 - Logica Universalis 8 (3-4):447-467.
The Inconsistency of Certain Formal Logic.Haskell B. Curry - 1942 - Journal of Symbolic Logic 7 (3):115-117.

View all 8 references / Add more references

Citations of this work BETA

Faithfulness for Naive Validity.Ulf Hlobil - 2019 - Synthese 196 (11):4759-4774.
The Cut‐Free Approach and the Admissibility‐Curry.Ulf Hlobil - 2018 - Thought: A Journal of Philosophy 7 (1):40-48.

View all 8 citations / Add more citations

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