Logica Universalis 8 (3-4):447-467 (2014)

Authors
Roy T. Cook
University of Minnesota
Abstract
A number of authors have argued that Peano Arithmetic supplemented with a logical validity predicate is inconsistent in much the same manner as is PA supplemented with an unrestricted truth predicate. In this paper I show that, on the contrary, there is no genuine paradox of logical validity—a completely general logical validity predicate can be coherently added to PA, and the resulting system is consistent. In addition, this observation lead to a number of novel, and important, insights into the nature of logical validity itself
Keywords Validity  paradox  Curry paradox  first-order logic  logical consequence  Alfred Tarski
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DOI 10.1007/s11787-014-0094-4
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References found in this work BETA

Saving Truth From Paradox.Hartry H. Field - 2008 - Oxford, England: Oxford University Press.
Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
The Logic of Provability.George S. Boolos - 1993 - Cambridge and New York: Cambridge University Press.
Deflating Logical Consequence.Lionel Shapiro - 2011 - Philosophical Quarterly 61 (243):320-342.

View all 11 references / Add more references

Citations of this work BETA

Emptying a Paradox of Ground.Jack Woods - 2018 - Journal of Philosophical Logic 47 (4):631-648.
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 17 citations / Add more citations

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