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There is No Paradox of Logical Validity

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A number of authors (including Field in Saving Truth From Paradox. Oxford University Press, Oxford, 2008; Shapiro in Philos Q 61:320–342, 2010; Whittle in Analysis 64:318–326, 2004; Beall and Murzi in J Philos 110:143–165, 2013) have argued that Peano Arithmetic (PA) 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 (classical) system is consistent. In addition, this observation (and the constructions required to make it) lead to a number of novel, and important, insights into the nature of logical validity itself.

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  1. Department of Philosophy, University of Minnesota-Twin Cities, 869 Heller Hall, 271 19th Ave. S., Minneapolis, MN, 55455, USA

    Roy T. Cook

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  1. Roy T. Cook
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Correspondence to Roy T. Cook.

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Cook, R.T. There is No Paradox of Logical Validity. Log. Univers. 8, 447–467 (2014). https://doi.org/10.1007/s11787-014-0094-4

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  • DOI: https://doi.org/10.1007/s11787-014-0094-4

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