NDLI: There is No Paradox of Logical Validity

Content Provider	Springer Nature Link
Author	Cook, Roy T.
Copyright Year	2014
Abstract	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.
Starting Page	447
Ending Page	467
Page Count	21
File Format	PDF
ISSN	16618297
Journal	Logica Universalis
Volume Number	8
Issue Number	3-4
e-ISSN	16618300
Language	English
Publisher	Springer Basel
Publisher Date	2014-01-11
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Validity paradox Curry paradox first-order logic logical consequence Alfred Tarski Classical first-order logic Philosophical and critical Mathematics Computer Science Logic
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Logic

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There is No Paradox of Logical Validity