There is No Paradox of Logical Validity

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)447-467
Number of pages21
JournalLogica Universalis
Issue number3-4
StatePublished - Dec 6 2014

Bibliographical note

Publisher Copyright:
© 2014, Springer Basel.


  • Primary 03B10
  • Secondary 03A05


Dive into the research topics of 'There is No Paradox of Logical Validity'. Together they form a unique fingerprint.

Cite this