Open Access
2017 Inferentialism and Quantification
Owen Griffiths
Notre Dame J. Formal Logic 58(1): 107-113 (2017). DOI: 10.1215/00294527-3768059


Logical inferentialists contend that the meanings of the logical constants are given by their inference rules. Not just any rules are acceptable, however: inferentialists should demand that inference rules must reflect reasoning in natural language. By this standard, I argue, the inferentialist treatment of quantification fails. In particular, the inference rules for the universal quantifier contain free variables, which find no answer in natural language. I consider the most plausible natural language correlate to free variables—the use of variables in the language of informal mathematics—and argue that it lends inferentialism no support.


Download Citation

Owen Griffiths. "Inferentialism and Quantification." Notre Dame J. Formal Logic 58 (1) 107 - 113, 2017.


Received: 23 September 2013; Accepted: 24 May 2014; Published: 2017
First available in Project Euclid: 25 November 2016

zbMATH: 06686420
MathSciNet: MR3595344
Digital Object Identifier: 10.1215/00294527-3768059

Primary: 03B10 , 03B35 , 03B65

Keywords: inferentialism , logical consequence , logical constants , proof theory , quantifiers

Rights: Copyright © 2017 University of Notre Dame

Vol.58 • No. 1 • 2017
Back to Top