, Volume 42, Issue 1, pp 25-48
Date: 03 Sep 2011

Higher-Order Sorites Paradox

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The naive theory of vagueness holds that the vagueness of an expression consists in its failure to draw a sharp boundary between positive and negative cases. The naive theory is contrasted with the nowadays dominant approach to vagueness, holding that the vagueness of an expression consists in its presenting borderline cases of application. The two approaches are briefly compared in their respective explanations of a paramount phenomenon of vagueness: our ignorance of any sharp boundary between positive and negative cases. These explanations clearly do not provide any ground for choosing the dominant approach against the naive theory. The decisive advantage of the former over the latter is rather supposed to consist in its immunity to any form of sorites paradox. But another paramount phenomenon of vagueness is higher-order vagueness: the expressions (such as ‘borderline’ and ‘definitely’) introduced in order to express in the object language the vagueness of the object language are themselves vague. Two highly plausible claims about higher-order vagueness are articulated and defended: the existence of “definitely ω ” positive and negative cases and the “radical” character of higher-order vagueness itself. Using very weak logical principles concerning vague expressions and the ‘definitely’-operator, it is then shown that, in the presence of higher-order vagueness as just described, the dominant approach is subject to higher-order sorites paradoxes analogous to the original ones besetting the naive theory, and therefore that, against the communis opinio, it does not fare substantially better with respect to immunity to any form of sorites paradox.

This paper has long been in the works (an early reference to it can be found already in [19, p. 180], footnote 10). Earlier versions of the paper’s material have been presented in 2004 at the Arché Vagueness Seminar (University of St Andrews); in 2005 at the 9th NPAPC (University of York), where David Efird gave a valuable response; in 2006 at a Vagueness Workshop (University of Freibourg, in Ovronnaz), where Reto Givel gave another valuable response, and at the 6th GAP Conference on Philosophy: Foundations and Applications (Berlin Free University); in 2007 at the 1st UCLA/USC Graduate Student Conference in Philosophy (UCLA), where Gabe Rabin gave yet another valuable response. I would like to thank all these audiences for very stimulating comments and discussions. Special thanks go to Hartry Field, Mario Gómez-Torrente, Patrick Greenough, Richard Heck, Dan López de Sa, Sebastiano Moruzzi, Peter Pagin, Walter Pedriali, Steve Read, Robbie Williams, Tim Williamson, Crispin Wright and to several anonymous referees. In writing this paper, I have benefitted, at different stages, from an AHRC Doctoral Award, a RIP Jacobsen Fellowship, an AHRC Postdoctoral Research Fellowship and a UNAM Postdoctoral Research Fellowship, as well as from partial funds from the project FFI2008-06153 of the Spanish Ministry of Science and Innovation on Vagueness and Physics, Metaphysics, and Metametaphysics, from the project CONSOLIDER-INGENIO 2010 CSD2009-00056 of the Spanish Ministry of Science and Innovation on Philosophy of Perspectival Thoughts and Facts (PERSP) and from the European Commission’s 7th Framework Programme FP7/2007-2013 under grant FP7-238128 for the European Philosophy Network on Perspectival Thoughts and Facts (PETAF).