Higher-Order Sorites Paradox

Journal of Philosophical Logic 42 (1):25-48 (2013)

Authors
Elia Zardini
Universidade de Lisboa
Abstract
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 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
Keywords Borderline cases  Higher-order vagueness  Ignorance  Sorites paradox  Tolerance
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DOI 10.1007/s10992-011-9211-5
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References found in this work BETA

Saving Truth From Paradox.Hartry Field - 2008 - Oxford University Press.
Vagueness.Timothy Williamson - 1994 - Routledge.
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Vagueness, Truth and Logic.Kit Fine - 1975 - Synthese 30 (3-4):265-300.

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Citations of this work BETA

Vagueness: Subvaluationism.Pablo Cobreros - 2013 - Philosophy Compass 8 (5):472-485.
Neutralism and the Observational Sorites Paradox.Patrick Greenough - forthcoming - In Ali Abasnezhad & Otavio Bueno (eds.), Synthese Special Edition. Springer.
Luminosity and Determinacy.Elia Zardini - 2013 - Philosophical Studies 165 (3):765-786.
Vagueness: Why Do We Believe in Tolerance?Paul Égré - 2015 - Journal of Philosophical Logic 44 (6):663-679.

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