Higher-Order Sorites Paradox

Journal of Philosophical Logic 42 (1):25-48 (2013)
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 (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.
Keywords Borderline cases  Higher-order vagueness  Ignorance  Sorites paradox  Tolerance
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References found in this work BETA
D. Barnett (2011). Does Vagueness Exclude Knowledge? Philosophy and Phenomenological Research 82 (1):22 - 45.
Cian Dorr (2003). Vagueness Without Ignorance. Philosophical Perspectives 17 (1):83–113.

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Citations of this work BETA
Pablo Cobreros (2013). Vagueness: Subvaluationism. Philosophy Compass 8 (5):472-485.
Elia Zardini (2013). Luminosity and Determinacy. Philosophical Studies 165 (3):765-786.
Similar books and articles
Diana Raffman (2009). Demoting Higher-Order Vagueness. In Sebastiano Moruzzi & Richard Dietz (eds.), Cuts and Clouds. Vaguenesss, its Nature and its Logic. Oxford University Press. 509--22.
Susanne Bobzien (2002). Chrysippus and the Epistemic Theory of Vagueness. Proceedings of the Aristotelian Society 102 (1):217-238.
Elia Zardini (2008). A Model of Tolerance. Studia Logica 90 (3):337 - 368.
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