A Paradox of Higher-Order Vagueness

The naive approach to vagueness maintains that the nature of the vagueness of an expression basically consists in its not having boundaries between positive and negative cases of application in an appropriate ordering (a “soritical series”), whilst having both positive and negative cases in it. The naive approach is contrasted with the nowadays dominant approach to vagueness, maintaining that the nature of the vagueness of an expression consists in its presenting borderline cases of application in a soritical series. The latter approach encompasses extant semantic, ontic, epistemic and psychological theories, which differ from one another only in their interpretation of what borderlineness consists in. The two approaches are briefly compared in their respective explanations of some paramount phenomena of vagueness (ignorance of cut-offs in a soritical series, smoothness of the change along the series, speakers’ inclination to accept a boundarylessness claim concerning the series). These explanations clearly do not provide any ground for choosing the dominant approach against the naive one. The decisive advantage of the former over the latter is rather supposed to consist in its immunity to any form of sorites paradox, famously leading from the intuitive claim, characteristic of the latter, that there are no boundaries between positive and negative cases of application to the unacceptable claim that either everything is a positive case or everything is a negative case. 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.