Higher-order Vagueness, Radical Unclarity, and Absolute Agnosticism

Bobzien, Susanne

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Higher-order Vagueness, Radical Unclarity, and Absolute Agnosticism

Susanne Bobzien

August 2010, Volume 10, No. 10, pp. 1-30

Permalink: http://hdl.handle.net/2027/spo.3521354.0010.010

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Abstract

The paper presents a new theory of higher-order vagueness. This theory is an improvement on current theories of vagueness in that it (i) describes the kind of borderline cases relevant to the Sorites paradox, (ii) retains the ‘robustness’ of vague predicates, (iii) introduces a notion of higher-order vagueness that is compositional, but (iv) avoids the paradoxes of higher-order vagueness. The theory’s central building-blocks: Borderlinehood is defined as radical unclarity. Unclarity is defined by means of competent, rational, informed speakers (‘CRISPs’) whose competence, etc., is indexed to the scope of the unclarity operator. The unclarity is radical since it eliminates clear cases of unclarity and, that is, clear borderline cases. This radical unclarity leads to a (bivalence-compatible, non-intuitionist) absolute agnosticism about the semantic status of all borderline cases. The corresponding modal system would be a non-normal variation on S4M.

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It is also successful on the second task a theory of borderline cases must fulfill: it accounts for the phenomenon of tolerance, that it seems that for any object a on D it holds that if it is F, so is its successor, and that there hence appears to be a seamless transition from the cases to which F applies to those to which it doesn’t apply. Suppose the first borderline case of F is an. Then even a crispFa(n) cannot rule out that an may be F. This reflects the fact that with respect to the question whether it is F, an is humanly indistinguishable from the last clearly F object, an-1. As far as any human can tell (discern), it is not the case that Fan-1 but not Fan. The same holds mutatis mutandis for the last borderline case. The reason why there is no noticeable ‘seam’ is that there is a borderline zone between the clearly F cases and the clearly not-F cases in which the uu-Principle applies. Because of (uu), objections like “but isn’t an distinguishable from an-1 in that it is indistinguishable both from the objects that are F and from the objects that are not F?” are unsuccessful. For, because of (uu), even though an, if it is a borderline case, has this double indistinguishability, it still cannot be told apart from objects that don’t have this double indistinguishability, such as an-1.

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