I—Columnar Higher-Order Vagueness, or Vagueness is Higher-Order Vagueness

Aristotelian Society Supplementary Volume 89 (1):61-87 (2015)
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Most descriptions of higher-order vagueness in terms of traditional modal logic generate so-called higher-order vagueness paradoxes. The one that doesn't is problematic otherwise. Consequently, the present trend is toward more complex, non-standard theories. However, there is no need for this.In this paper I introduce a theory of higher-order vagueness that is paradox-free and can be expressed in the first-order extension of a normal modal system that is complete with respect to single-domain Kripke-frame semantics. This is the system QS4M+BF+FIN. It corresponds to the class of transitive, reflexive and final frames. With borderlineness defined logically as usual, it then follows that something is borderline precisely when it is higher-order borderline, and that a predicate is vague precisely when it is higher-order vague.Like Williamson's, the theory proposed here has no clear borderline cases in Sorites sequences. I argue that objections that there must be clear borderline cases ensue from the confusion of two notions of borderlineness—one associated with genuine higher-order vagueness, the other employed to sort objects into categories—and that the higher-order vagueness paradoxes result from superimposing the second notion onto the first. Lastly, I address some further potential objections.

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Susanne Bobzien
Oxford University

References found in this work

Vagueness.Timothy Williamson - 1994 - New York: Routledge.
A New Introduction to Modal Logic.M. J. Cresswell & G. E. Hughes - 1996 - New York: Routledge. Edited by M. J. Cresswell.
Theories of Vagueness.Rosanna Keefe - 2000 - New York: Cambridge University Press.
Précis of Vagueness.Timothy Williamson - 1997 - Philosophy and Phenomenological Research 57 (4):921-928.
Wang's paradox.Michael Dummett - 1975 - Synthese 30 (3-4):201--32.

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