Mind 108 (429):127-143 (1999)

Abstract
Discussions of higher-order vagueness rarely define what it is for a term to have nth-order vagueness for n>2. This paper provides a rigorous definition in a framework analogous to possible worlds semantics; it is neutral between epistemic and supervaluationist accounts of vagueness. The definition is shown to have various desirable properties. But under natural assumptions it is also shown that 2nd-order vagueness implies vagueness of all orders, and that a conjunction can have 2nd-order vagueness even if its conjuncts do not. Relations between the definition and other proposals are explored; reasons are given for preferring the present proposal.
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DOI 10.1093/mind/108.429.127
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Very Improbable Knowing.Timothy Williamson - 2014 - Erkenntnis 79 (5):971-999.
The Dynamics of Vagueness.Chris Barker - 2002 - Linguistics and Philosophy 25 (1):1-36.
Ignorance of Ignorance.Kit Fine - 2018 - Synthese 195 (9):4031-4045.
Transformative Experience and the Shark Problem.Tim Campbell & Julia Mosquera - 2020 - Philosophical Studies 177 (11):3549-3565.

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