On the structure of higher-order vagueness

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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Pablo Cobreros (2013). Vagueness: Subvaluationism. Philosophy Compass 8 (5):472-485.

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