Vagueness, uncertainty and degrees of clarity

Synthese 174 (1):47 - 78 (2010)
In this paper we compare different models of vagueness viewed as a specific form of subjective uncertainty in situations of imperfect discrimination. Our focus is on the logic of the operator “clearly” and on the problem of higher-order vagueness. We first examine the consequences of the notion of intransitivity of indiscriminability for higher-order vagueness, and compare several accounts of vagueness as inexact or imprecise knowledge, namely Williamson’s margin for error semantics, Halpern’s two-dimensional semantics, and the system we call Centered semantics. We then propose a semantics of degrees of clarity, inspired from the signal detection theory model, and outline a view of higher-order vagueness in which the notions of subjective clarity and unclarity are handled asymmetrically at higher orders, namely such that the clarity of clarity is compatible with the unclarity of unclarity.
Keywords Higher-order vagueness  Clarity  Imperfect discrimination  Inexact knowledge  Non-transitivity  Signal detection theory  Centered semantics  Epistemic logic  Uncertainty  Metacognition
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DOI 10.2307/40587016
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