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Vagueness and Introspection

Abstract : We compare three strategies to model the notion of vague knowledge in epistemic logic. Williamson's margin for error semantics typically uses non-transitive Kripke structures, but invalidates the principle of positive introspection. On the contrary, Halpern's two-dimensional semantics preserves the introspection principle, but using more complex uncertainty relations that are transitive. We present a modification of the standard epistemic semantics, which validates introspection over one-dimensional non-transitive structures, and study its correspondence with Halpern's approach. While the semantics can be seen as the diagonalization of an explicit two-dimensional semantics, it affords a more intuitive representation of the uncertainty characteristic of vague knowledge. We examine the implications of the semantics concerning higher-order vagueness and the status of the non-transitivity of perceptual indiscriminability. We respond to a potential objection against our approach by giving a dynamic model of the way subjects with inexact knowledge make successive approximations of their margin of error.
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Contributor : Paul Égré <>
Submitted on : Thursday, April 12, 2007 - 5:23:16 PM
Last modification on : Friday, July 2, 2021 - 9:58:02 AM
Long-term archiving on: : Friday, September 21, 2012 - 2:06:23 PM


  • HAL Id : ijn_00141415, version 1



Denis Bonnay, Paul Egré. Vagueness and Introspection. 2007. ⟨ijn_00141415⟩



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