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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Pré-publication, Document de travail
Version of March 05, 2007. An extended abstract of the paper appeared in the Proceedings of the 2.. 2007
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https://jeannicod.ccsd.cnrs.fr/ijn_00141415
Contributeur : Paul Egré <>
Soumis le : jeudi 12 avril 2007 - 17:23:16
Dernière modification le : jeudi 11 janvier 2018 - 06:19:08
Document(s) archivé(s) le : vendredi 21 septembre 2012 - 14:06:23

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  • HAL Id : ijn_00141415, version 1

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Denis Bonnay, Paul Egré. Vagueness and Introspection. Version of March 05, 2007. An extended abstract of the paper appeared in the Proceedings of the 2.. 2007. 〈ijn_00141415〉

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