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Inexact Knowledge with Introspection

Journal of Philosophical Logic volume 38, pages 179–227 (2009)Cite this article

Abstract

Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson’s margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of modular knowledge, in which iterated modalities and simple modalities are not on a par. We show how the semantics helps to solve Williamson’s luminosity paradox, and argue that it corresponds to an integrated model of perceptual and introspective knowledge that is psychologically more plausible than the one defended by Williamson. We formulate a generalized version of the semantics, called token semantics, in which modalities are iteration-sensitive up to degree n and insensitive beyond n. The multi-agent version of the semantics yields a resource-sensitive logic with implications for the representation of common knowledge in situations of bounded rationality.

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Authors and Affiliations

  1. Département d’Etudes Cognitives, IHPST, Ecole Normale Supérieure, Paris, France

    Denis Bonnay

  2. Département d’Etudes Cognitives, Institut Jean-Nicod, EHESS/ENS/CNRS, Ecole Normale Supérieure, Paris, France

    Paul Égré

Authors
  1. Denis Bonnay
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  2. Paul Égré
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Correspondence to Denis Bonnay or Paul Égré.

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Bonnay, D., Égré, P. Inexact Knowledge with Introspection. J Philos Logic 38, 179–227 (2009). https://doi.org/10.1007/s10992-008-9087-1

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  • DOI: https://doi.org/10.1007/s10992-008-9087-1

Keywords

  • Inexact knowledge
  • Epistemic logic
  • Kripke semantics
  • Token semantics
  • Centered semantics
  • Introspection
  • Luminosity
  • Vagueness
  • Margin for error
  • Common knowledge
  • Bounded rationality