Inexact Knowledge with Introspection

Journal of Philosophical Logic 38 (2):179-227 (2009)
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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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Denis Bonnay
Université Paris Nanterre

Citations of this work

Common knowledge.Peter Vanderschraaf - 2008 - Stanford Encyclopedia of Philosophy.
Inexact knowledge and dynamic introspection.Michael Cohen - 2021 - Synthese 199 (3-4):5509-5531.
Brute ignorance.Sam Carter - 2025 - Philosophy and Phenomenological Research 110 (1):113-128.

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References found in this work

Modal Logic: Graph. Darst.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - New York: Cambridge University Press. Edited by Maarten de Rijke & Yde Venema.
Vagueness.Timothy Williamson - 1994 - British Journal for the Philosophy of Science 46 (4):589-601.
Vagueness.Delia Graff & Timothy Williamson (eds.) - 1994 - London and New York: Ashgate.
Modal logic.Yde Venema - 2000 - Philosophical Review 109 (2):286-289.

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