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The fundamental problem of logical omniscience

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Hawke2019_JPL_logicalomniscience_CC.pdf (911.6Kb)
Date
20/12/2019
Author
Hawke, Peter
Özgün, Aybüke
Berto, Franz
Funder
European Research Council
Grant ID
681404
Keywords
Aboutness
Subject matter
Logical omniscience
Dynamic epistemic logic
Thick content
BC Logic
T-NDAS
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Abstract
We propose a solution to the problem of logical omniscience in what we take to be its fundamental version: as concerning arbitrary agents and the knowledge attitude per se. Our logic of knowledge is a spin-off from a general theory of thick content, whereby the content of a sentence has two components: (i) an intension, taking care of truth conditions; and (ii) a topic, taking care of subject matter. We present a list of plausible logical validities and invalidities for the logic of knowledge per se for arbitrary agents, and isolate three explanatory factors for them: (1) the topic-sensitivity of content; (2) the fragmentation of knowledge states; (3) the defeasibility of knowledge acquisition. We then present a novel dynamic epistemic logic that yields precisely the desired validities and invalidities, for which we provide expressivity and completeness results. We contrast this with related systems and address possible objections.
Citation
Hawke , P , Özgün , A & Berto , F 2019 , ' The fundamental problem of logical omniscience ' , Journal of Philosophical Logic , vol. Online First . https://doi.org/10.1007/s10992-019-09536-6
Publication
Journal of Philosophical Logic
Status
Peer reviewed
DOI
https://doi.org/10.1007/s10992-019-09536-6
ISSN
0022-3611
Type
Journal article
Rights
Copyright © The Author(s) 2019. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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  • University of St Andrews Research
URI
http://hdl.handle.net/10023/19205

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