The Fundamental Problem of Logical Omniscience

Peter HAWKE, Aybüke Özgün, Francesco BERTO*

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)727-766
Number of pages40
JournalJournal of Philosophical Logic
Volume49
Issue number4
Early online date20 Dec 2019
DOIs
Publication statusPublished - 1 Aug 2020
Externally publishedYes

Bibliographical note

Funding Information:
Many thanks to our anonymous referees for astute and constructive comments. Special thanks to Alexandru Baltag for stimulating feedback that significantly influenced the contents of Section ??. Versions of the present work were presented at the following conferences and workshops: the fourth meeting of the ?From Shared Evidence to Group Attitudes? project, University of Bayreuth, April 18-19, 2018; ?Reasoning in Social Contexts? at the Royal Netherlands Academy of Arts and Sciences, Amsterdam, May 31-June 2, 2018; ?Models of Bounded Reasoning in Individuals and Groups? at the Lorentz Center, Leiden, July 2-6, 2018; the Super-Special seminar slot at Arch?, University of St Andrews, November 29, 2018; and the ?Workshop on the Occasion of Johan van Benthem?s 70th birthday? in Amsterdam, June 12, 2019. We thank these audiences for their helpful questions and remarks. This research is published within the project ?The Logic of Conceivability?, funded by the European Research Council (ERC CoG), Grant Number 681404.

Publisher Copyright:
© 2019, The Author(s).

Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

Keywords

  • Aboutness
  • Dynamic epistemic logic
  • Logical omniscience
  • Subject matter
  • Thick content

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