The Fundamental Problem of Logical Omniscience

Peter HAWKE; Aybüke ÖZGÜN; Francesco BERTO

doi:10.1007/s10992-019-09536-6

The Fundamental Problem of Logical Omniscience

Peter HAWKE, Aybüke ÖZGÜN, Francesco BERTO^*

^*Corresponding author for this work

Research output: Journal Publications › Journal Article (refereed) › peer-review

18 Citations (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 language	English
Pages (from-to)	727-766
Number of pages	40
Journal	Journal of Philosophical Logic
Volume	49
Issue number	4
Early online date	20 Dec 2019
DOIs	https://doi.org/10.1007/s10992-019-09536-6
Publication status	Published - Aug 2020
Externally published	Yes

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

Access to Document

10.1007/s10992-019-09536-6

Cite this

@article{d1b37b75f6bc41e684002dd571c7dc54,

title = "The Fundamental Problem of Logical Omniscience",

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.",

keywords = "Aboutness, Dynamic epistemic logic, Logical omniscience, Subject matter, Thick content",

author = "Peter HAWKE and Ayb{\"u}ke {\"O}ZG{\"U}N and Francesco BERTO",

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: {\textcopyright} 2019, The Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2020",

month = aug,

doi = "10.1007/s10992-019-09536-6",

language = "English",

volume = "49",

pages = "727--766",

journal = "Journal of Philosophical Logic",

issn = "0022-3611",

publisher = "Springer Netherlands",

number = "4",

}

TY - JOUR

T1 - The Fundamental Problem of Logical Omniscience

AU - HAWKE, Peter

AU - ÖZGÜN, Aybüke

AU - BERTO, Francesco

N1 - 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.

PY - 2020/8

Y1 - 2020/8

N2 - 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.

AB - 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.

KW - Aboutness

KW - Dynamic epistemic logic

KW - Logical omniscience

KW - Subject matter

KW - Thick content

UR - http://www.scopus.com/inward/record.url?scp=85077025621&partnerID=8YFLogxK

U2 - 10.1007/s10992-019-09536-6

DO - 10.1007/s10992-019-09536-6

M3 - Journal Article (refereed)

AN - SCOPUS:85077025621

SN - 0022-3611

VL - 49

SP - 727

EP - 766

JO - Journal of Philosophical Logic

JF - Journal of Philosophical Logic

IS - 4

ER -

The Fundamental Problem of Logical Omniscience

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this