A Dynamic Solution to the Problem of Logical Omniscience

Journal of Philosophical Logic 48 (3):501-521 (2019)
  Copy   BIBTEX


The traditional possible-worlds model of belief describes agents as ‘logically omniscient’ in the sense that they believe all logical consequences of what they believe, including all logical truths. This is widely considered a problem if we want to reason about the epistemic lives of non-ideal agents who—much like ordinary human beings—are logically competent, but not logically omniscient. A popular strategy for avoiding logical omniscience centers around the use of impossible worlds: worlds that, in one way or another, violate the laws of logic. In this paper, we argue that existing impossible-worlds models of belief fail to describe agents who are both logically non-omniscient and logically competent. To model such agents, we argue, we need to ‘dynamize’ the impossible-worlds framework in a way that allows us to capture not only what agents believe, but also what they are able to infer from what they believe. In light of this diagnosis, we go on to develop the formal details of a dynamic impossible-worlds framework, and show that it successfully models agents who are both logically non-omniscient and logically competent.

Similar books and articles

Dynamic Epistemic Logic and Logical Omniscience.Mattias Skipper Rasmussen - 2015 - Logic and Logical Philosophy 24 (3):377-399.
Non-Ideal Epistemic Spaces.Jens Christian Bjerring - 2010 - Dissertation, Australian National University
Logical omniscience as infeasibility.Sergei Artemov & Roman Kuznets - 2014 - Annals of Pure and Applied Logic 165 (1):6-25.
Using abstract resources to control reasoning.Richard W. Weyhrauch, Marco Cadoli & Carolyn L. Talcott - 1998 - Journal of Logic, Language and Information 7 (1):77-101.
Epistemic logic for rule-based agents.Mark Jago - 2009 - Journal of Logic, Language and Information 18 (1):131-158.
Non-Normal Worlds and Representation.Francesco Berto - 2012 - In Michal Peliš & Vít Punčochář (eds.), The Logica Yearbook. College Publications.
Impossible worlds and partial belief.Edward Elliott - 2019 - Synthese 196 (8):3433-3458.
Hintikka and Cresswell on Logical Omniscience.Mark Jago - 2006 - Logic and Logical Philosophy 15 (3):325-354.
Impossible Worlds: A Modest Approach.Daniel Nolan - 1997 - Notre Dame Journal of Formal Logic 38 (4):535-572.


Added to PP

829 (#15,622)

6 months
103 (#32,038)

Historical graph of downloads
How can I increase my downloads?

Author Profiles

Mattias Skipper
Inland Norway University of Applied Sciences

Citations of this work

Impossible Worlds.Francesco Berto - 2013 - Stanford Encyclopedia of Philosophy (2013):en ligne.
The Fundamental Problem of Logical Omniscience.Peter Hawke, Aybüke Özgün & Francesco Berto - 2020 - Journal of Philosophical Logic 49 (4):727-766.
Hyperintensionality.Francesco Berto & Daniel Nolan - 2021 - Stanford Encyclopedia of Philosophy.

View all 16 citations / Add more citations

References found in this work

Knowledge and belief.Jaakko Hintikka - 1962 - Ithaca, N.Y.,: Cornell University Press.
The nature of epistemic space.David J. Chalmers - 2011 - In Andy Egan & Brian Weatherson (eds.), Epistemic Modality. Oxford University Press.
Minimal Rationality.Christopher Cherniak - 1986 - MIT Press. Edited by Christopher Cherniak.
The Impossible: An Essay on Hyperintensionality.Mark Jago - 2014 - Oxford, United Kingdom: Oxford University Press.

View all 26 references / Add more references