Impossible worlds and logical omniscience: an impossibility result

Synthese 190 (13):2505-2524 (2013)
  Copy   BIBTEX

Abstract

In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents that are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents

Similar books and articles

Non-Ideal Epistemic Spaces.Jens Christian Bjerring - 2010 - Dissertation, Australian National University
Systems of modal logic for impossible worlds.Charles G. Morgan - 1973 - Inquiry: An Interdisciplinary Journal of Philosophy 16 (1-4):280 – 289.
Mundos imposibles.Pescador José Hierro - 1985 - Theoria 1 (1):143-157.
A classically-based theory of impossible worlds.Edward N. Zalta - 1997 - Notre Dame Journal of Formal Logic 38 (4):640-660.
Counterpossibles.Barak Krakauer - 2012 - Dissertation, University of Massachusetts
Impossible Worlds.Francesco Berto - 2013 - Stanford Encyclopedia of Philosophy (2013):en ligne.
Real impossible worlds : the bounds of possibility.Ira Georgia Kiourti - 2010 - Dissertation, University of St Andrews
Epistemic logic for rule-based agents.Mark Jago - 2009 - Journal of Logic, Language and Information 18 (1):131-158.
Constructing worlds.Mark Jago - 2012 - Synthese 189 (1):59-74.
Hintikka and Cresswell on Logical Omniscience.Mark Jago - 2006 - Logic and Logical Philosophy 15 (3):325-354.

Analytics

Added to PP
2011-04-02

Downloads
1,548 (#6,015)

6 months
145 (#18,693)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

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.

View all 21 citations / Add more citations

References found in this work

On the Plurality of Worlds.David K. Lewis - 1986 - Malden, Mass.: Wiley-Blackwell.
The Logic of Decision.Richard C. Jeffrey - 1965 - New York, NY, USA: University of Chicago Press.
Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
On the Plurality of Worlds.David Lewis - 1986 - Revue Philosophique de la France Et de l'Etranger 178 (3):388-390.
Inquiry.Robert C. Stalnaker - 1984 - Cambridge University Press.

View all 42 references / Add more references