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

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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
Keywords Impossible worlds  Logical omniscience  Rationality  Resource-bounded reasoning  Logical reasoning
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DOI 10.1007/s11229-011-0038-y
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References found in this work BETA

On the Plurality of Worlds.David Lewis - 1986 - 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.
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Citations of this work BETA

Impossible Worlds.Francesco Berto - 2013 - Stanford Encyclopedia of Philosophy (2013).
A Dynamic Solution to the Problem of Logical Omniscience.Mattias Skipper & Jens Bjerring - 2019 - Journal of Philosophical Logic 48 (3):501-521.
Granularity Problems.Jens Christian Bjerring & Wolfgang Schwarz - 2017 - Philosophical Quarterly 67 (266):22-37.
Minimal Rationality and the Web of Questions.Daniel Hoek - forthcoming - In Dirk Kindermann, Peter van Elswyk & Andy Egan (eds.), Unstructured Content. Oxford University Press.

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