The Fundamental Problem of Logical Omniscience

Journal of Philosophical Logic 49 (4):727-766 (2020)
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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: an intension, taking care of truth conditions; and 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: the topic-sensitivity of content; the fragmentation of knowledge states; 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.

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Author Profiles

Peter Hawke
Lingnan University
Franz Berto
University of St. Andrews
Aybüke Özgün
University of Amsterdam

References found in this work

Knowledge and its limits.Timothy Williamson - 2000 - New York: Oxford University Press.
Knowledge and lotteries.John Hawthorne - 2004 - New York: Oxford University Press.
Knowledge and belief.Jaakko Hintikka - 1962 - Ithaca, N.Y.,: Cornell University Press.
Meaning and Necessity: A Study in Semantics and Modal Logic.Rudolf Carnap - 1947 - Chicago, IL, USA: University of Chicago Press.
Thought.Gilbert Harman - 1973 - Princeton, NJ, USA: Princeton University Press.

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