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.
Citation
Hawke , P , Özgün , A & Berto , F 2019 , ' The fundamental problem of logical omniscience ' , Journal of Philosophical Logic , vol. Online First . https://doi.org/10.1007/s10992-019-09536-6
Publication
Journal of Philosophical Logic
Status
Peer reviewed
ISSN
0022-3611Type
Journal article
Collections
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