Aybuke Ozgun and Peter Hawke (ILLC/UvA)

The Fundamental Problem of Logical Omniscience

Abstract: In this work, 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 and implausible principles 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 compare our logical system to related ones and exhibit soundness and completeness results. At the end we discuss some of the possible objections to our account and offer replies and, where necessary, refinements.

This is joint work with Peter Hawke and Francesco Berto.