Principles of epistemic logic I: Knowledge

Abstract

All epistemic logics come with some idealizations. Not all such idealizations seem acceptable. A large family of epistemic logics assume that if ⌜φ‎⌝ and ⌜ψ‎⌝ are logically equivalent, so are ⌜One knows that φ‎⌝ and ⌜One knows that ψ‎⌝. This assumption, characteristic of normal epistemic logics but also of many non-normal ones, is acceptable only if the objects of knowledge can be construed as sets of possible worlds known under some mode of presentation or other, where knowledge-ascriptions do not yet make those modes explicit. Unlike fine-grained conceptions that reject the assumption, such coarse-grained conceptions of the objects of knowledge have the untoward consequence that failures of logical omniscience are no longer expressible in the logic. But even on coarse-grained conceptions, epistemic logic cannot be expected to be normal. Fine-grained conceptions allow for failures of logical omniscience to be expressible in the logic. On balance, fine-grained conceptions are to be preferred. Against this backdrop, candidate principles for inclusion in the logic of knowledge are critically reviewed in the light of general epistemological considerations. Very few survive closer scrutiny.