caa a22 4500 605539006 CHVBK 20210128100904.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s10992-013-9306-2 doi (NATIONALLICENCE)springer-10.1007/s10992-013-9306-2 Holliday Wesley Department of Philosophy, University of California, 314 Moses Hall #2390, 94720-2390, Berkeley, CA, USA aut Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism [Elektronische Daten] [Wesley Holliday] Epistemic closure has been a central issue in epistemology over the last forty years. According to versions of the relevant alternatives and subjunctivist theories of knowledge, epistemic closure can fail: an agent who knows some propositions can fail to know a logical consequence of those propositions, even if the agent explicitly believes the consequence (having "competently deduced” it from the known propositions). In this sense, the claim that epistemic closure can fail must be distinguished from the fact that agents do not always believe, let alone know, the consequences of what they know—a fact that raises the "problem of logical omniscience” that has been central in epistemic logic. This paper, part I of II, is a study of epistemic closure from the perspective of epistemic logic. First, I introduce models for epistemic logic, based on Lewis's models for counterfactuals, that correspond closely to the pictures of the relevant alternatives and subjunctivist theories of knowledge in epistemology. Second, I give an exact characterization of the closure properties of knowledge according to these theories, as formalized. Finally, I consider the relation between closure and higher-order knowledge. The philosophical repercussions of these results and results from part II, which prompt a reassessment of the issue of closure in epistemology, are discussed further in companion papers. As a contribution to modal logic, this paper demonstrates an alternative approach to proving modal completeness theorems, without the standard canonical model construction. By "modal decomposition” I obtain completeness and other results for two non-normal modal logics with respect to new semantics. One of these logics, dubbed the logic of ranked relevant alternatives, appears not to have been previously identified in the modal logic literature. More broadly, the paper presents epistemology as a rich area for logical study. The Author(s), 2014 Epistemic closure nationallicence Epistemic logic nationallicence Epistemology nationallicence Modal logic nationallicence Relevant alternatives nationallicence Safety nationallicence Sensitivity nationallicence Subjunctivism nationallicence Tracking nationallicence Journal of Philosophical Logic Springer Netherlands 44/1(2015-02-01), 1-62 0022-3611 44:1<1 2015 44 10992 https://doi.org/10.1007/s10992-013-9306-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10992-013-9306-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Holliday Wesley Department of Philosophy, University of California, 314 Moses Hall #2390, 94720-2390, Berkeley, CA, USA aut NATIONALLICENCE 773 0- Journal of Philosophical Logic Springer Netherlands 44/1(2015-02-01), 1-62 0022-3611 44:1<1 2015 44 10992