Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism

Journal of Philosophical Logic 44 (1):1-62 (2015)
Authors
Wesley H. Holliday
University of California, Berkeley
Abstract
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.
Keywords epistemic closure  epistemic logic  epistemology  modal logic  relevant alternatives  safety  sensitivity  subjunctivism  tracking  non-normal modal logic
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DOI 10.1007/s10992-014-9338-2
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References found in this work BETA

Knowledge and its Limits.Timothy Williamson - 2000 - Oxford University Press.
Epistemic Luck.Duncan Pritchard - 2005 - Oxford University Press UK.
Knowledge and Lotteries.John Hawthorne - 2003 - Oxford University Press.
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Citations of this work BETA

Lewis on Iterated Knowledge.Bernhard Salow - 2016 - Philosophical Studies 173 (6):1571-1590.
Safety, Explanation, Iteration.Daniel Greco - 2016 - Philosophical Issues 26 (1):187-208.
Counterfactual Theories of Knowledge and the Notion of Actuality.Jan Heylen - 2016 - Philosophical Studies 173 (6):1647-1673.

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