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Cover page of Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism

Epistemic Closure and Epistemic Logic I: Relevant Alternatives and Subjunctivism

(2015)

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.

Cover page of Measure semantics and qualitative semantics for epistemic modals

Measure semantics and qualitative semantics for epistemic modals

(2013)

In this paper, we explore semantics for comparative epistemic modals that avoid the entailment problems shown by Yalcin (2006, 2009, 2010) to result from Kratzer’s (1991) semantics. In contrast to the alternative semantics presented by Yalcin and Lassiter (2010, 2011) based on finitely additive measures, we introduce semantics based on qualitatively additive measures, as well as semantics based on purely qualitative orderings, including orderings on propositions derived from orderings on worlds in the tradition of Kratzer (1991, 2012). All of these semantics avoid the entailment problems that result from Kratzer’s semantics. Our discussion focuses on methodological issues concerning the choice between different semantics.