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This paper explores some consequences of Lewis’s (Australas J Philos 74(4):549–567, 1996) understanding of how knowledge is compartmentalized. It argues, first, that he underestimates how badly it impacts his view. When knowledge is compartmentalized, it lacks at least one of two essential features of Lewis’s account: (a) Elusiveness—familiar skeptical possibilities, when relevant, are incompatible with everyday knowledge. (b) Knowledge is a modality—when a thinker knows that p, there is no relevant possibility where p is false. Lewis proposes compartmentalized knowledge to keep treating knowledge as a modality while mitigating one of its unrealistic epistemological implications: In normal modal epistemic logic (and standard possible world semantics), a thinker always counts as knowing the strongest proposition that follows from the set of all the individual propositions that this thinker knows. Lewis’s compartmentalization proposal is that thinkers merely know the conjunctions of propositions that are known in each of, but not across, their compartments. The irony is that in avoiding overblown knowledge the view now allows for thinkers to attend to skeptical error possibilities and yet knowledge is present. The account avoids inflation of knowledge in one sense only to acquire another type of knowledge the view denies subjects can have. This problem motivates an inspection of knowledge accounts whose intra-compartment closure principles are weaker than those that are valid in normal modal-logic. The conclusion is that some formulations of closure can avoid the challenge Lewis’s view faces. Nevertheless, even these closure principles pose a barrier—perhaps an implausible barrier—for knowledge of ignorance. Even when the reasoning supporting the lack of knowledge is sound, a subject cannot always know she doesn’t know. Interestingly, this obstacle is one that knowledge of knowledge doesn’t seem to face.
KeywordsCompartmentalization Knowledge David Lewis Modal epistemic logic Normal modal logic Knowledge closure Skepticism Contextualism Subject sensitive invariantism Preface paradox Lottery paradox
I presented several versions of this paper at Lund University; Stockholm University’s 2016 international epistemology workshop; Israel’s 2017 Philosophical Association conference; The Logic, Language, and Cognition Center at the Hebrew University; ECUP 9 at LMU Munich; University of Arizona; and University of Sheffield. I would like to thank everyone who attended. For discussions, comments, objections, and suggestions that significantly improved this paper I’m indebted to Stewart Cohen, Juan Comesaña, Julien Dutant, David Enoch, Paul Faulkner, Mikael Janvid, Moshe Halbertal, John Hawthorne, Maria Lasonen-Aarnio, Ofra Magidor, Ittay Nissan-Rozen, Erik J Olsson, Peter Pagin, Baron Reed, Daniel Rothschild, and Assaf Sharon.
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