Abstract
According to a popular closure principle for epistemic justification, if one is justified in believing each of the premises in set Φ and one comes to believe thatψon the basis of competently deducingψfrom Φ—while retaining justified beliefs in the premises—then one is justified in believing thatψ. This principle isprima faciecompelling; it seems to capture the sense in which competent deduction is an epistemically secure means to extend belief. However, even the single‐premise version of this closure principle is in conflict with certain seemingly good inferences involving the epistemic possibility modal ♢. According to other compelling principles concerning competent deduction and epistemic justification, one can competently infer ¬♢φfrom ¬φin deliberation even though there are cases in which one can justifiably believe ¬φbut would be unjustified in believing ¬♢φ. Thus, as we argue, philosophers must choose between unrestricted closure for justification and the validity of these other principles.
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