According to the traditional view of the causal structure of a coincidence, the several parts of a coincidence are produced by independent causes. I argue that the traditional view is mistaken; even the several parts of a coincidence may have a common cause. This has important implications for how we think about the relationship between causation and causal explanation—and in particular, for why coincidences cannot be explained.

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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 that w on the basis of competently deducing w from Φwhile retaining justified beliefs in the premises-then one is justified in believing that w. This principle is prima facie compelling; 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 ¬}φ from ¬φ in deliberation even though there are cases in which one can justifiably believe ¬φ but 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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