When one considers one's own persistence over time from the first-person perspective, it seems as if facts about one's persistence are “further facts,” over and above facts about physical and psychological continuity. But the idea that facts about one's persistence are further facts is objectionable on independent theoretical grounds: it conflicts with physicalism and requires us to posit hidden facts about our persistence. This essay shows how to resolve this conflict using the idea that imagining from the first-person point of view is a guide to centered possibility, a type of possibility analyzed in terms of centered worlds.

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