If psychological continuity is a matter of degree rather than a discrete threshold, then the boundary marking when a 'person' begins is arbitrary and conventional, not metaphysically fixed.

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Matter of degree(describing how psychological continuity works): Something that comes in different amounts or intensities rather than being either completely present or completely absent; it's not an all-or-nothing situation.
arbitrary(Debate over Locke's watch passage and natural kind classification): Does not mean 'random' or that all qualities are equally adequate as differentia; refers instead to the availability of multiple similarly good and natural grounds for classification.
conventional(social ontology): In ordinary usage, 'conventional' may mean merely that a phenomenon is social, or that something about it is arbitrary or a matter of choice. In social ontology, however, 'conventional' is understood more precisely, following variants of David Lewis's 1969 analysis or analyses that challenge Lewis's approach.
discrete threshold(contrasted with matter of degree): A clear, sharp cutoff point where something switches from one state to another—like flipping a light switch from off to on with no in-between.

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