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It is not the case that Psychological continuity admits of degrees, making it unsuitable as a criterion for the all-or-nothing relation of numerical identity.
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1.
All fundamental physical relations (mass, charge, spatiotemporal location) admit of degrees, yet successfully ground determinate identity conditions.
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2.
The all-or-nothing appearance of identity may reflect our linguistic practices, not metaphysical reality; vagueness in criteria doesn't entail vague identity.
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3.
Psychological continuity could determine identity via a threshold: sufficient continuity constitutes identity, just as 'heap' works despite grain vagueness.
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Reasons Against
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1.
Numerical identity is a fundamental logical relation that is determinate: either X is identical to Y or it is not, admitting no middle ground.
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2.
Psychological continuity demonstrably varies by degree across cases (memory chains, personality overlap, intentions), not present uniformly.
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3.
If a criterion for identity permits borderline cases, it fails to capture what identity actually is—a precise metaphysical relation.
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