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It is not the case that A rigid designator need only denote the same entity across possible worlds, not across times of a single world (Kripke, Naming and Necessity).
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Reasons For
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Reason for
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1.
If a name rigidly designates an entity across possible worlds, temporal continuity within our actual world seems equally fundamental to that designation.
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2.
The distinction between modal and temporal difference appears arbitrary: both involve tracking identity through varied scenarios of change.
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3.
Temporal parts theory and 4D ontology challenge whether time-indexed identity requires weaker designation than world-indexed identity.
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Reasons Against
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Reason against
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1.
Possible worlds represent modal space (what could be), while time represents actual sequence; these are fundamentally different metaphysical dimensions.
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2.
Names rigidly designate entities qua their essential identity, which persists across counterfactuals but not necessarily through temporal stages.
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3.
Kripke's account explains why 'Aristotle' picks out the same person in all possible worlds yet allows temporal change without identity failure.
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