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It is not the case that There exist non-normal modal frameworks where cross-world individual covariance does not generate the global covariance required by weak global supervenience.
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Reasons For
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Reason for
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1.
If individuals supervene on their properties cross-world, and all individuals are identical, global properties must correlate identically by composition.
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2.
The claim conflates accessibility relations (structural) with property covariance (metaphysical), obscuring whether the distinction is genuine or notational.
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3.
Non-normal frames alone don't generate counterexamples without specifying which global properties fail to covary—the claim lacks concrete modal semantics.
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Reasons Against
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Reason against
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1.
Non-normal frames permit accessibility relations without reflexivity/transitivity, allowing worlds identical in individuals but differing globally.
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2.
Cross-world covariance of individuals (same properties across worlds) needn't guarantee global property covariance if frame topology permits independent variation.
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3.
Weak global supervenience requires all global duplicates share properties; non-normal frames can separate individual from global-level determination.
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