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It is not the case that There is no viable conception of vector properties on which vector properties are both necessarily extrinsic and capable of being fundamental
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Reasons For
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Reason for
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Alternative conceptions of vector properties on which they cannot be intrinsic have not been shown to also permit vector properties to be fundamental
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Reasons Against
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Reason against 1 of 2
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1.
Fundamental properties, per Lewis's Humean supervenience, must be freely recombinable across possible worlds without modal remainder.
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2.
Vector properties essentially encode directional relations to external spatial frameworks, making their instantiation modally dependent on relational facts.
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3.
Any property whose complete characterization requires reference to extrinsic relata cannot satisfy the free recombinability criterion for fundamentality.
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Reason against 2 of 2
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1.
Earman's symmetry arguments show that vector magnitudes are only well-defined relative to coordinate systems, which are extrinsic representational structures.
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2.
A property that is only determinate relative to an extrinsic representational structure cannot be ontologically fundamental, since fundamentalia must be intrinsically determinate.
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3.
Therefore every conception that preserves the necessarily extrinsic character of vectors simultaneously disqualifies them from serving as fundamental properties.
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