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Inverse View
It is not the case that Schlick and the logical empiricists argued that metric relations are fixed by coordinative definitions, not discovered as intrinsic features of manifolds.
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Reasons For
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Reason for
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1.
Physical spacetime has intrinsic causal and topological structure that constrains which metric choices are empirically adequate.
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2.
Conventionalism conflates the freedom to choose coordinate systems with the freedom to assign any metric relations to reality.
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3.
Some metric facts (like light cone structure) are discovered through experiment, not merely stipulated by definition.
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Reasons Against
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Reason against
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1.
Metric properties like distance units depend on human choice of measurement standards, not mind-independent physical facts.
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2.
Different coordinate systems describe identical physical situations with different metric relations, showing metrics are conventional.
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3.
Empirical content concerns only relations between observations, not the abstract mathematical structure underlying description.
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