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It is not the case that Reichenbach's coordinative definitions, though conventional in form, carry synthetic content by determining which physical geometry applies to spacetime.
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Reasons For
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Reason for
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1.
If coordinative definitions are purely conventional, they cannot carry synthetic content—conventions are stipulative and lack factual truth-conditions by definition.
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2.
Any purported synthetic content merely reflects hidden assumptions about measurement already smuggled into the definition, not genuine physical discovery.
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3.
All geometric descriptions remain empirically equivalent under appropriate coordinative redefinitions, showing geometry is conventional rather than substantive.
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Reasons Against
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Reason against
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1.
Coordinative definitions establish which measurement procedures count as determining spatial/temporal distances, thereby constraining physical geometry empirically.
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2.
Different coordinative choices (e.g., rigid vs. non-rigid rods) yield different geometric descriptions of the same physical situation, showing they carry substantive content.
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3.
Even if the choice among geometries is conventional, selecting which conventions apply to spacetime requires factual knowledge about measurement and physics.
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