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It is not the case that Spatiotemporal separability admits multiple precise formulations (Earman, Howard) that are not all logically equivalent.
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Reasons For
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Reason for
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1.
Different formulations may be notational variants expressing identical constraints under translation, making 'non-equivalence' merely apparent.
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2.
If all major formulations successfully capture intuitions about spatial independence, their differences may be semantically insubstantial.
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Reasons Against
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Reason against
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1.
Earman and Howard each formalize separability using different logical structures (modal operators vs. mereological composition).
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2.
A formulation permitting action-at-a-distance differs logically from one requiring local interactions, yet both claim to capture separability.
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3.
Demonstrating non-equivalence requires only showing one formulation permits scenarios the other forbids—this is straightforwardly possible.
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