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    Poincaré demonstrated that geometry is conventional: we c... — Carmelics
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    Challenges→Without the assumption that bodies exist independently of place, astronomical and other measurements lose their validity.

    Poincaré demonstrated that geometry is conventional: we can always reinterpret physical facts by adopting a different geometry paired with different physical laws.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 1.Physical observations underdetermine geometry: identical empirical data fits Euclidean geometry with one force law or non-Euclidean geometry with another.
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    • 2.Conventions about coordinate systems and measurement standards are human choices that don't correspond to mind-independent geometric facts about space itself.
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    • 3.General relativity shows we can describe the same spacetime using infinitely many coordinate systems, suggesting geometry is a descriptive tool, not a discovery.
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    Reasons Against

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    Reason against
    ?
    • 1.Not all geometric descriptions are equally convenient or predictively powerful; one geometry+laws pair typically outperforms alternatives, suggesting one tracks reality better.
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    • 2.Saying geometry is purely conventional conflates the choice of *description* with the choice of *what is being described*—the underlying space has determinate structure.
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    • 3.If any geometry-plus-physics pairing works equally well, empirical science becomes impossible; we need constraints on what counts as a legitimate alternative interpretation.
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    Related

    Conventions about coordinate systems and measurement standards are human choices...General relativity shows we can describe the same spacetime using infinitely man...If any geometry-plus-physics pairing works equally well, empirical science becom...Not all geometric descriptions are equally convenient or predictively powerful; ...
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    Physical observations underdetermine geometry: identical empirical data fits Euc...Saying geometry is purely conventional conflates the choice of *description* wit...Without the assumption that bodies exist independently of place, astronomical an...

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