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    If mathematical necessity can obtain mind-independently, ... — Carmelics
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    Challenges→Objects cannot have spatio-temporal structure independently of our representing them as spatio-temporal

    If mathematical necessity can obtain mind-independently, spatio-temporal structure grounded in mathematics (as in Euclidean geometry) may likewise be mind-independent.

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    Reasons For

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    Reason for
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    • 1.Mathematical truths (like 2+2=4) hold necessarily regardless of minds, so their ontological status is mind-independent.
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    • 2.If mathematics describes spatial structure in Euclidean geometry, and mathematics is mind-independent, then that structure is too.
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    • 3.Physical laws appear to instantiate mathematical relationships, suggesting mathematics grounds reality rather than merely describing it.
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    Reasons Against

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    • 1.Mathematical necessity may be a property of concepts, not objects—true in all possible worlds but not evidence of mind-independent existence.
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    • 2.Euclidean geometry describes *possible* structures, not necessarily the *actual* spatio-temporal structure instantiated in our universe.
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    • 3.The inference from 'mathematical truths are mind-independent' to 'spatio-temporal structures are mind-independent' commits a category error.
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    Related

    Euclidean geometry describes *possible* structures, not necessarily the *actual*...If mathematics describes spatial structure in Euclidean geometry, and mathematic...Mathematical necessity may be a property of concepts, not objects—true in all po...Mathematical truths (like 2+2=4) hold necessarily regardless of minds, so their ...
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    Objects cannot have spatio-temporal structure independently of our representing ...Physical laws appear to instantiate mathematical relationships, suggesting mathe...The inference from 'mathematical truths are mind-independent' to 'spatio-tempora...

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