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    Field's Newtonian gravitational theory, expressed purely ... — Carmelics
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    Challenges→We ought to be committed to the existence of mathematical entities.

    Field's Newtonian gravitational theory, expressed purely in terms of spacetime regions, shows mathematics functions as a useful fiction rather than a description of real entities.

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    Reasons For

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    Reason for
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    • 1.Field's formulation eliminates mathematical objects (numbers, vectors) from fundamental ontology, replacing them with purely spacetime structures.
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    • 2.Multiple mathematically distinct systems describe identical physical phenomena, suggesting math is a representation tool rather than reality itself.
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    • 3.Spacetime regions exist mind-independently, whereas mathematical entities depend on human convention and symbolic systems for instantiation.
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    Reasons Against

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    Reason against
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    • 1.Spacetime regions themselves are abstract geometric objects that require mathematical properties to be physically differentiated and individuated.
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    • 2.If math is mere fiction, Field's reformulation merely trades explicit mathematics for covert mathematics embedded in topological and mereological structure.
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    • 3.The predictive success of mathematical theories suggests they track real patterns in nature, not merely useful fictions divorced from reality.
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    Related

    Field's formulation eliminates mathematical objects (numbers, vectors) from fund...If math is mere fiction, Field's reformulation merely trades explicit mathematic...Multiple mathematically distinct systems describe identical physical phenomena, ...Spacetime regions exist mind-independently, whereas mathematical entities depend...
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    Spacetime regions themselves are abstract geometric objects that require mathema...The predictive success of mathematical theories suggests they track real pattern...We ought to be committed to the existence of mathematical entities.

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