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    Therefore, Euclidean geometry expresses contingent struct... — Carmelics
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    Challenges→Euclidean geometry possesses certainty and necessity

    Therefore, Euclidean geometry expresses contingent structural assumptions about space, not necessary truths.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Non-Euclidean geometries are mathematically consistent, showing Euclidean axioms aren't logically necessary.
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    • 2.General relativity describes spacetime as non-Euclidean, suggesting physical space doesn't require Euclidean structure.
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    • 3.We could coherently imagine or construct spaces following different axioms, indicating Euclidean geometry is contingent.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Euclidean geometry may express necessary truths about the structure of possible space itself, not just empirical space.
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    • 2.Non-Euclidean systems describe different structural *possibilities*, but don't prove Euclidean assumptions are merely contingent.
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    Related

    Euclidean geometry may express necessary truths about the structure of possible ...Euclidean geometry possesses certainty and necessityGeneral relativity describes spacetime as non-Euclidean, suggesting physical spa...Non-Euclidean geometries are mathematically consistent, showing Euclidean axioms...
    +2 moreShow less
    Non-Euclidean systems describe different structural *possibilities*, but don't p...We could coherently imagine or construct spaces following different axioms, indi...

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    claim
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