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    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Euclidean geometry possesses certainty and necessity

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.The discovery of consistent non-Euclidean geometries (Riemann, Lobachevsky) demonstrates that Euclid's parallel postulate is not logically necessary.
      ?

      Think about whether this reason is strong or weak

    • 2.If a proposition can be coherently denied without contradiction, it cannot qualify as a priori necessary in Kant's sense.
      ?

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

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.General relativity empirically confirmed that physical space conforms to non-Euclidean geometry in regions of significant mass-energy curvature.
      ?

      Think about whether this reason is strong or weak

    • 2.A geometric system whose applicability to the actual world depends on empirical verification cannot claim the context-independent certainty synthetic a priori status requires.
      ?

      Think about whether this reason is strong or weak

    • 3.Euclidean geometry is thus best understood as one formal system among many, whose truth is relative to axiom choice, not guaranteed by pure reason.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Euclidean geometry consists of synthetic a priori statements
      ?

      Think about whether this reason is strong or weak

    • 2.Synthetic a priori knowledge does not rely on experience and is therefore necessary and certain
      ?

      Think about whether this reason is strong or weak

    • 3.Knowledge that is both non-tautological and independent of experience can still be necessarily true
      ?

      Think about whether this reason is strong or weak

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    Strongest counterpoint
    Explore the most compelling reason on the other side.