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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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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Poincaré argued in 'Science and Hypothesis' that geometric axioms are conventions, not truths, so privileging one conic over others requires extra-projective justification.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Some geometric properties are invariant across all consistent axiom systems, suggesting deeper truths about structure independent of convention.
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      Think about whether this reason is strong or weak

    • 2.Conics possess distinct metric and topological properties (closed vs. open) that constrain which can serve equivalent roles in physical descriptions.
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      Think about whether this reason is strong or weak

    • 3.Calling axioms 'conventions' conflates logical independence with epistemic arbitrariness—choice doesn't entail all choices are equally justified.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Euclidean, hyperbolic, and elliptic geometries are all logically consistent, suggesting axioms describe possible worlds, not necessary truths.
      ?

      Think about whether this reason is strong or weak

    • 2.Within projective geometry, all conics are equivalent under projective transformations, so selecting one requires criteria external to projection itself.
      ?

      Think about whether this reason is strong or weak

    • 3.Physics required non-Euclidean geometry to describe spacetime, confirming axioms reflect conventional choices rather than absolute reality.
      ?

      Think about whether this reason is strong or weak

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    Explore the most compelling reason on the other side.