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    Carmelics

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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 Projective geometry presupposes an ambient space with enough structure to define collinearity, harmonic conjugates, and incidence relations.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Projective geometry can be defined purely axiomatically (Desargues' theorem, axioms of incidence) without reference to any ambient space whatsoever.
      ?

      Think about whether this reason is strong or weak

    • 2.Harmonic conjugates and cross-ratios are definable through synthetic constructions (complete quadrilaterals) that don't require metric or field structure.
      ?

      Think about whether this reason is strong or weak

    • 3.Modern category-theoretic formulations treat projective geometry as a structure arising from abstract incidence axioms, not presupposing ambient space.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Harmonic conjugates and cross-ratios require a field structure that presupposes an underlying ambient space with metric or affine properties.
      ?

      Think about whether this reason is strong or weak

    • 2.Incidence relations (point-line containment) are meaningless without a topological or set-theoretic framework defining distinct geometric objects.
      ?

      Think about whether this reason is strong or weak

    • 3.Collinearity presupposes a notion of 'betweenness' or alignment that only emerges from an ordered or structured ambient continuum.
      ?

      Think about whether this reason is strong or weak

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