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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that After geometric axioms are established, it is no longer necessary to resort to sense perceptions in geometric proofs.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Kant argued that geometric proofs require construction in pure intuition, not merely logical derivation from axioms.
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    • 2.The act of constructing figures in intuition is a non-discursive cognitive operation irreducible to axiom-manipulation.
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    • 3.Therefore, spatial intuition remains epistemically active in proof, not merely in axiom selection.
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    Reason for 2 of 2
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    • 1.Poincaré demonstrated that multiple incompatible axiom sets yield equally consistent geometries, making axiom choice empirically underdetermined.
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    • 2.If axiom choice itself depends on conventions shaped by sensorimotor experience, sense perception is never fully expelled from geometric reasoning.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.The axioms must embody the whole empirical material elaborated by geometry.
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    • 2.All other geometric statements must be proved from the axioms by strictly deductive methods.
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    • 3.Everything needed to prove geometric statements must be recorded in the axioms without exception.
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