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    After geometric axioms are established, it is no longer n... — Carmelics
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    Home/Skepticism
    HistoryEditSee Inverse

    After geometric axioms are established, it is no longer necessary to resort to sense perceptions in geometric proofs.

    Skepticism
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    Related

    All other geometric statements must be proved from the axioms by strictly deduct...Everything needed to prove geometric statements must be recorded in the axioms w...If axiom choice itself depends on conventions shaped by sensorimotor experience,...Kant argued that geometric proofs require construction in pure intuition, not me...
    +4 moreShow less
    Poincaré demonstrated that multiple incompatible axiom sets yield equally consis...The act of constructing figures in intuition is a non-discursive cognitive opera...The axioms must embody the whole empirical material elaborated by geometry.Therefore, spatial intuition remains epistemically active in proof, not merely i...

    Similar

    All other geometric statements must be proved from the axioms by stric...83%Everything needed to prove geometric statements must be recorded in th...80%Conclusions occurring in a geometric proof are justified by prior stat...80%Basic geometric concepts are simple and irreducible notions of this ki...79%

    Source

    AI-extracted1/3 agreementValid
    SEP: geometry-19th
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    Pasch viewed geometry as a natural science, whose successful utilization by other sciences and in practical life rests “exclusively on the fact that geometrical concepts originally agreed exactly with empirical objects” (Pasch 1882, p. iii). Geometry distinguishes itself from other natural sciences because it obtains only very few concepts and laws directly from experience, and aims at obtaining from them the laws of more complex phenomena by purely deductive means. The empirical foundation of g
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit