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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.
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Reasons For
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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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