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    Physical measurements cannot definitively distinguish bet... — Carmelics
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    Supports→Poincaré demonstrated that multiple incompatible axiom sets yield equally consistent geometries, making axiom choice empirically underdetermined.

    Physical measurements cannot definitively distinguish between geometries at human scales; curvature effects require astronomical or quantum observations with inherent measurement uncertainty.

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    Key Terms

    Astronomical observations(as used in philosophy of science)
    Measurements and studies of objects and phenomena in space, like stars, planets, and galaxies, which occur at scales too large for humans to directly observe.
    Curvature(as the geometric property being normalized)
    A measurement of how much a surface bends or curves at any given point; the more a surface curves, the higher its curvature.
    Geometries(as used in epistemology and physics)
    Different mathematical systems for describing shapes and spaces—like flat geometry (Euclidean) versus curved geometry (non-Euclidean), which describe space differently.
    Measurement uncertainty(as used in epistemology and science)
    The idea that any measurement tool or process has built-in limits and cannot give you a perfectly exact answer—there's always some margin of error or unknown.

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    Physical measurements(as what abstract axioms are linked to)
    Concrete data you collect by actually observing or testing something in the real world—like measuring distance with a ruler or timing something with a clock.
    Quantum observations(as used in philosophy of science and physics)
    Measurements of extremely tiny things like atoms and subatomic particles, which behave differently from everyday objects and are affected by the act of measuring them.

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    Poincaré demonstrated that multiple incompatible axiom sets yield equally consis...

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