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    Logical necessity and empirical consistency are distinct:... — Carmelics
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    Challenges→The discovery of consistent non-Euclidean geometries (Riemann, Lobachevsky) demonstrates that Euclid's parallel postulate is not logically necessary.

    Logical necessity and empirical consistency are distinct: non-Euclidean systems may be consistent without showing Euclid's postulate isn't necessary for Euclidean space itself.

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    The discovery of consistent non-Euclidean geometries (Riemann, Lobachevsky) demo...

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    The discovery of consistent non-Euclidean geometries (Riemann, Lobachevsky) demo...

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