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    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The space problem (das Raumproblem) arises as a genuine philosophical and mathematical question: how can metric relations be determined on a continuous manifold M?

    ?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.Poincaré's conventionalism holds that the topology and continuity of space underdetermine geometry, but this underdetermination shows geometry is conventional, not that it requires independent grounding.
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    • 2.Weyl's separation of topological and metrical structure, inherited from Riemann, presupposes a realist reading of manifold structure that Poincaré's géométrie de position explicitly rejects.
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    • 3.If the choice of metric is a free conventional act constrained only by simplicity, then no philosophical account of metric determination is needed beyond pragmatic justification.
      ?

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    Reason for 2 of 2
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    • 1.Schlick and the logical empiricists argued that metric relations are fixed by coordinative definitions, not discovered as intrinsic features of manifolds.
      ?

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    • 2.If metric is a matter of conventional stipulation rather than objective determination, the 'space problem' dissolves into a question of pragmatic choice, not genuine metaphysical inquiry.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Riemann's separation thesis shows that a continuous manifold's topological structure does not by itself determine its metrical structure.
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    • 2.If metrical structure is not entailed by the manifold's continuity properties, then the basis for metric relations requires independent explanation.
      ?

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