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    Topological and ordinal relations (betweenness, continuit... — Carmelics
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    Challenges→All relations in the objective spatio-temporal order can ultimately be known quantitatively.

    Topological and ordinal relations (betweenness, continuity, connectedness) are irreducibly qualitative structural features of space-time.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Metric structure (distances) can be derived from topological continuity and order relations, but not vice versa.
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    • 2.Connectivity and betweenness are invariant under continuous deformations, suggesting they capture fundamental structural properties independent of quantitative description.
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    • 3.Physical laws (causality, light-cones) depend essentially on topological separation and ordering, not merely on metric quantities.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.All topological and ordinal properties require an underlying metric or coordinate system to be physically instantiated and measured.
      ?

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    • 2.Betweenness and continuity are definable in purely algebraic-metric terms; their 'qualitative' status is merely notational convenience, not ontological.
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    • 3.Quantum mechanics suggests space-time structure may be fundamentally discrete or non-topological at small scales, undercutting claims of irreducible topological primacy.
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    Related

    All relations in the objective spatio-temporal order can ultimately be known qua...All topological and ordinal properties require an underlying metric or coordinat...Betweenness and continuity are definable in purely algebraic-metric terms; their...Connectivity and betweenness are invariant under continuous deformations, sugges...
    +3 moreShow less
    Metric structure (distances) can be derived from topological continuity and orde...Physical laws (causality, light-cones) depend essentially on topological separat...Quantum mechanics suggests space-time structure may be fundamentally discrete or...

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    claim
    Perspectives
    2 (1 for, 1 against)
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