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    Representing 'brighter than' as a transitive, asymmetric ... — Carmelics
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    Challenges→Representing two objects as 'brighter than' one another does not require representing them as part of a larger brightness space.

    Representing 'brighter than' as a transitive, asymmetric relation presupposes an ordered structure isomorphic to a brightness continuum.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Transitive relations logically require an ordering principle; without structural isomorphism to a continuum, transitivity collapses into inconsistency.
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    • 2.Brightness is empirically measurable on continuous scales (lumens, candelas), confirming our relational language mirrors actual physical structure.
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    • 3.Our ability to reliably compare three objects (A>B>C) suggests underlying continuous ordering; discrete or circular structures would generate contradictions.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Many transitive relations (dominance hierarchies, logical entailment) lack continuum structure yet remain perfectly consistent and expressible.
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    • 2.Just-noticeable-difference thresholds show brightness perception is discrete-like, not continuous—presupposing a continuum misrepresents actual cognition.
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    • 3.Mathematical formalism can represent 'brighter than' via partial orders or lattices without assuming isomorphism to any physical continuum.
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    Connections

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    Perception1 linkedPhilosophy of Language1 linked

    Related

    Brightness is empirically measurable on continuous scales (lumens, candelas), co...Just-noticeable-difference thresholds show brightness perception is discrete-lik...Many transitive relations (dominance hierarchies, logical entailment) lack conti...Mathematical formalism can represent 'brighter than' via partial orders or latti...
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    Our ability to reliably compare three objects (A>B>C) suggests underlying contin...Representing two objects as 'brighter than' one another does not require represe...Transitive relations logically require an ordering principle; without structural...

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    2 (1 for, 1 against)
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