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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that The conceptual coherence of a limiting case does not require that the limit be achievable or instantiable, only that it be consistently defined.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
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    • 1.Consistent definition alone permits vacuous or incoherent concepts; we also need grounding in concrete cases to ensure empirical meaningfulness.
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    • 2.A limit case divorced from any possible instantiation may be logically consistent but lack the conceptual content needed to explain actual phenomena.
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    • 3.The distinction between 'consistently defined' and 'instantiable' obscures that our understanding of limits derives from recognizing approaching cases in reality.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Mathematics routinely uses uninstantiable limits (infinity, infinitesimals) as rigorous theoretical tools without requiring physical realization.
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    • 2.Logical consistency is the only criterion needed for meaningful abstract concepts; instantiability conflates conceptual with physical possibility.
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    • 3.Many scientific laws describe idealized limiting cases (frictionless motion, perfect vacuums) that are conceptually clear yet physically impossible.
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