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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that The success and plausibility of purely formal (Pythagorean) analogies in physics should evoke puzzlement.

    ?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.Mathematical structures capture deep nomological regularities in nature, so formal analogies track real physical relationships rather than being mysterious coincidences.
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    • 2.Wigner's 'unreasonable effectiveness of mathematics' is explicable if physical laws are themselves mathematical structures, as structural realists like Ladyman and French argue.
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    • 3.If mathematics and physics share the same underlying structure, Pythagorean analogies succeeding is expected, not puzzling.
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    Reason for 2 of 2
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    • 1.Schrödinger's use of Hamilton's optical-mechanical analogy was historically informed by known physical theory, not purely formal symbol manipulation divorced from physics.
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    • 2.Post-hoc descriptions of derivations as 'purely formal' often obscure the physical intuitions and theoretical commitments that actually guided the analogy's construction.
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    • 3.If the puzzlement rests on a misleading reconstruction of scientific practice, the phenomenon requiring explanation is less radical than claimed.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Schrödinger's derivation of the relativistic wave equation relies on manipulations and substitutions based on purely mathematical analogies with no known physical basis.
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    • 2.The resulting equation proved successful despite the absence of any physical grounding for the analogy.
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