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    The success and plausibility of purely formal (Pythagorea... — Carmelics
    Home/Skepticism
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    The success and plausibility of purely formal (Pythagorean) analogies in physics should evoke puzzlement.

    Skepticism
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
    ?
    • 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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    Connections

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    Philosophy of Language1 linked

    Related

    If mathematics and physics share the same underlying structure, Pythagorean anal...If the puzzlement rests on a misleading reconstruction of scientific practice, t...Mathematical structures capture deep nomological regularities in nature, so form...Post-hoc descriptions of derivations as 'purely formal' often obscure the physic...
    +4 moreShow less
    Schrödinger's derivation of the relativistic wave equation relies on manipulatio...Schrödinger's use of Hamilton's optical-mechanical analogy was historically info...The resulting equation proved successful despite the absence of any physical gro...Wigner's 'unreasonable effectiveness of mathematics' is explicable if physical l...

    Similar

    A purely formal analogy with no physical significance cannot support a...86%Past success of Pythagorean analogies in physics provides reason to co...85%Philosopher-scientists such as Herschel and Whewell held that analogie...83%Material analogy and formal analogy are independent of one another80%

    Source

    AI-extracted1/3 agreementValid
    SEP: reasoning-analogy
    View source passageHide passage
    Analogical arguments support the hypothesis that in each of these cultures, rock art symbolizes hallucinogenic experiences. Currie examines criteria that focus on assumptions about stability of cultural traits and environment-culture relationships. Currie (2016, 2018) and Wylie (Wylie and Chapman 2016) also stress the importance of robustness reasoning that combines analogical arguments of moderate strength with other forms of evidence to yield strong conclusions. Practice-based approaches can
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit