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    Wigner's 'unreasonable effectiveness of mathematics' is e... — Carmelics
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    Challenges→The success and plausibility of purely formal (Pythagorean) analogies in physics should evoke puzzlement.

    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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    Reasons For

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    Reason for
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    • 1.Mathematics describes structural relationships; physical laws describe how systems relate. If laws ARE structures, mathematics naturally applies.
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    • 2.Only structural realism avoids both the mystery of applicability and commitment to unobservable properties physics doesn't require.
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    • 3.Our most successful theories (QM, relativity) are formulated as abstract mathematical structures, not descriptions of intrinsic properties.
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    Reasons Against

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    • 1.Calling laws 'mathematical structures' relabels the problem rather than solving it—it explains neither why mathematics exists nor why it fits.
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    • 2.Structural realism faces the regress problem: describing only relational structure requires that relations relate to something determinate.
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    • 3.Many domains (biology, geology) resist mathematical formalization yet remain empirically successful, suggesting effectiveness isn't fundamental.
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    Related

    Calling laws 'mathematical structures' relabels the problem rather than solving ...Many domains (biology, geology) resist mathematical formalization yet remain emp...Mathematics describes structural relationships; physical laws describe how syste...Only structural realism avoids both the mystery of applicability and commitment ...
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    Our most successful theories (QM, relativity) are formulated as abstract mathema...Structural realism faces the regress problem: describing only relational structu...The success and plausibility of purely formal (Pythagorean) analogies in physics...

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