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    The notion of explanatory power of mathematics in science... — Carmelics
    Home/Modality & Possibility
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    The notion of explanatory power of mathematics in science has no ontological import and cannot be used in the enhanced indispensability argument.

    Modality & PossibilityTruth & Knowledge
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    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Mathematical explanations function as representational tools that reveal structural relationships, not as causal mechanisms that produce phenomena (Pincock 2012).
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    • 2.Representational adequacy requires only that mathematical structures be applicable, not that the entities they describe exist independently (Balaguer 1998).
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    • 3.The enhanced indispensability argument conflates inferential utility with existential commitment, a distinction Azzouni's deflationary nominalism systematically upholds.
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    Reason for 2 of 2
    ?
    • 1.If mathematical entities were ontologically implicated by explanatory power, replacing one mathematical framework with an equivalent one would alter the ontology of science, which is absurd (Field 1980).
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    • 2.The existence of provably equivalent mathematical redescriptions of the same phenomenon—as in Euler's bridges and graph-theoretic reformulations—entails that explanatory success tracks modal structure, not particular abstract objects.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Alternative mathematical explanations of the same scientific phenomenon exist, appealing to different mathematical entities.
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    • 2.If multiple distinct mathematical entities can explain the same phenomenon, no single entity's existence is established by that explanatory role.
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    Related

    Alternative mathematical explanations of the same scientific phenomenon exist, a...If mathematical entities were ontologically implicated by explanatory power, rep...If multiple distinct mathematical entities can explain the same phenomenon, no s...Mathematical explanations function as representational tools that reveal structu...
    +3 moreShow less
    Representational adequacy requires only that mathematical structures be applicab...The enhanced indispensability argument conflates inferential utility with existe...The existence of provably equivalent mathematical redescriptions of the same phe...

    Similar

    Fictionalists cannot adequately respond to the Quine-Putnam indispensa...88%The enhanced indispensability argument fails to establish Platonism ab...84%Baker's version of the indispensability argument focuses on the explan...84%The enhanced indispensability argument requires that a specific mathem...82%

    Source

    AI-extracted1/3 agreementValid
    SEP: mathematics-explanation
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    One of the aspects of the enhanced indispensability argument that has generated much attention is that the argument seems to presuppose a form of inference to the best explanation. An inference to the best explanation licenses, when one is presented with several alternative explanations of the same phenomenon, the acceptance as true of the best among such explanations. In addition to raising the crucial issue of determining whether a certain argument is a mathematical explanation of a scientific
    Extraction notes

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

    Details

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