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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that The notion of explanatory power of mathematics in science has no ontological import and cannot be used in the enhanced indispensability argument.

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    Reasons For

    1 perspective
    Reason for
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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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    Reasons Against

    2 perspectives
    Reason against 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 against 2 of 2
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    • 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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