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    The enhanced indispensability argument fails to establish... — Carmelics
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    The enhanced indispensability argument fails to establish Platonism about mathematical entities.

    Modality & PossibilityTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Mathematical explanations that appear indispensable can be recast as structural or representational facts about physical systems, per Pincock's mapping account.
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    • 2.If mathematical entities function as representational tools rather than causal contributors, their explanatory role does not require they exist as abstract objects.
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    • 3.Balaguer's full-blooded Platonism and its nominalist rivals are empirically equivalent, so indispensability to explanation cannot adjudicate between them.
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    Reason for 2 of 2
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    • 1.Rosen and Burgess argue that mathematical nominalism is defensible precisely because mathematical discourse can be understood as involving no genuine ontological commitment.
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    • 2.If the nominalist can paraphrase away apparent reference to mathematical entities without explanatory loss, the enhanced argument's inference to Platonism is blocked by an equally good rival hypothesis.
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    • 3.Inference to the best explanation requires ruling out equally explanatory alternatives, and nominalist reconstructions of mathematical explanations have not been demonstrated to be inferior.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Inference to the best explanation is used differently in arguments for scientific realism than in arguments for mathematical realism.
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    • 2.If the inferential structure differs between scientific and mathematical realism, parity of reasoning between the two positions does not hold.
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    • 3.Without parity of reasoning, the enhanced indispensability argument cannot transfer the justification for scientific realism to mathematical realism.
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    Modality & PossibilityTruth & Knowledge

    Connections

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    Skepticism2 linkedCausation1 linked

    Related

    Balaguer's full-blooded Platonism and its nominalist rivals are empirically equi...If mathematical entities function as representational tools rather than causal c...If the inferential structure differs between scientific and mathematical realism...If the nominalist can paraphrase away apparent reference to mathematical entitie...
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    Inference to the best explanation is used differently in arguments for scientifi...Inference to the best explanation requires ruling out equally explanatory altern...Mathematical explanations that appear indispensable can be recast as structural ...

    Similar

    The enhanced indispensability argument requires that a specific mathem...92%The indispensability argument does not refute mathematical fictionalis...88%Fictionalists cannot adequately respond to the Quine-Putnam indispensa...88%If mathematical entities can be shown to be dispensable even in part, ...87%

    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

    Rosen and Burgess argue that mathematical nominalism is defensible precisely bec...
    Without parity of reasoning, the enhanced indispensability argument cannot trans...
    Type
    claim
    Perspectives
    3 (2 for, 1 against)
    Edits
    1 edit