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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
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    42
    Home/Original/inverse
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    Inverse View

    It is not the case that The enhanced indispensability argument fails to establish Platonism about mathematical entities.

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    Reasons For

    1 perspective
    Reason for
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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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    Reasons Against

    2 perspectives
    Reason against 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 against 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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