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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that Nominalists who reject thin-truth-ism and accept the standard criterion of ontological commitment must adopt either a paraphrase view or a fictionalist view of mathematical sentences.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Hartry Field's error theory demonstrates a third option: mathematical sentences are systematically false, yet indispensable for representing physical structure.
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    • 2.A nominalist can accept that '3 is prime' is literally false while explaining its instrumental utility without paraphrase or fictionalist pretense.
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    • 3.Error theory thus escapes the dichotomy by denying mathematical sentences have truth-apt content requiring ontological commitment.
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    Reason for 2 of 2
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    • 1.Quine's criterion of ontological commitment applies only to sentences in our best confirmed scientific theories, not to all grammatically well-formed sentences.
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    • 2.A nominalist can argue, following Jody Azzouni, that mathematical vocabulary is 'ontologically deflating'—its surface grammar does not trigger Quinean commitment.
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    • 3.If the criterion is domain-restricted rather than universal, the forced dichotomy between paraphrase and fictionalism dissolves without abandoning thin-truth-ism's rejection.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Thin-truth-ism is rejected.
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    • 2.The standard criterion of ontological commitment is accepted.
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    • 3.Mathematical sentences like '3 is prime' appear to commit us to the existence of abstract objects.
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