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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that We ought to be committed to the existence of mathematical entities.

    ?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.Mathematical statements can be nominalistically paraphrased without quantifying over abstract entities, as Hartry Field demonstrates in 'Science Without Numbers'.
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    • 2.If a theory can be reformulated without positing certain entities while retaining empirical adequacy, indispensability provides no ontological warrant for those entities.
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    • 3.Field's Newtonian gravitational theory, expressed purely in terms of spacetime regions, shows mathematics functions as a useful fiction rather than a description of real entities.
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    Reason for 2 of 2
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    • 1.Scientific confirmation accrues to theories as holistic empirical packages, but mathematical posits contribute no distinctive empirical content that could be selectively confirmed.
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    • 2.Confirmational holism, as Sober argues against Quine, does not extend to mathematical auxiliaries since they are not tested by any possible experimental outcome.
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    • 3.Entities whose existence makes no difference to any observable prediction are not genuinely indispensable in the epistemically relevant sense required for ontological commitment.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Mathematics is indispensable for our best scientific theories.
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    • 2.We ought to believe our best scientific theories.
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    • 3.We ought to be committed to the entities that our best theories quantify over.
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