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    We ought to be committed to the existence of mathematical... — Carmelics
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    Home/Modality & Possibility
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    We ought to be committed to the existence of mathematical entities.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 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 against 2 of 2
    ?
    • 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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    Modality & PossibilityTruth & Knowledge

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    2 topics

    Philosophy of Language2 linkedSkepticism1 linked

    Related

    Confirmational holism, as Sober argues against Quine, does not extend to mathema...Entities whose existence makes no difference to any observable prediction are no...Field's Newtonian gravitational theory, expressed purely in terms of spacetime r...If a theory can be reformulated without positing certain entities while retainin...
    +6 moreShow less
    Mathematical statements can be nominalistically paraphrased without quantifying ...Mathematics is indispensable for our best scientific theories.Our best scientific theories quantify over mathematical entities.

    Similar

    We are ontologically committed to mathematical entities86%The existence of mathematical entities is already presupposed in the d...83%Sentences exist as entities we are committed to believing in78%If multiple distinct mathematical entities can explain the same phenom...78%

    Source

    AI-extracted1/3 agreementValid
    SEP: mathematics-explanation
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    There is actually a variety of classical indispensability arguments (see Colyvan 2001 and Panza and Sereni 2016) but the general structure of the argument runs as follows. One begins with the premise that mathematics is indispensable for our best science. But, second premise, we ought to believe our best theories. Thus, we ought to be committed to the kind of entities that our best theories quantify over. In general this is an argument in favor of Platonism, as our best science quantifies over m
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Scientific confirmation accrues to theories as holistic empirical packages, but ...
    We ought to be committed to the entities that our best theories quantify over.
    We ought to believe our best scientific theories.
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit