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    The disagreement between platonism and fictionalism is on... — Carmelics
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    Home/Philosophy of Language
    HistoryEditSee Inverse

    The disagreement between platonism and fictionalism is ontological, not semantic

    Modality & Possibility
    ?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.Platonists believe in abstract objects
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    • 2.Fictionalists do not believe in abstract objects
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    • 3.Neither platonists nor fictionalists disagree about any semantic theses regarding mathematical language
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Fictionalists like Hartry Field accept the same compositional semantics for mathematical sentences as platonists, making the semantic agreement a substantive theoretical commitment, not a trivial consequence.
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    • 2.A shared semantic theory that assigns truth conditions referencing abstract objects creates an implicit ontological commitment that cannot be cleanly separated from the semantic thesis itself.
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    • 3.Quine's criterion of ontological commitment entails that semantic decisions about logical form directly determine what entities one is committed to, collapsing the supposed ontology/semantics distinction.
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    Reason against 2 of 2
    ?
    • 1.Crispin Wright and Bob Hale's neo-Fregean program demonstrates that the truth of abstraction principles like Hume's Principle is itself a semantic matter that logically entails the existence of numbers.
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    • 2.If semantic facts about mathematical language can entail ontological conclusions, then the dispute between platonism and fictionalism cannot be characterized as purely ontological without remainder.
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    Topics

    Philosophy of LanguageModality & Possibility

    Connections

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    Truth & Knowledge3 linked

    Related

    A shared semantic theory that assigns truth conditions referencing abstract obje...Crispin Wright and Bob Hale's neo-Fregean program demonstrates that the truth of...Fictionalists do not believe in abstract objectsFictionalists like Hartry Field accept the same compositional semantics for math...
    +4 moreShow less
    If semantic facts about mathematical language can entail ontological conclusions...Neither platonists nor fictionalists disagree about any semantic theses regardin...Platonists believe in abstract objectsQuine's criterion of ontological commitment entails that semantic decisions abou...

    Similar

    Arguments based on semantic theses cannot distinguish fictionalism fro...91%Neither platonists nor fictionalists disagree about any semantic these...83%The platonist/fictionalist semantic theory is better than other semant...81%The dispute between fictionalism and paraphrase nominalism is an empir...81%

    Source

    AI-extracted1/3 agreementValid
    SEP: fictionalism-mathematics
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    If the arguments given so far are correct, then the only remaining views—the only philosophies of mathematics that haven’t been ruled out—are platonism and fictionalism. Thus, to complete their argument, fictionalists need merely to provide an argument for premise (5); in other words, they just need to argue against platonism. But this turns out to be a lot harder than arguing against the various non-fictionalistic versions of anti-platonism considered above. As we’ve seen, fictionalists can arg
    Extraction notes

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

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit