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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 The disagreement between platonism and fictionalism is ontological, not semantic

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 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 for 2 of 2
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    • 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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