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    The platonist/fictionalist semantic theory is better than... — Carmelics
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    Home/Philosophy of Language
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    The platonist/fictionalist semantic theory is better than other semantic theories of mathematical discourse

    No other argument is betterPhilosophy of Language
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    1 reason for
    2 reasons against

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    Reasons For

    1 perspective
    Reason for
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    • 1.Ordinary mathematical claims are best interpreted at face value as making claims about objects, because typical mathematicians do not have positive intentions to be speaking nonliterally
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    • 2.There are features of the intentions of typical mathematicians inconsistent with the idea that mathematical utterances are about physical or mental objects
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    • 3.There is nothing in the intentions of typical mathematicians inconsistent with the idea that mathematical sentences are about abstract objects
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Speaker intentions are not decisive for semantic theory, since competent speakers routinely have no determinate intentions about the ontological commitments of their utterances.
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    • 2.Wittgenstein's rule-following considerations show that meaning is grounded in public linguistic practice and use, not in speakers' mental states or intentions.
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    • 3.A use-based semantic theory can accommodate mathematical discourse without positing abstract objects or fictional surrogates, making the platonist/fictionalist framework theoretically unnecessary.
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    Reason against 2 of 2
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    • 1.Hellman's modal structuralism provides face-value readings of mathematical claims as truths about possible structures rather than abstract objects, satisfying the same data about speaker intentions.
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    • 2.If a viable alternative theory matches the platonist/fictionalist account's consistency with speaker-intention data, then P4's claim that it is the *only* such theory is demonstrably false.
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    • 3.The existence of multiple intention-consistent semantic theories defeats the argument's uniqueness claim without requiring rejection of any individual datum about mathematical practice.
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    Topics

    Philosophy of LanguageNo other argument is better

    Connections

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    Truth & Knowledge3 linkedAll sources support it1 linked

    Related

    A use-based semantic theory can accommodate mathematical discourse without posit...Hellman's modal structuralism provides face-value readings of mathematical claim...If a viable alternative theory matches the platonist/fictionalist account's cons...Ordinary mathematical claims are best interpreted at face value as making claims...
    +6 moreShow less
    Speaker intentions are not decisive for semantic theory, since competent speaker...The existence of multiple intention-consistent semantic theories defeats the arg...

    Similar

    The platonist/fictionalist semantic theory is the only theory consiste...87%Neither platonists nor fictionalists disagree about any semantic these...87%The disagreement between platonism and fictionalism is ontological, no...81%Arguments based on semantic theses cannot distinguish fictionalism fro...81%

    Source

    AI-extracted1/3 agreementValid
    SEP: fictionalism-mathematics
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    But platonists and fictionalists are not committed to the thesis that people have positive intentions to be talking about abstract objects. Rather, they can say the following: (i) ordinary mathematical claims are best interpreted at face value—and, hence, as making claims about objects—because typical mathematicians (and, indeed, typical examples of ordinary folk) do not have positive intentions to be speaking nonliterally when they utter mathematical sentences; and (ii) there are features of th
    Extraction notes

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

    Details

    The platonist/fictionalist semantic theory is the only theory consistent with al...
    There are features of the intentions of typical mathematicians inconsistent with...
    There is nothing in the intentions of typical mathematicians inconsistent with t...
    Wittgenstein's rule-following considerations show that meaning is grounded in pu...
    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit