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    A sentence like '2+2=4' can be fully explained by its rol... — Carmelics
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    Challenges→Extensional sentences containing numerical singular terms, if true, are ontologically committed to numbers.

    A sentence like '2+2=4' can be fully explained by its role in inferential practice without positing abstract objects as referents.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Mathematical truths remain stable and useful across all contexts where we apply inferential rules, requiring no appeal to abstract objects.
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    • 2.Positing abstract objects creates epistemological problems: how do finite minds access causally inert entities outside space and time?
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    • 3.Inferential role semantics successfully explains why '2+2=4' is valid—its meaning derives from its relationships within a formal system.
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    Reasons Against

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    Reason against
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    • 1.Inferential roles alone cannot explain why '2+2=4' is necessarily true while '2+2=5' is necessarily false without positing objective facts.
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    • 2.Different formal systems have different inference rules; without abstract mathematical objects, it's unclear which system is 'correct.'
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    • 3.Inferential practices themselves require grounding: why do these particular rules rather than others constitute valid mathematical practice?
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    Connections

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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Different formal systems have different inference rules; without abstract mathem...Extensional sentences containing numerical singular terms, if true, are ontologi...Inferential practices themselves require grounding: why do these particular rule...Inferential role semantics successfully explains why '2+2=4' is valid—its meanin...
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    Inferential roles alone cannot explain why '2+2=4' is necessarily true while '2+...Mathematical truths remain stable and useful across all contexts where we apply ...Positing abstract objects creates epistemological problems: how do finite minds ...

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    2 (1 for, 1 against)
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