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    Wittgenstein's grammatical equivalence thesis conflates t... — Carmelics
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    Challenges→Mathematical induction does not function as an inference that derives a universal conclusion from two premises

    Wittgenstein's grammatical equivalence thesis conflates the justificatory role of induction with its semantic content, which logicians like Boolos distinguish carefully.

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    Reasons For

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    • 1.Wittgenstein treats induction as a rule-following practice defined by grammar, not justified by logical foundations.
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    • 2.Boolos's second-order logic distinguishes justification (why induction works) from meaning (what induction expresses).
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    • 3.Conflating these roles obscures how induction gains legitimacy through use rather than prior semantic determination.
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    Reasons Against

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    • 1.Wittgenstein's grammar already encompasses both justificatory and semantic dimensions—no genuine conflation occurs.
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    • 2.Boolos's distinction may not apply cleanly to induction, since its meaning and justification are deeply intertwined.
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    • 3.The claim assumes 'conflation' is problematic without showing it produces actual logical or philosophical errors.
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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    Boolos's distinction may not apply cleanly to induction, since its meaning and j...Boolos's second-order logic distinguishes justification (why induction works) fr...Conflating these roles obscures how induction gains legitimacy through use rathe...Mathematical induction does not function as an inference that derives a universa...
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    The claim assumes 'conflation' is problematic without showing it produces actual...Wittgenstein treats induction as a rule-following practice defined by grammar, n...Wittgenstein's grammar already encompasses both justificatory and semantic dimen...

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