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    Game formalism likely implies mathematical utterances are... — Carmelics
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    Game formalism likely implies mathematical utterances are unsinnig (nonsensical) rather than merely sinnlos (lacking sense)

    Philosophy of LanguageTruth & Knowledge
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    2 reasons against

    Reasons For

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    Reason for
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    • 1.Game formalism treats mathematical utterances as strings of meaningless marks
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    • 2.Wittgenstein distinguishes sinnlos (senseless, including tautologies and contradictions) from unsinnig (nonsensical)
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    • 3.Strings of meaningless marks would fall into the unsinnig category rather than the sinnlos category
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    Reasons Against

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    Reason against 1 of 2
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    • 1.Hilbert's formalism distinguishes between real (contentual) and ideal (formal) statements, not between meaningful and meaningless marks.
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    • 2.Ideal mathematical statements function analogously to Wittgenstein's sinnlos propositions: they lack direct empirical content but serve systematic, rule-governed roles.
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    • 3.A statement can be sinnlos within a formal system while remaining syntactically well-formed and operationally significant, placing game formalism closer to sinnlos than unsinnig.
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    Reason against 2 of 2
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    • 1.Wittgenstein's unsinnig category applies to violations of logical grammar, not merely to statements lacking empirical reference or propositional content.
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    • 2.Game formalist symbols operate under explicit, consistent syntactic rules that constitute a species of grammar, satisfying the minimal condition for avoiding unsinnig status.
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    Related

    A statement can be sinnlos within a formal system while remaining syntactically ...Game formalism treats mathematical utterances as strings of meaningless marksGame formalist symbols operate under explicit, consistent syntactic rules that c...Hilbert's formalism distinguishes between real (contentual) and ideal (formal) s...
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    Ideal mathematical statements function analogously to Wittgenstein's sinnlos pro...Strings of meaningless marks would fall into the unsinnig category rather than t...Wittgenstein distinguishes sinnlos (senseless, including tautologies and contrad...Wittgenstein's unsinnig category applies to violations of logical grammar, not m...

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    Care must be taken, however. Wittgenstein distinguishes utterances which are sinnlos, which lack sense (including logical tautologies and contradictions here) from those which are unsinnig, nonsensical; it is not clear into which class mathematical utterances fall. One might well think that the game formalist should treat mathematical utterances, on that view just strings of meaningless marks, as unsinnig, not just sinnlos. One clear difference from game formalism however is this: for Wittgenste
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    claim
    Perspectives
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