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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Wittgenstein argued that Gödel sentences are grammatical illusions produced by misapplying mathematical notation, not genuine semantic incompleteness.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
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    • 1.Gödel sentences are mechanically constructible and their unprovability is mathematically rigorous, not dependent on linguistic or notational interpretation.
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    • 2.Multiple independent formal systems (Peano arithmetic, ZFC) exhibit incompleteness, suggesting a genuine mathematical phenomenon, not a grammatical artifact.
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    • 3.Even if Gödel sentences are 'self-referential,' this doesn't explain them away—it explains *why* they expose real limits to formal provability within axiom systems.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Wittgenstein's later philosophy emphasizes that meaning derives from use in language-games, not abstract formal properties independent of practice.
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    • 2.Self-referential constructions like Gödel sentences violate ordinary mathematical communication norms and may reflect notational confusion rather than truth.
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    • 3.The apparent 'incompleteness' vanishes when we treat formal systems as tools for specific purposes rather than metaphysical descriptions of mathematical reality.
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