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    Lucas and Putnam's debates show that attributing truth to... — Carmelics
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    Challenges→There must be true arithmetical sentences which are not provable

    Lucas and Putnam's debates show that attributing truth to Gödel sentences requires adopting a Platonist semantic framework that is itself philosophically contested, not a neutral starting point.

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    Key Terms

    Gödel sentences(mathematical logic)
    Special mathematical statements named after logician Kurt Gödel that are true but cannot be proven within their own system—the classic example of incompleteness.
    Lucas(as a philosopher in debates about artificial intelligence and mathematics)
    John Lucas, a British philosopher who argued that human minds can do things that computers cannot, based on Gödel's mathematical discoveries.
    Philosophically contested(philosophy)
    Debated or disagreed upon by philosophers—meaning experts in philosophy don't all agree whether something is true.
    Platonist semantic framework(as a way of explaining how we know mathematical truths)
    A philosophical approach that treats abstract things like numbers and truths as real objects existing in a non-physical realm, independent of what anyone thinks.

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    Putnam
    # Putnam "Putnam" most commonly refers to **Hilary Putnam** (1926-2016), an influential American philosopher who made major contributions to philosophy of mind, language, and science. He is famous for thought experiments like the "brain in a vat" scenario, which explores questions about reality and how we know what's real. His work fundamentally changed how philosophers think about the relationship between our minds, language, and the external world.
    attributing truth(as used when discussing whether Gödel sentences are genuinely true)
    The act of saying that something is true or claiming that a statement corresponds to reality.
    neutral starting point(to contrast with contested philosophical positions)
    An assumption or framework that everyone accepts as obviously true without needing justification or debate.

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    There must be true arithmetical sentences which are not provable

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