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    Penelope Maddy and others in the set-theoretic naturalism... — Carmelics
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    Challenges→ZFC set theory cannot serve as a sufficient basis for the mathematics of infinity.

    Penelope Maddy and others in the set-theoretic naturalism tradition argue that ZFC's open-endedness is a feature reflecting the richness of the infinite, not a failure of sufficiency.

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    Key Terms

    Open-endedness(as a feature of ZFC)
    The quality of not being completely finished or closed off; in this case, ZFC's ability to potentially discover or construct new infinite sets without limit.
    Penelope Maddy(cited as the source of this argument)
    A contemporary philosopher who studies the nature of mathematics and has argued that sets (mathematical groupings) can actually exist as physical objects in the real world.
    Set-theoretic naturalism(as the philosophical tradition being discussed)
    A philosophical approach that says we should study mathematics the way scientists study nature—by looking at what actually works in mathematical practice, rather than starting with abstract philosophical theories.
    ZFC(Classical set theory as a foundation for mathematics)
    The axiom system ZF plus the axiom of choice (AC).

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    sufficiency(Used in Johnson's account as a broader standard than deductive validity)
    A criterion of cogent argument that replaces deductive validity, requiring that premises provide adequate support for the conclusion
    the infinite(Malebranche's view that strictly speaking there is no 'idea' of God distinct from God himself)
    That which is its own idea, not represented through a separate idea

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    Truth & Knowledge1 linkedSkepticism1 linked

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    ZFC set theory cannot serve as a sufficient basis for the mathematics of infinit...

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