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    In ZF without urelements, sets have no 'intrinsic' symmet... — Carmelics
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    Challenges→A symmetric function defined on a set of pairs cannot be a choice function on that set

    In ZF without urelements, sets have no 'intrinsic' symmetric indistinguishability of the kind the argument exploits, since all sets are distinguished by their membership structure.

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    Key Terms

    Intrinsic(describing the kind of continuities that ground identity)
    Something that belongs to or is part of something by its very nature, rather than coming from outside or being relational.
    Membership structure(as used in set theory)
    The pattern of what elements belong inside a set and what those elements contain—basically, the internal organization that makes a set unique.
    Symmetric indistinguishability(as used in philosophy of identity and physics)
    When two things are so similar that you literally cannot tell them apart, even in theory—swapping them makes no difference whatsoever.
    Urelements(in set theory)
    Basic objects in set theory that aren't sets themselves—they're the fundamental building blocks, like atoms, that other sets are built from.
    ZF (Zermelo-Fraenkel set theory)

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    (as used in mathematical logic)
    The standard foundation of modern mathematics—a set of agreed-upon rules for how collections (sets) work and interact.

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    Truth & Knowledge1 linkedModality & Possibility1 linked

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    A symmetric function defined on a set of pairs cannot be a choice function on th...

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