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    Therefore the permutation argument, following Fraenkel-Mo... — Carmelics
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    Challenges→A symmetric function defined on a set of pairs cannot be a choice function on that set

    Therefore the permutation argument, following Fraenkel-Mostowski methodology, demonstrates the independence of AC from weaker systems rather than the impossibility of choice functions in standard set theory.

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    Key Terms

    AC (Axiom of Choice)(as used in set theory)
    A basic assumption in mathematics that allows you to make infinitely many arbitrary choices all at once—something that seems obvious but is actually quite controversial.
    Fraenkel-Mostowski methodology(a technical approach in set theory)
    A specific mathematical framework (named after mathematicians Abraham Fraenkel and Andrzej Mostowski) used to construct special models of set theory where certain things can be true or false.
    Independence(Peer disagreement epistemology)
    The epistemic principle that one's assessment of first-order evidence should be kept independent from (i.e., not influenced by) higher-order evidence about peer disagreement
    Permutation Argument(Putnam's model-theoretic argument against metaphysical realism)
    An argument showing that the truth-value of a sentence remains unchanged when predicates are reassigned non-standard extensions across all possible worlds.

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    Standard set theory(the conventional system that NF is being compared to)
    The most widely accepted mathematical system for dealing with collections of objects, usually called ZFC; it's what most mathematicians use as their foundation.
    Weaker systems(in set theory and logic)
    Mathematical or logical frameworks that have fewer rules or assumptions than standard systems, making them less powerful at proving things.
    choice functions(Formal semantics of indefinites)
    Functions that select a member from a set, used as a semantic mechanism to account for the scopal behavior of indefinites without syntactic movement

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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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