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    Made withinDC&Austin
    Home/Original/inverse
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    Inverse View

    It is not the case that Given a well-ordering of any set (provable from AC itself), a canonical choice function exists that is not symmetric yet satisfies all formal requirements of a choice function.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Calling a choice function 'canonical' while admitting it lacks symmetry seems to conflate formal adequacy with philosophical canonicality—a category error.
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    • 2.AC's utility lies in proving *existence* of choice functions, not constructing specific ones; the claim overstates what AC provides.
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    • 3.Any well-ordering is dependent on arbitrary choices in its construction, making dependent choice functions equally non-canonical as the original problem.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Well-orderings are constructive mathematical objects that break symmetry by definition, enabling canonical selections without appeal to arbitrary choice.
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    • 2.A choice function need only satisfy the formal requirement of selecting one element per set; symmetry is an aesthetic preference, not a logical requirement.
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    • 3.AC proves well-orderings exist; leveraging their asymmetry for canonical choice functions demonstrates AC's constructive potential beyond non-constructive existence claims.
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