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    The argument presupposes that symmetry over all permutati... — Carmelics
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    Challenges→A symmetric function defined on a set of pairs cannot be a choice function on that set

    The argument presupposes that symmetry over all permutations is required, but choice functions need only be definable relative to a fixed well-ordering of the domain.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Choice functions in set theory require only a method for selecting elements, not invariance under all possible relabelings of the domain.
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    • 2.Well-orderings are legitimate mathematical structures that can define determinate selections without invoking permutation-invariant properties.
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    • 3.Demanding full permutation symmetry is a stronger constraint than necessary and conflates definability with structural independence from representation.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.If choice functions depend on a fixed well-ordering, they lack intrinsic justification and become artifacts of arbitrary representational choices.
      ?

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    • 2.Permutation-invariance requirements exist precisely to identify properties genuinely inherent to a domain, independent of how we happen to label it.
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    • 3.Relativizing choice to a specific well-ordering makes the function's behavior contingent on non-mathematical choices, undermining objectivity.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    A symmetric function defined on a set of pairs cannot be a choice function on th...Choice functions in set theory require only a method for selecting elements, not...Demanding full permutation symmetry is a stronger constraint than necessary and ...If choice functions depend on a fixed well-ordering, they lack intrinsic justifi...
    +3 moreShow less
    Permutation-invariance requirements exist precisely to identify properties genui...Relativizing choice to a specific well-ordering makes the function's behavior co...Well-orderings are legitimate mathematical structures that can define determinat...

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    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
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