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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that 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.

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

    Reasons For

    1 perspective
    Reason for
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    • 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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      Think about whether this reason is strong or weak

    • 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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