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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that If class bijections require definable functions, the step from equinumerosity with the ordinals to a global well-ordering presupposes definable choice functions, making the argument question-begging.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Class bijections needn't be *definable* in a fixed language—they can exist as formal relations within set theory independent of our ability to describe them.
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    • 2.AC or global well-ordering can be derived from equinumerosity arguments without constructing explicit choice functions, using category-theoretic or structural methods.
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    • 3.The charge of begging the question requires showing the conclusion is assumed in premises; merely using set-theoretic tools does not establish circularity.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Definability constraints are unavoidable: any function we actually construct or reason about must be specifiable in some language or formal system.
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    • 2.The argument conflates two distinct notions: equinumerosity (cardinality) and well-orderability (structure), requiring additional justification to bridge them.
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    • 3.Without explicit choice functions, deriving a global well-ordering from equinumerosity with ordinals appears to smuggle in set-theoretic principles rather than derive them.
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