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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Cardinality-based magnitude claims require a prior account of 'largeness' that is independent of the cardinal hierarchy being described.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.'Largeness' in mathematics is explicitly defined through cardinality (injections, bijections)—no prior account needed; definitions suffice.
      ?

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    • 2.Requiring independent 'largeness' regresses infinitely: any prior account itself needs justification, making the claim self-defeating.
      ?

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    • 3.Cardinal comparisons work successfully without external intuitions, shown by consistent formal results in set theory and model theory.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Cardinality alone (set size) cannot ground intuitions about magnitude without conceptual circularity—we need independent criteria for 'large.'
      ?

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    • 2.Mathematical hierarchies (natural numbers, reals, cardinals) are formal structures that presuppose an intuitive notion of scale or excess.
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    • 3.Comparing infinities requires a meta-framework about relative abundance that transcends purely enumerative definitions.
      ?

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