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    Cardinality-based magnitude claims require a prior accoun... — Carmelics
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    Challenges→A weakly compact inaccessible cardinal is exceedingly large

    Cardinality-based magnitude claims require a prior account of 'largeness' that is independent of the cardinal hierarchy being described.

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    1 reason for
    1 reason against

    Reasons For

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    Reason for
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    • 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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    Reasons Against

    1 perspective
    Reason against
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    • 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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    Related

    'Largeness' in mathematics is explicitly defined through cardinality (injections...A weakly compact inaccessible cardinal is exceedingly largeCardinal comparisons work successfully without external intuitions, shown by con...Cardinality alone (set size) cannot ground intuitions about magnitude without co...
    +3 moreShow less
    Comparing infinities requires a meta-framework about relative abundance that tra...Mathematical hierarchies (natural numbers, reals, cardinals) are formal structur...Requiring independent 'largeness' regresses infinitely: any prior account itself...

    Details

    Type
    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit