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    L's 'thinness' is relative to a background universe; from... — Carmelics
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    Challenges→L cannot recognize that κ is a measurable cardinal

    L's 'thinness' is relative to a background universe; from within L, all cardinals satisfy L's own definability conditions.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.L is definable within ZFC but not absolutely definable; its thinness depends on comparing it against V, which is background-relative.
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    • 2.Within L's own internal logic, all ordinals and cardinals satisfy L's constructibility conditions by definition—no external comparison needed.
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    • 3.Different models of set theory contain different versions of L with different cardinalities, confirming L's properties are relative to ambient universe.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.If L's thinness is merely relative, this threatens absolutism about mathematical truth; some claim L's structure should be intrinsically objective.
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    • 2.The claim conflates two distinct facts: L being definable relative to V, versus cardinal properties being relative; the latter seems to confuse internal and external perspectives.
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    • 3.From within L, the claim that 'all cardinals satisfy L's conditions' is trivially true but uninformative; it obscures that fewer sets exist in L than V.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Different models of set theory contain different versions of L with different ca...From within L, the claim that 'all cardinals satisfy L's conditions' is triviall...If L's thinness is merely relative, this threatens absolutism about mathematical...L cannot recognize that κ is a measurable cardinal
    +3 moreShow less
    L is definable within ZFC but not absolutely definable; its thinness depends on ...The claim conflates two distinct facts: L being definable relative to V, versus ...Within L's own internal logic, all ordinals and cardinals satisfy L's constructi...

    Details

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