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    Carmelics

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    LoyalLoyalJusticeJustice
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    It is not the case that Scott's 1961 theorem shows measurable cardinals destroy V=L by producing non-constructible sets, revealing that 'compatibility' conceals a deeper modal distinction between what can be consistently asserted and what can actually obtain simultaneously.

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    Reasons For

    1 perspective
    Reason for
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    • 1.The claim conflates logical consistency with metaphysical compatibility; Scott's result shows incompatibility, not a hidden modal distinction between them.
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    • 2.Without independent criteria for what 'actually obtains simultaneously,' appealing to modal distinctions risks non-falsifiable speculation beyond mathematics proper.
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    • 3.Set theory's standard semantics already accounts for V=L's falsity without invoking modal collapse; additional modal apparatus adds complexity without explanatory gain.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Scott's theorem proves measurable cardinals cannot coexist with V=L, establishing that consistency alone insufficient to determine actual set-theoretic reality.
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    • 2.Distinguishing consistent assertability from simultaneous actuality respects the mathematical insight that multiple consistent theories cannot all describe one universe.
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    • 3.Modal operators properly capture that 'possibly constructible' and 'actually constructible' have different truth conditions, explaining why V=L fails under measurability.
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