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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    It is not the case that Cantor himself distinguished between 'consistent multiplicities' (sets) and 'inconsistent multiplicities' (absolute infinities), treating the latter as mathematically real but beyond formal set membership.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Cantor's notion of 'absolute infinity' lacks rigorous definition; calling something 'mathematically real' without formal criteria is metaphysically obscure.
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    • 2.Modern set theory successfully formalizes transfinite hierarchy through proper classes and type restrictions without invoking unmathematizable absolutes.
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    • 3.Attributing mathematical reality to entities beyond formal membership conflates psychological intuition with ontological commitment, inviting unfalsifiable claims.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Cantor's philosophical writings explicitly reference 'absolute infinity' as distinct from transfinite sets, suggesting he recognized limits to formal systems.
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    • 2.The paradoxes of set theory (Russell, Burali-Forti) demonstrate that treating all multiplicities uniformly leads to contradiction, validating Cantor's distinction.
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    • 3.Mathematical reality can extend beyond what formal systems capture; consistency within ZFC doesn't exhaust what mathematicians intuitively understand as infinite.
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