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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that The consistency of ZFC+φ+V=L establishes only proof-theoretic compatibility, not genuine ontological cohabitation in any intended model.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.If ZFC+φ+V=L is consistent, then by completeness theorem, some model exists satisfying all three components genuinely, not just formally.
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    • 2.Proof-theoretic compatibility *is* the standard criterion for ontological cohabitation in modern model theory and mathematical logic.
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    • 3.Distinguishing 'proof-theoretic' from 'genuine' ontological cohabitation assumes an unexplained metaphysical standard beyond mathematical semantics.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Consistency proofs only show absence of derivable contradiction, not that any model actually satisfies all axioms simultaneously.
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    • 2.V=L is a contentious principle rejected by many set theorists; proof-theoretic compatibility doesn't resolve foundational disagreements.
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    • 3.Intended models require semantic satisfaction conditions beyond formal derivability; consistency is insufficient for ontological claims.
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