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    Made withinDC&Austin
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    It is not the case that If we adopt a background ontology of full powersets as primitive (as in Zermelo's 1930 quasi-categoricity results), CH has a determinate truth value, making second-order truth absolute relative to that stronger framework.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Quasi-categoricity defines models only up to isomorphism, not intrinsic truth; isomorphic models can differ in CH's truth value interpretation.
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    • 2.Taking full powersets as primitive merely shifts the problem: we still lack canonical justification for why *this* powerset conception is the right one.
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    • 3.Determinacy relative to a framework ≠ absolute determinacy; framework-relativity itself concedes that CH's status depends on prior philosophical choices.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Second-order logic with full powersets achieves quasi-categoricity: it pins down models up to isomorphism, eliminating Löwenheim-Skolem ambiguity.
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    • 2.If an ontology uniquely determines a mathematical structure, truths about that structure become determinate relative to that framework.
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    • 3.CH's truth value is fixed in V (von Neumann hierarchy with full powersets); adopting this as primitive makes CH's status absolute within that domain.
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