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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that A property that can be destroyed or created by set-theoretic forcing does not robustly ground claims about absolute cardinal magnitude.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Forcing preserves cardinality relations within each model; what changes is which model we inhabit, not whether facts hold absolutely in that model.
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    • 2.A property can be robust (determined by basic axioms) even if multiple consistent extensions exist, just as physical laws are robust despite multiple possible worlds.
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    • 3.Forcing's existence-compatibility shows pluralism about models, not that cardinal magnitude lacks determinate grounding within each model's structure.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Forcing can change whether certain sets have specific cardinalities (e.g., Cohen reals alter continuum size), yet the underlying set-theoretic universe remains consistent.
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    • 2.If cardinal magnitude were absolute, no forcing extension could modify cardinality facts without contradiction. Forcing's consistency shows cardinality is model-dependent.
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    • 3.Properties robust to all ground-theoretic variation would constrain mathematical possibility in ways forcing demonstrates they do not.
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