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    The original claim tacitly assumes full semantics, but th... — Carmelics
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    Challenges→There are structures of every infinite cardinality which are not second-order characterizable.

    The original claim tacitly assumes full semantics, but the choice of semantics is a substantive philosophical commitment, not a logical given, so the claim is semantics-relative rather than an absolute logical fact.

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    Key Terms

    absolute logical fact(as used in metaphysics and logic)
    A truth that holds everywhere and always, based purely on logic itself, independent of any choices humans make about how to interpret things.
    logical given(as used in formal logic)
    Something that must be true based purely on the rules of logic alone, without needing any additional choices or assumptions.
    philosophical commitment(as used in metaphysics and epistemology)
    A deliberate choice to believe or accept something as true; it's a position you're taking a stand on, not just a neutral fact.
    semantics(Distinguished from metasemantics and pragmatics in Kaplan 1989)
    The domain that concerns the facts about what meanings words or phrases have.
    semantics-relative

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    (as used in philosophy of language and logic)
    Dependent on which meaning-system or interpretation you choose; something that changes depending on how you define your terms.
    substantive(classification of linguistic forms by their role in expressing categories of thought)
    The linguistic form required to express thought's apprehension of independent objects
    tacitly assumes(as used in logical analysis)
    To assume something without saying it out loud or being fully aware you're assuming it—like building a conclusion on an unstated background belief.

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    Modality & Possibility1 linkedSkepticism1 linked

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    There are structures of every infinite cardinality which are not second-order ch...

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