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    Any effective translation between modal and first-order l... — Carmelics
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    Challenges→The translation function Trans presupposes a fixed domain across modal contexts, smuggling in a Barcan-style assumption that S4 itself does not require.

    Any effective translation between modal and first-order logic requires *some* domain specification; calling this 'smuggling in' conflates necessary with problematic presuppositions.

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    Key Terms

    Domain specification(a necessary requirement when translating between these logical systems)
    Clearly defining what objects or things you're talking about—for example, specifying whether you mean 'all people on Earth' or 'all fictional characters' when making a logical claim.
    Modal logic(logic)
    A system of logic that deals with concepts like possibility, necessity, and what could or must be true.
    Translation (in logic)(as used in logic)
    Converting statements from one logical system into another while trying to preserve their meaning.
    first-order logic(Distinguished from the higher-order logic used in Montague semantics)
    A logic in which there are only variables for basic entities, as opposed to higher-order logic
    necessary (in philosophy)

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    (as used in modal logic and metaphysics)
    Something that must be true or must happen; the opposite of contingent or accidental. A necessary truth couldn't possibly be false.
    presuppositions(Collingwood, An Essay on Metaphysics)
    The foundational assumptions or commitments that govern thought within a given domain of inquiry, which Collingwood later identified as the proper subject matter of philosophical (metaphysical) investigation.

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    The translation function Trans presupposes a fixed domain across modal contexts,...

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