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    Fine's 1975 incompleteness results demonstrate that not a... — Carmelics
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    Challenges→Compactness and Löwenheim-Skolem properties hold for modal logics K and S4.

    Fine's 1975 incompleteness results demonstrate that not all modal logics are complete with respect to first-order definable frame classes, undermining the translation-inheritance argument.

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    Key Terms

    Completeness (in logic)(refers to whether intuitionistic logic can prove everything that should be provable)
    A property where a logical system is powerful enough that if something is actually true, it can be proven using the rules of that system.
    Definable(in logic)
    Able to be described or specified using a particular set of rules or language—for example, you could 'define' all even numbers using mathematical notation.
    Fine, Kit(The statement references Fine's framework as the basis for the argument)
    A contemporary philosopher known for developing supervaluationism, a theory about how language handles vague or fuzzy concepts.
    Incompleteness results(as used in mathematical logic)
    Mathematical theorems proving that in any logical system complex enough to describe math, there will always be true statements that the system cannot prove to be true.

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    Modal logic(logic)
    A system of logic that deals with concepts like possibility, necessity, and what could or must be true.
    Translation-inheritance argument(Fine's results showed this argument doesn't always work)
    A philosophical strategy that tries to prove a logical system is complete by showing it can be translated into another, simpler system known to be complete.
    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
    frame (in modal logic)(modal logic)
    In modal logic, a framework that shows which possible worlds are connected to each other and can be accessed from one another.

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    2 topics

    Proof of definition segments1 linkedModality & Possibility1 linked

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    Compactness and Löwenheim-Skolem properties hold for modal logics K and S4.

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