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    The Lindström-style collapse of many-sorted logic into FO... — Carmelics
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    Challenges→Many-sorted logic cannot be considered a proper (strict) extension of first-order logic

    The Lindström-style collapse of many-sorted logic into FOL depends on encoding sorts as unary predicates, which presupposes a metatheoretic translation that alters the intended semantics of sort-partitioned domains.

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    Key Terms

    FOL (First-Order Logic)(as a logical framework)
    The standard formal language used in mathematics and philosophy where you can make statements about individual objects and their properties, but not directly quantify over properties themselves.
    Intended semantics(the meaning that gets weakened in Henkin's approach)
    The original, 'correct' meaning a logical system was designed to have—what the creator actually meant it to represent.
    Lindström(as a historical reference)
    Per Lindström was a Swedish logician who proved important theorems about the limits and powers of different logical systems.
    Sort-partitioned domains(as used in logic)
    A collection of objects in a logical system that has been divided into separate categories or groups (partitions), where each category follows different rules.

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    Unary predicates(as a logical concept)
    A formal way of expressing properties that apply to single objects—for example, 'is red' or 'is a number' are unary predicates because they describe one thing at a time.
    collapse(Everett's no-collapse interpretation of quantum mechanics)
    The transition of a quantum-mechanical state from a superposition to a single definite outcome; Everett denies this occurs.
    encoding(Contrasted with exemplification; characterized as 'internal' predication. E.g., the winged horse encodes the property winged without exemplifying it.)
    The mode of predication attributed to non-existent objects, by which such objects bear a property without instantiating it in the ordinary sense.
    many-sorted logic(Logic foundations and translations)
    A logic that accommodates reasoning about more than one sort (type) of objects, generalizing first-order logic by allowing multiple base types.
    metatheoretic(Used to characterize the role of logical semantics)
    Providing a framework for theorizing about the relationship between symbols (used externally in language and internally in thought) and the world, rather than positing cognitive entities for computational manipulation
    translation(Cartesian relational motion; Pr II 30)
    The motion of a body relative to its neighboring bodies, i.e., a change of contiguous neighborhood.

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    Proof of definition segments1 linkedPhilosophy of Language1 linked

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