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    Russell's ramified type theory demands that propositional... — Carmelics
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    Supports→A coherent semantics of Russell's formalized language cannot be provided on the basis that values of propositional functions are sentences.

    Russell's ramified type theory demands that propositional functions and their values occupy distinct ontological levels, prohibiting sentences from serving dual roles as both values and substituends.

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    Key Terms

    Ontological levels(as used in philosophy of mind)
    Different layers or categories of what exists—like how the same thing could be described as 'atoms,' 'molecules,' or 'a person,' each level being a different way of categorizing reality.
    Russell
    # Russell Russell most commonly refers to **Bertrand Russell**, a highly influential British philosopher, logician, and social critic (1872-1970) who fundamentally changed how we think about logic, language, and knowledge. He's famous for showing that common-sense reasoning can contain hidden contradictions and for arguing that philosophy should use the precision of mathematics to solve problems. Russell also became a prominent public intellectual who wrote about everything from religion to nuclear weapons, making him one of the most important thinkers of the 20th century.
    Substituends(as things that propositional function values cannot be at the same time)
    Things that can be plugged in or substituted for something else—in this case, items that could be used as replacements in logical expressions.
    Values (in logic)

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    (as the outputs that must be distinct from propositional functions themselves)
    The results or outputs you get from a propositional function—if a propositional function is a template, its values are the specific true-or-false statements you get by filling it in.
    propositional functions(PM's logical system)
    A foundational element of the logic of Principia Mathematica (PM), distinct from Frege's use of concepts (functions from objects to truth values)
    ramified type theory
    A theory that introduces a hierarchy of propositions and propositional functions by assigning them orders, where every function must have a higher order than its arguments

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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

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    A coherent semantics of Russell's formalized language cannot be provided on the ...

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