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    Russell's substitutional theory shows that eliminating cl... — Carmelics
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    Challenges→The extensionality of classes is a derived result, not a postulate.

    Russell's substitutional theory shows that eliminating classes via propositional functions requires intensional distinctions that extensionality actively destroys, making derivation circular.

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    Key Terms

    Circular derivation(The problem the statement says Russell's theory creates)
    When you try to prove something but end up using that very thing you're trying to prove as part of your argument—a logical dead end.
    Classes(as mathematical/logical groupings)
    Groups or sets of objects that share something in common; a way of collecting similar things together.
    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.
    Substitutional theory(A specific philosophical approach Russell developed)

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    Russell's attempt to solve a logical problem by replacing references to abstract objects (like classes or sets) with descriptions of concrete things instead.
    extensional(logic and philosophy of probability)
    A property of relations (like material implication) that Nagel claimed Reichenbach's probability implication lacks
    extensionality(classical logic and regimentation of theories)
    The property of a theory whereby a predicate may be replaced by a co-extensive predicate without change of truth-value of the containing sentence, and likewise an embedded sentence may be replaced by a sentence of the same truth-value
    intensional(as used in logic and philosophy of language)
    Relating to meaning, context, or how something is described, rather than just what the thing is—for example, 'the morning star' and 'the evening star' refer to the same object (Venus) but intensionally they're different descriptions.
    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)

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    Modality & Possibility1 linkedPhilosophy of Language1 linked

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    The extensionality of classes is a derived result, not a postulate.

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