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    Carmelics

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    Made withinDC&Austin
    Statements
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    Perspectives
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    Home/Original/inverse
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    Inverse View

    It is not the case that The paradoxes of set theory are resolved by reducing assertions about sets to assertions about propositional functions.

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Zermelo's axiomatic set theory resolves the same paradoxes without eliminating sets or invoking propositional functions.
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    • 2.When an alternative framework resolves paradoxes with weaker ontological revision, the stronger revision requires additional justification beyond mere paradox-resolution.
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    • 3.Russell's reduction therefore overcorrects, eliminating sets as a category when restricting comprehension axioms suffices—as Zermelo demonstrated in 1908.
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    Reason for 2 of 2
    ?
    • 1.Russell's type hierarchy requires the axiom of reducibility, which Ramsey and Wittgenstein argued is an empirical assumption smuggled into logic.
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    • 2.If the axiom of reducibility is not a logical truth, the reduction of sets to propositional functions fails to resolve paradoxes on purely logical grounds.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Assertions about sets can be reduced to assertions about propositional functions.
      ?

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    • 2.The restriction that a function of one type cannot apply to a function of the same type blocks the paradoxes.
      ?

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