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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Russell's substitutional theory and the no-class theory require ramification to avoid paradoxes arising from propositional functions defined over all propositions.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Ramification severely restricts expressive power, making it difficult to formalize legitimate mathematical principles like induction.
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    • 2.The claim conflates the source of paradox; careful syntactic restrictions or alternative semantics may suffice without ramification's costs.
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    • 3.Substitutional theories face their own issues: substitution domains require prior specification, creating regress rather than solving it.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Unrestricted quantification over all propositions generates self-referential contradictions (like the liar paradox in propositional form).
      ?

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    • 2.Ramification creates a hierarchy preventing propositional functions from quantifying over their own level, blocking reflexive paradoxes.
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    • 3.Both substitutional and no-class theories preserve classical logic while avoiding the ontological costs of type-theoretic alternatives.
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