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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 type hierarchy requires the axiom of reducibility, which Ramsey and Wittgenstein argued is an empirical assumption smuggled into logic.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Reducibility follows logically from the ramified hierarchy itself if one accepts that only predicative functions are genuinely definable.
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    • 2.Calling reducibility 'empirical' conflates metaphysical claims with empirical ones; it remains a formal axiom choice, not an observation about nature.
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    • 3.Ramsey's own later work abandoned the ramified hierarchy entirely, suggesting his critique targeted Russell's approach rather than proving reducibility empirical.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Reducibility asserts that all propositional functions are equivalent to predicative ones, which is not derivable from logical axioms alone.
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    • 2.Ramsey and Wittgenstein correctly identified that this assumption goes beyond formal logic into claims about the structure of reality or language.
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    • 3.Without reducibility, Russell's system cannot prove that all well-formed sentences have truth-values, making it incomplete as a logical foundation.
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