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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 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.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.The axiom of reducibility, though unprovable, may be a constitutive principle defining what counts as logical rather than an empirical claim needing proof.
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    • 2.Paradoxes are resolved by the type hierarchy structure itself; reducibility merely simplifies the system without being essential to paradox prevention.
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    • 3.Distinguishing 'purely logical' from 'mathematical' is ambiguous; foundational axioms supporting logic may not require independent justification as logical truths.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The axiom of reducibility is not derivable from standard logical axioms, making it a substantive mathematical assumption rather than a logical truth.
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    • 2.Without reducibility, type theory cannot guarantee all propositional functions correspond to legitimate sets, leaving impredicative definitions unresolved.
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    • 3.If paradox resolution requires only logical truths, then any non-logical assumption undermines claims of purely logical grounds for that resolution.
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