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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that The formula x = a ∨ x = b implicitly quantifies over the totality of sets to isolate {a,b}, making its use in P4 viciously circular on predicativist grounds.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.The disjunction x = a ∨ x = b is a finite, constructive definition requiring no quantification over infinite domains.
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    • 2.Predicativists permit impredicative operations on finite sets; circularity only arises with infinite totalities.
      ?

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    • 3.The formula defines {a,b} relative to a and b as given parameters, not by quantifying over all possible sets.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Predicativism requires that sets be definable without quantifying over larger domains containing the set itself.
      ?

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    • 2.The formula x = a ∨ x = b quantifies over all possible values of x to determine membership in {a,b}.
      ?

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    • 3.If {a,b} exists prior to this quantification, the quantifier presupposes the totality it purports to construct.
      ?

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